Práctica 1

I. Ejercicios sobre interés simple 1 - Calcule el interés simple que producen $14,500.00 al 8% en 9 meses y 20 días. Datos: I= ? P= $ 14,500.00 i= 8% anual = 0.08 anual n= 9 meses, 20 días = 9.66 meses = 0.805

año

I = P*i*n I = (14500*0.08*0.805) I = $933.80 I = P*i*n $ 933.80 2 - A qué tasa de interés, un capital de $5,000.00 ha generado $850.00 después de 6 meses y 10 días. Datos: P= $ 5,000.00 I= $ 850.00 n = 6 meses, 10 días = 6.33 meses = 0.5275 año i= ? i = I / Pn i = 850/(5000*0.5275) i = 32.23% i = I / P*n 32.23% 3. En qué tiempo $4,200.00 generan $750.00 de interés simple al 8%. Datos: P= $ 4,200.00 I= $ 750.00 i= 8% anual = 0.08 anual n= ? n = I / P*i => n = 750/(4200*0.08) => n = 2.23 años => n = 2 años 0.23 *12 = 2.76meses 0.76*30 = 22 días => n = 2 años, 2 meses y 22 días 4. Qué capital genera $1,200.00 de interés simple al 13% durante 6 meses. Datos: P= ? I= $ 1,200.00 i= 13% anual = 0.13 anual n=6 meses= 0.5 años P = I / i*n => P = 1200 / (0.13)*(0.5) => P = $18,461.54 P = I / i*n = $ 18,461.54

n = I / P*i =

2.23

5. Calcule el interés simple generado por $3,200.00, al 7.5% durante 11 meses. Datos: P= $ 3,200.00 I= ? i= 7.5% anual = 0.075 anual n=11meses= 0.916 años I = P*i*n => I = 3200*0.075*0.916 => I = $219.84 I = P*i*n = $ 219.84 6. Calcule el interés simple obtenido de 1/3 de $6,000.00 al 18%, durante 9 meses. Datos: P= $ 6,000.00 Po= $6000/3 = $ 2,000.00 I= ? i= 18% anual = 0.18 anual n = 9 meses = 0.75 años I = Po*i*n => I = 2000*0.18*0.75 => I = $270.00 I = Po*i*n =

$

270.00

7. Calcule el interés simple generado por $20,000, al 15 y 1/2 % anual, desde ahora hasta el 28 de diciembre de 2004. Datos: P= $ 20,000.00 I= ? i= 15.5% anual = 0.155 anual n = desde ahora hasta el 28 de diciembre de 2004. n = 363 - 51 = 312 días => n = 312 días/365 días => n = 0.854 años I = P*i*n => I = 20000*0.155*0.854 => I = $2647.40 I = P*i*n = $ 2,647.40

años

8 de diciembre de 2004.

II. Ejercicios sobre monto simple. 1. Encontrar el monto simple de $5,400.00 colocados al 4.5% durante tres años 4 meses. Datos: P= $ 5,400.00 i= 4.5% anual = 0.045 anual n = 3 años, 4 meses => n = 3.333 años S= ? S = P + I => S = P(1 + i*n) => S = 5400{1+[(0.045)*(3.333)]} => S =$6,209.92 S = P + I => S = P(1 + i*n) = $ 6,209.92

2. Se concedió un préstamo por $18,700.00 para 5 años, al final de los cuales se recibieron $22,400.00 en concepto de monto ¿A qué tasa se proporcionó el préstamo? Datos: P= $ 18,700.00 S= $ 22,400.00 n= 5 años i= ? Despejando: S = P(1 + i*n) i = (S – P)/(P*n) => i = (22400 - 18700)/(18700*5) => i = 0.03957 ≈ 0.04 * 100 => i = 4% Tenemos: i = (S – P) / (P*n) = 4%

3. Una persona que había prestado $4,600.00 al 4.5%, recibió $6,049.00 por capital e interés simple. ¿Cuánto tiempo tuvo co Datos: P= $ 4,600.00 S= $ 6,049.00 i= 4.5% anual = 0.045 anual n=? ? Despejando: S = P(1 + i*n) Tenemos: n = (S – P)/(P*i) => n = (6049-4600)/(4600*0.045) => n = 7 años n = (S – P) / (P*i) = 7 años

4. El 20 de julio de 1997 se prestaron ¢8,000.00 al 2 y 1/2 mensual. Calcule cuál fue el total que entregó el deudor el 25 de ju Datos: P= ₡ 8,000.00 S= ? i= 2.5% mensual 30% anual = 0.3 anual n = Del 20 de julio de 1997 al 25 de junio de 1998 => 365 (días del año)-201 (# de días al 20 de julio de 1997) = 164 (díaspara terminar el año 1997) + 176 (días al 25 de julio de 1998) = 340 días n = 340 días = 0.9315 años S = P(1 + i*n) => S = 8000 [1 + (0.3*0.9315)] => M = ¢10,235.60 S = P(1 + i*n) = ₡ 10,235.60

I = S - P => I = 10235.60-8000 => I = ¢2,235.60

2,400.00 en concepto de monto simple.

imple. ¿Cuánto tiempo tuvo colocado el capital?

e entregó el deudor el 25 de junio de 1998.

julio de 1997)

III. Ejercicios sobre interés compuesto:

1. ¿Cuánto debe depositar hoy, para que dentro de cuatro años reciba la suma de $5,000, suponiendo que la caja paga 10% a Datos: P= S= i= n=

$

? 5,000.00 10% anual = 4 años

0.1 anual

P = S/(1 +i)n => P = 5000/(1+0.10)4 => P = $3,415.07

$

(3,415.07)

2. ¿Cuál sería su respuesta, si en el problema previo la tasa fuera de capitalización semestral? Datos: P=? S = $5,000 j= i=j/2=10/2= m= n=m*2= 4*2=

$

? 5,000.00 10% 5% 4 8

capitalizable semestralmente = 0.1 capitalizable semestralmente = 0.05 semestral años semestres P = S/(1 +i)n => P = 5000/(1+0.05)8 => P = $3384.20

3. ¿Cuál será el monto de $4,000 al cabo de 3 años, si un banco X ofrece el 12% de interés capitalizable semestralmente. Datos: P = $4,000 $ S=? j= i = j/2 = 12/2 = m= n=m*2=3*2=

4,000.00 ? 12% 6% 3 6

capitalizable semestralmente = 0.12 capitalizable semestralmente semestral = 0.06 semestral años semestres S = P(1 + i)n => S = 4000(1+0.06)6 => S = $5,674.08

4. Encontrar el monto de ¢100 al fin de 6 años, si el interés al que se encuentran colocado es del 5% tasa anual efectiva. (O año) Datos: P= S= i= n=

₡

100.00 ? 5% anual efectiva = 0.05 anual efectiva 6 años S = P(1 + i)n => S = 100(1+0.05)6 => S = ¢134.01

₡

134.01

5. Encontrar el monto de ¢3,000 al fin de 12 años si se invierten a una tasa anual de 5% convertible anualmente. Datos: P= S=? i= n=

₡

3,000.00 ? 5% anual, convertible anualmente = 0.05 anual, convertible anualmente 12 años n

12

S = P(1 + i) => S = 3000(1+0.05) => S = ¢5,387.57

6. Encontrar el monto de ¢5,000 al 4% acumulable semestralmente durante 8 años. Datos: P= S= j= i = j/2 = 4/2 = n= m = 8*2 =

₡

5,000.00 ? 4% 2% 8 16

acumulable semestralmente = 0.04 acumulable semestralmente semestral = 0.02 semestral años semestres n 16 S = P(1 + i) => S = 5000(1+0.02) => S = ¢6,863.93

7. ¿Qué monto vale más al 9%: $1,000 el día de hoy o $2,500 después de 8 años? Datos: i= n= P1 =

9% anual = 0.09 anual 8 años $

1,000.00 presente

S1 =

?

P2 =

?

S2 =

$

S1 = P(1 + i)n => S1 = 1000(1+0.09)8 => S1 = $1,992.56

2,500.00 después de 8 años n

8

P2 = S2/(1 +i) => P1 = 2500/(1+0.09) => P1 = $1,264.66

8. A una tasa de crecimiento del 9%, ¿cuánto tiempo se necesita para que una suma se duplique? Datos: Capital = P Monto = 2P i = 9% anual = 0.09 anual n=?

n = Ln(M/P)/Ln(1+ i) n = Ln(2P/P)/Ln(1+ 0.09) n = Ln(2)/Ln(1.09) => n = 8.04 años u 8.04 períodos

9. Suponga que usted tuviera una cierta cantidad de efectivo disponible, ¿Cuánto dinero estaría dispuesto a prestarle a algui conviniera en pagarle $50,000 dentro de cinco años, si las tasas de interés son del 8%? Datos: P= S= i= n=

$

? 50,000.00 8% anual = 0.08 anual 5 años P = S/(1 +i)n => P = 50000/(1+0.08)5 => P = $34,029.16

10. Una persona pide prestada la cantidad de $1,000 para pagarla dentro de 5 años a una tasa de interés del 20% anual. ¿Cu pagaría esta persona al final del quinto año? Datos: P= S= i= n=

$

1,000.00 ? 20% anual = 0.2 anual 5 años S = P(1 + i)n=>S = 1000(1+0.2)5=>S = $2,488.32

$

2,488.32

11. Un estudiante universitario, que actualmente está cursando su último semestre de la carrera y que paga actualmente un colegiatura de 500, desea conocer lo que sus futuros hijos pagarán de colegiatura semestral en la universidad. Para esto asu la colegiatura aumentará 20% por semestre y que su primer hijo ingresará a la Universidad a cursar una carrera profesional d de 20 años. Datos: A = $500 P=? S=? i=

$

500.00 ? ? 20% semestral = 0.2 semestral

m = 20 años = 40 semestres 20 años n=m*2=20*2=

40 semestres Sí solamente queremos encontrar S tomando los $500 como principal, tenemos: S = P*(1+i)n = 500(1+0.2)40 => S = $734,885.78 P= S/(1+i)n=>P= 734,885.78/(1.2)40=>P= $500.00

$734,885.78 ($500.00)

Sí tomamos los $500 como la anualidad y no como principal, tenemos: S = A*,*(1+i)ⁿ-1+/i- => S = 500*,*(1.2)40-1]/(0.2)} => S = $3,671,928.92 P = A*{[ 1- (1+i)-n]/i} => P = 500*{[1-(1.2)-40]/(0.2)}= $2,498.30 A = P/{[1-(1+i)-n]/i} => A = (P*i)/[1-(1+i)-n] = (2498.30*0.2)/[1-(1.2)-40]} => P = $500.00

12. Una empresa ha solicitado al banco un préstamo por la cantidad de $100.000,00. El banco, para este tipo de préstamos, o un plazo de seis meses a un interés del 1,5% mensual. Si la empresa recibe $100.000,00 menos los intereses generados por e préstamo, ¿cuál es el interés real mensual en esta transacción? Datos: P0 =

$ 100,000.00

S0 =

$ 109,344.33

i0 =

1.5% mensual = 0.015 mensual

n0 = I0 =

6 meses = 0.5 años $

9,344.33 S0 = P0*(1 + i0)n => S0 = 100000(1+0.015)6 => S0 = $109,344.33 I0 = S0 - P0 = 109344.33 - 100000 => I0 = $9,344.33 Preal = P0 - I0=>Preal = 100000 - 9344.33=>Preal = $90,655.57

ireal = ? n1 = 1 año n

6

6

Sí: Preal*(1+ireal) = Sreal => 90655.57*(1+ireal) = 100000 => (1+ireal) = 100000/90655.57 => ireal = 0.165 *100 => ireal = 1.65% mensual Esto significa que 1.65% mensual va a ser equivalente a una tasa de interés anual de: P=P i = 1.65% mensual = 0.0165 mensual j = ? anual m = 1 año n = 12 meses

Por tasas equivalentes: P*(1+i)n = P*(1+j)m => P*(1.0165)12 = P+(1+j/1)1 => P*(1.0165)12/P = 1 => j = 0.21699*100 = 21.70% es la tasa de interés anual efectiva o real.

13. ¿Cuánto tiempo tomaría una cantidad $P en triplicarse, si la tasa de interés es de 10% anual capitalizable cada semestre?

13. ¿Cuánto tiempo tomaría una cantidad $P en triplicarse, si la tasa de interés es de 10% anual capitalizable cada semestre? Datos: Capital = P Monto = 3P j = 10% anual capitalizable semestralmente i = j/2 = 10/2 = 5% = 0.05 semestral n=? n = Ln(M/P)/Ln(1+ i) n = Ln(3P/P)/Ln(1+ 0.05) n = Ln(3)/Ln(1.05) => n = 22.52 semestres = 22 semestres 3 meses = 22.52 períodos

14. Ante la perspectiva del alto costo de la educación universitaria, un padre de familia resuelve establecer un fondo para c costos. Al cabo de 17 años el fondo debe alcanzar un monto de ¢150,000,00. Si el depósito, por ser a largo plazo, paga el 18% ¿Qué cuotas anuales uniformes a partir del fin de este año, debe depositar el padre de familia para garantizar la educación d hijo? Datos: S= i= n= A=

₡ 150,000.00 18% anual = 0.18 anual 17 años ? Vencida A = S/{[(1+i) -1]/i} => A = 150000/{[(1.18)17-1]/0.18} => A = ¢1,722.79 n

15. Usted tiene 20 años de edad y piensa depositar $100 en una cuenta que le redituará 8% anual durante 45 años. a. ¿Cuánto tendrá en ella cuando cumpla 65 años? Datos: P= $ 100.00 i= 8% anual = 0.08 anual n= 45 años S= ? n

45

S = P*(1+i) = $100 X (1 + 0.08) = $3,192.04

$

3,192.04

b. ¿Qué parte corresponderá al interés simple y qué al interés compuesto? Sí P = $100 => IT = S - P => IT = $3192 - $100 => IT = $3,092.00 Is = P*i*n = $100*0.08*45 = $360.00 Ic = IT - Is = $3092 - $360 = $2,732 c. Si pudiera encontrar una cuenta que le pagara el 9% anual, ¿Cuánto tendría a los 65 años de edad? Datos: P= $ 100.00 i= 9% anual = 0.09 anual n= 45 años

S=

? S = P*(1+i)n = $100 X (1 + 0.09)45 = $4,833.73

$

4,832.73

16. Supongamos que nuestro dinero gana interés a una tasa porcentual anual (TPA o j) de 6% por año que se capitaliza mensualmente. Ello significa que el interés se abona a la cuenta mensualmente en el décimo segundo mes a la tasa declarad tanto, la tasa verdadera es en realidad 1/2% al mes (esto es 0.005 mensual en forma decimal). Encuentre la tasa anual efect o i). Datos: Tasa Nominal = TPA = J = m= n = m*12 = j= i = j/12 = 6/12 =

6% 1 12 6% 0.5%

anual = 0.06 anual año meses anual = 0.06 anual 0.005 mensual

Tasa Efectiva = ie = TAE = [(1 + i)n - 1] => ie = [(1 + 0.005)12 - 1] => ie = 0.0617 => ie = 6.17%

17. Un hermano suyo cumple 10 años y recibe un bono de ahorro de $100 dólares que se vence en cinco años. Este tipo de b paga nada antes de la fecha de vencimiento. Al sumar el valor monetario de todos los obsequios que recibió en el cumpleañ hermano se equivoca y al bono le asigna un valor de $100.00 a. ¿Cuánto vale realmente el bono si la tasa de descuento es de 8% anual y si el bono no se vence en otros cinco años? Datos: S= $ 100.00 i= 8% anual = 0.08 anual n= 5 años P= ? P = S / (1+ i)n => P = $100/ (1+0.08)5 => P = $68.06 b. ¿Cómo podría usted explicar el error de su hermano para que éste lo entienda? El bono valdrá $100 en cinco años, para el presente vale $68.06.

18. Un bono de ahorro de $100 se vende a $75. La segunda mejor alternativa de inversión es una cuenta bancaria que reditú ¿Es una buena inversión el proyecto de bono de ahorro? Datos: S= i= n= P=

$

100.00 8% anual = 0.08 anual 1 años ? Bono de ahorro para un año: P = S / (1+ i)n => P = $100/ (1+0.08)1 => P = $92.59 $92.59 - $75 = $17.59 Vale la pena el proyecto de bono de ahorro, porque además de invertir menos de lo que en realidad vale, el beneficiobeneficio sera mayor que

de invertir menos de lo que en realidad vale, el beneficiobeneficio sera mayor que en la cuenta bancaria.

19. Tiene la oportunidad de comprar un terreno en $10,000. Sabe con seguridad que en cinco años costará $20,000. Puede g anual si deposita el dinero en el banco, ¿vale la pena la inversión en bienes raíces? Datos: P0 = S0 = $20,000 i= n= P1 =

? $

$

S1 =

Por valor presente:

20,000.00 8% anual = 0.08 anual 5 años 10,000.00

n

5

P0 = S0 / (1+ i) => P0 = $20000/ (1+0.08) => P = $13,612.6

$13612 - $10000= $3612.12 Vale la pena la inversión en b Por valor futuro: S1 = P1*(1+i)n => S1 = $10000*(1+0.08)5 = $14,693.28

?

$20000 - $14693.28 = $5,306.72 Vale la pena la inversión

20. Supongamos que necesitamos obtener un préstamo de $5,000 para comprar un automóvil. Vamos a un banco y nos ofre préstamo a una tasa de interés de 12% anual. Acudimos entonces a un amigo que se compromete a prestarnos esa cantidad pagamos $9,000 en un plazo de cuatro años. ¿Cuál de los dos préstamos nos conviene más? Datos: P0 =

$

S0 =

5,000.00

n

12% anual = 0.12 anual 4

P1 =

? $

4

P1 = S1 / (1+ i) => P1= 9000/ (1+0.12) => P = $5,719.66

?

i= n=

S1 =

Por valor presente:

$5,719.66 - $5,000= $719.66 Conviene más el el préstam De otra forma: VPN = $5,000 - $5,719.66 = - $719.66 Q Por valor futuro: n

4

S0 = P0*(1+i) => S0 = $5000*(1+0.12) = $7,867.60

9,000.00

$9,000 - $7,867.60 = $1,132.40 Conviene más el el présta

21. Cada año usted deposita $1,000 en una cuenta que paga a una tasa de interés de 10% anual, empezando inmediatament ¿Cuánto tendrá después de dos años, si no retira nada antes de ese tiempo? Datos: P1 = $1,000

$

1,000.00

n1 =

2 años

P2 = $1,000

$

1,000.00

n2 =

1 años

ST = S1 + S2 i=

? 10% anual = 0.1 anual S1 = P1*(1+i)n => S1 = 1000*(1+0.10)2 = $1,210.00

$

1,210.00

S2 = P2*(1+i) => S2 = 1000*(1+0.10) = $1,100.00

$

1,100.00

ST = S1 + S2 = 1210 + 1100 => ST = $2,310.00

$

2,310.00

n

1

22. Supongamos que depositamos ahora $1,000 y luego $2,000 al cabo de un año. Si la tasa de interés es 10% anual, ¿cuánto tendremos al final de los dos años? Datos: P1 = $ 1,000.00 P2 =

$

ST = S1 + S2

2,000.00 ?

i= n1=

10% anual = 0.10 anual 2 años

n2 =

1 año S1 = P1*(1+i)n => S1 = 1000*(1+0.10)2 = $1,210.00 n

$1,210.00

1

S2 = P2*(1+i) => S2 = 2000*(1+0.10) = $2,200.00

$2,200.00

ST = S1 + S2 = 1210 + 2200 => ST = $3,410.00

$3,410.00

23. Si nos proponemos ahorrar $100 anuales durante los tres próximos años, ¿Cuánto habremos acumulado al final de ese la tasa de interés es 10% anual? Datos: P1 =

$

100.00

S1 = P1*(1+i) => S1 = 100*(1+0.10) = $133.10

P2 =

$

100.00

S2 = P2*(1+i)n => S2 = 100*(1+0.10)2 = $121.00

P3 =

$

100.00

S3 = P3*(1+i) => S3 = 100*(1+0.10) = $110.00

i=

n

n

3

1

10% anual = 0.1 anual

ST = S1 + S2 + S3 = ?

ST = S1 + S2 + S3= 133.10 + 121 + 110 => ST = $364.10

n1 =

3 años

n2 =

2 años

n3 =

1 año

24. ¿Cuánto deberíamos poner en un fondo con una tasa de interés del 10% anual para obtener $100 anuales durante los tre próximos años? Datos: PT = P1 + P2 + P 3 = ? S1 =

$

100.00

P1 = S1/(1+i)n => P1 = 100/(1+0.10)3 = $75.13

S2 =

$

100.00

P2 = S2/(1+i) => P2 = 100/(1+0.10) = $82.65

S3 =

$

100.00

P3 = S3/(1+i) => P3 = 100/(1+0.10) = $90.91

i=

n

2

n

1

10% anual = 0.10 anual

n1 = 3 años

3 años

n2=

2 años

n3=

1 año

PT = P1+P2+P3 = 75.13 + 82.65 + 90.91 => PT = $248.69

25. Tiene usted 65 años y estudia la conveniencia de comprar una anualidad a una compañía de seguros. Con una inversión d

25. Tiene usted 65 años y estudia la conveniencia de comprar una anualidad a una compañía de seguros. Con una inversión d $10,000 dólares, la aseguradora le pagará $1,000 anuales por el resto de su vida. Si puede obtener 8% anual sobre el dinero depositado en una cuenta bancaria y esperar vivir 80 años, ¿vale la pena comprar la anualidad? ¿Qué interés implícito le est pagando la compañía de seguros? ¿Cuánto debería vivir para que le convenga adquirir la anualidad? a) ¿vale la pena comprar la anualidad? Datos: P= F= A=

? ? $

Encontrando el VP de las anualidades: -n

P = A*[1 - (1 + i) ]/i Anualidad ordinaria

1,000.00

i= n=

8% anual = 0.08 anual 15 años

P = A*[1 - (1 + i)-n]/i = 1000*[1 - (1 + 0.08)-15]/0.08 => P = $8,559.48

Esa cantidad debería depositar para obtener $1,000 anuales que es men tanto no vale la pena comprar la anualidad. F = A*,*(1+i)ⁿ-1+/i- = 1000*,*(1.08)15-1]/0.08} = $27,152.11 P = A*,* 1-(1+i)¯ⁿ+/i- =1000*,*1-(1.08)-15]/0.08} = $8,559.48

VPN = 10000 - 8559.48 = $1,440.52 Que es lo que se pagaría demás si se compra la anualidad, por tanto no c Sí P = $ 10,000.00 de la inversión Se toma como valor negativo en la formula.

A = P*i/[1-(1+i)-n] = [10000*(0.08)]/[1-(1.08)-15] = $1,168.30 Es la anualidad que tendría que pagar la aseguradora por una inversión d

b) ¿Qué interés implícito le está pagando la compañía de seguros? i=

5.56%

Esta tasa me pagaría la aseguradora ,si hago la inversión de $10,000.00, anualidad de $1000.00 durante 15 años .

c) ¿Cuánto debería vivir para que le convenga adquirir la anualidad? Sí tomamos como P = n=

$ 10,000.00 Se toma como valor negativo en la formula. 21 años debería vivir para que sea conveniene adquirir la inversión de la aseguradora.

26. Acaba usted de decidir comprar una casa y necesita un préstamo de $100,000. Un banco le ofrece un préstamo hipoteca liquidará en un plazo de 30 años, con 360 pagos mensuales. Si la tasa de interés es de 12% anual, ¿cuánto pagará mensualm (aunque la tasa se cotiza como una tasa porcentual anual, TPA, en realidad es de 1% mensual). Otro banco le ofrece un prés hipotecario a 15 años, con pagos mensuales de $1,100. ¿Cuál opción le conviene más? Datos: Banco A P= S= A= j= i= j/12 =

$ 100,000.00 ? ? 12% anual = 0.12 anual 1% mensual = 0.01 mensual

m= n = m*12 =

30 años 360 meses A= P*{i/[1-(1+i)-n]} = 100000{0.01/[1-(1.01)-360]} = $1,028.61 F = A*,*(1+i)ⁿ-1+/i- = 1028.61*,*(1.01)360-1]/0.01} = $3,594,955.05

Datos: Banco B P= S= A= j=

? ? $

i = j/12 = m = 15 años n = m*12 =

P = A*,* 1-(1+i) ¯ ⁿ+/i- =1100*,*1-(1.01)-180]/0.01} = $91,6

1,100.00 12% anual = 0.12 anual

F = A*,*(1+i)ⁿ-1+/i- = 1100*,*(1.01)180-1]/0.01} = $549,538

1% mensual = 0.01 mensual 15 años 180 meses

La opción del banco B conviene más, porque el préstamo mucho menor y se reduce el tiempo de la deuda a la mit

27. Va usted a comprar un automóvil y piensa obtener un préstamo de $1,000 que pagará en abonos durante un año, a una t porcentual anual de 12% (1% mensual), que liquidará en 12 abonos mensuales iguales. Calcule el valor de la cuota y elabore “deber ser” del préstamo. Datos: P= S= A= j= i = j/12 = m= n = m*12 =

$

1,000.00 ? ? 12% 1% 1 12

-n

-12

A= P*{i/[1-(1+i) ]} = 1000*{0.01/[1-(1.01) ]} = $88.85

anual = 0.12 anual mensual = 0.01 mensual año meses

El "Deber Ser" del préstamo Tabla de amortización Mes

Saldo inicial

Pago total

1

1,000.00

88.85

2

921.15

88.85

3

841.51

88.85

4

761.08

88.85

5

679.84

88.85

6

597.79

88.85

7

514.92

88.85

8

431.22

88.85

9

346.68

88.85

10

261.30

88.85

11

175.07

88.85

12

87.97

88.85

Totales

1,066.20

, suponiendo que la caja paga 10% anual.

Sí fuera: i= n = 4*2 = P= $

(3,384.20)

s capitalizable

$

5,674.08

o es del 5% tasa anual efectiva. (O sea por

10% semestral = 0.1 semestral 8 semestres $ 5,000.00

P = S/(1 +i)n => P = 5000/(1+0.1)8 => P = $2332.54

onvertible anualmente.

₡

5,387.57

₡

6,863.93

$

1,992.56

Vale más los $2,500 después de 8 años porque su valor presente y su valor futuro son mayores. $

(1,254.67)

estaría dispuesto a prestarle a alguien que

$ (34,029.16)

tasa de interés del 20% anual. ¿Cuánto

Esto pagará la persona al final del quinto año.

carrera y que paga actualmente una tral en la universidad. Para esto asume que d a cursar una carrera profesional dentro

mo principal, tenemos: Esto es lo que pagarán, en total, al final de los 40 semestres o al entrar a la universidad dentro de 20 años.

al, tenemos:

,671,928.92

$ 3,671,928.92 ($2,498.30) Esto sería la colegiatura semestral que pagarían al entrar a la universidad.

)/[1-(1.2)-40]} => P = $500.00

$500.00

anco, para este tipo de préstamos, otorga menos los intereses generados por el

$ 109,344.33 Esto es el total que pagará la empresa al final de los seis meses. $

9,344.33

$ 90,655.67

Esto es lo que le cobrarán de interese a la empresa por el préstamo. Esto es lo que realmente recibe la empresa del préstamo solicitado.

6

0 => (1+ireal) = 100000/90655.57 => 1+ireal =

6

a tasa de interés anual de:

2

= P+(1+j/1)1 => P*(1.0165)12/P = 1+j => 1.21699 - 1 = j fectiva o real.

anual capitalizable cada semestre?

=> ireal = 1.0165 - 1 1.10307

anual capitalizable cada semestre?

3 meses = 22.52 períodos

suelve establecer un fondo para cubrir esos to, por ser a largo plazo, paga el 18% anual, milia para garantizar la educación de su

= ¢1,722.79

% anual durante 45 años.

ños de edad?

₡

(1,722.79)

6% por año que se capitaliza imo segundo mes a la tasa declarada. Por imal). Encuentre la tasa anual efectiva (TAE

6.17%

vence en cinco años. Este tipo de bono no sequios que recibió en el cumpleaños, su

se vence en otros cinco años?

$

(68.06)

n es una cuenta bancaria que reditúa 8%.

$

(92.59)

porque además beneficio sera mayor que

Cuenta bancaria para un año sí P = S = P*(1+i)n = 75*(1.08)1 = $81.00

$

75.00

$

81.00

beneficio sera mayor que

inco años costará $20,000. Puede ganar 8%

5

$20000/ (1+0.08) => P = $13,612.66

$ 12.12 Vale la pena la inversión en bienes raíces.

(13,611.66)

10000*(1+0.08)5 = $14,693.28

$ (14,693.28) $5,306.72 Vale la pena la inversión en bienes raíces.

móvil. Vamos a un banco y nos ofrecen un mpromete a prestarnos esa cantidad si le

4

9000/ (1+0.12) => P = $5,719.66

$

(5,719.66)

19.66 Conviene más el el préstamo bancario = $5,000 - $5,719.66 = - $719.66 Quiere decir que como el VPN da negativo no conviene la alternativa del amigo.

4

5000*(1+0.12) = $7,867.60

$ 1,132.40 Conviene más el el préstamo bancario

7,867.60

anual, empezando inmediatamente.

De forma más directa, con la fórmula: VFA i, t = a{[(1 + i)n – 1+/i- *(1+i) Entonces:

VFA i,t = 1000{[(1.1)2 -1]/0.1} * (1.1) VFA i,t = $2,310.00

$ 2,310.00

sa de interés es 10% anual, ¿cuánto

De otra forma: ST = S1 + S2 = $

3,410.00

bremos acumulado al final de ese lapso si la

De forma más directa, con la fórmula: VFA i, t = a{[(1 + i)n – 1+/i- *(1+i) Entonces:

> ST = $364.10

VFA i,t = 100{[(1.1)3 -1]/0.1} * (1.1) VFA i,t = $364.10

$

364.10

btener $100 anuales durante los tres

$75.13 $

82.64

$

90.91

De forma más directa, con la fórmula: VPA i, t = a{[1 - (1 + i)-n]/i} Entonces:

-3

VPA i,t = 100{[1 - (1.1) ]/(0.1)} VPA i,t = $248.69

=> PT = $248.69

$248.69

ñía de seguros. Con una inversión de

ñía de seguros. Con una inversión de e obtener 8% anual sobre el dinero alidad? ¿Qué interés implícito le está anualidad?

-n

P = A*[1 - (1 + i) ]/i Anualidad ordinaria

0.08)-15]/0.08 => P = $8,559.48

$

(8,559.48)

obtener $1,000 anuales que es menor que los $10,000. Por

1]/0.08} = $27,152.11

)-15]/0.08} = $8,559.48

$27,152.11 $

(8,559.48)

compra la anualidad, por tanto no conviene; es mejor en el banco.

1-(1.08)-15] = $1,168.30 $ (1,168.30) la aseguradora por una inversión de $10,000.

de $10,000.00, por la cual me pagaría una

ersión de la aseguradora.

nco le ofrece un préstamo hipotecario que % anual, ¿cuánto pagará mensualmente? sual). Otro banco le ofrece un préstamo

S = A*[(1 + i)n - 1]/i Anualidad ordinaria

-(1.01)-360]} = $1,028.61

$

(1,028.61)

) 360-1]/0.01} = $3,594,955.05$ (3,594,964.13)

=1100*,*1-(1.01)-180]/0.01} = $$91,653.83 (91,653.83)

100*,*(1.01)180-1]/0.01} = $549,538.21 $ 549,538.22

conviene más, porque el préstamo o VP es menor, el monto o VF también es el tiempo de la deuda a la mitad, aunque las anualidades son un poco

á en abonos durante un año, a una tasa alcule el valor de la cuota y elabore el

-12

000*{0.01/[1-(1.01) ]} = $88.85 $

(88.85)

Deber Ser" del préstamo Tabla de amortización Interés pagado

Capital pagado

S aldo insolu to

10.00

78.85

921.15

9.21

79.64

841.51

8.42

80.43

761.08

7.61

81.24

679.84

6.80

82.05

597.79

5.98

82.87

514.92

5.15

83.70

431.22

4.31

84.54

346.68

3.47

85.38

261.30

2.61

86.24

175.07

1.75

87.10

87.97

0.88

87.97

0.00

66.20

1,000.00

mestral = 0.1 semestral

1)8 => P = $2332.54

$ (2,332.54)

valor futuro

sidad dentro de 20 años.

ernativa del amigo.

{[(1 + i)n – 1+/i- *(1+i)

órmula: VPA i, t = a{[1 - (1 + i)-n]/i} -3

(1.1) ]/(0.1)} $

(248.69)

n

]/i Anualidad ordinaria

]/i Anualidad ordinaria

Tabla para Calcular Número Exacto de Días Entre Dos Fechas. Día del mes Enero Febrero Marzo Abril Mayo Junio Julio Agosto Septiembre Octubre 1 1 32 60 91 121 152 182 213 244 274 2 2 33 61 92 122 153 183 214 245 275 3 3 34 62 93 123 154 184 215 246 276 4 4 35 63 94 124 155 185 216 247 277 5 5 36 64 95 125 156 186 217 248 278 6 6 37 65 96 126 157 187 218 249 279 7 7 38 66 97 127 158 188 219 250 280 8 8 39 67 98 128 159 189 220 251 281 9 9 40 68 99 129 160 190 221 252 282 10 10 41 69 100 130 161 191 222 253 283 11 11 42 70 101 131 162 192 223 254 284 12 12 43 71 102 132 163 193 224 255 285 13 13 44 72 103 133 164 194 225 256 286 14 14 45 73 104 134 165 195 226 257 287 15 15 46 74 105 135 166 196 227 258 288 16 16 47 75 106 136 167 197 228 259 289 17 17 48 76 107 137 168 198 229 260 290 18 18 49 77 108 138 169 199 230 261 291 19 19 50 78 109 139 170 200 231 262 292 20 20 51 79 110 140 171 201 232 263 293 21 21 52 80 111 141 172 202 233 264 294 22 22 53 81 112 142 173 203 234 265 295 23 23 54 82 113 143 174 204 235 266 296 24 24 55 83 114 144 175 205 236 267 297 25 25 56 84 115 145 176 206 237 268 298 26 26 57 85 116 146 177 207 238 269 299 27 27 58 86 117 147 178 208 239 270 300 28 28 59 87 118 148 179 209 240 271 301 29 29 88 119 149 180 210 241 272 302 30 30 89 120 150 181 211 242 273 303 31 31 90 151 212 243 304

Para años bisiestos, febrero tiene 29 días y el número de cada día a partir del 1 de marzo es uno más el número dado en la ta

Noviembre Diciembre Día del mes 305 335 1 306 336 2 307 337 3 308 338 4 309 339 5 310 340 6 311 341 7 312 342 8 313 343 9 314 344 10 315 345 11 316 346 12 317 347 13 318 348 14 319 349 15 320 350 16 321 351 17 322 352 18 323 353 19 324 354 20 325 355 21 326 356 22 327 357 23 328 358 24 329 359 25 330 360 26 331 361 27 332 362 28 333 363 29 334 364 30 365 31

es uno más el número dado en la tabla.

Tabla para Calcular Monto con Interés Compuesto. M=

1.0050000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

=(1+i/p)np 0.006667 0.667% 1.006666667 1.013377778 1.020133630 1.026934520 1.033780751 1.040672622 1.047610440 1.054594509 1.061625139 1.068702640 1.075827325 1.082999507 1.090219504 1.097487634 1.104804218 1.112169579 1.119584043 1.127047937 1.134561590 1.142125334 1.149739502 1.157404432 1.165120462 1.172887932 1.180707185 1.188578566 1.196502423 1.204479106 1.212508966 1.220592360 1.228729642 1.236921173 1.245167314 1.253468430 1.261824886 1.270237052 1.278705299 1.287230001 1.295811534 1.304450278 1.313146613

i/p = 0.007500 0.750% 1.007500000 1.015056250 1.022669172 1.030339191 1.038066735 1.045852235 1.053696127 1.061598848 1.069560839 1.077582545 1.085664415 1.093806898 1.102010449 1.110275528 1.118602594 1.126992114 1.135444555 1.143960389 1.152540092 1.161184142 1.169893023 1.178667221 1.187507225 1.196413529 1.205386631 1.214427031 1.223535233 1.232711748 1.241957086 1.251271764 1.260656302 1.270111224 1.279637058 1.289234336 1.298903594 1.308645371 1.318460211 1.328348663 1.338311278 1.348348612 1.358461227

0.500% 0.008750 0.875% 1.008750000 1.017576563 1.026480357 1.035462061 1.044522354 1.053661924 1.062881466 1.072181679 1.081563269 1.091026947 1.100573433 1.110203450 1.119917731 1.129717011 1.139602035 1.149573552 1.159632321 1.169779104 1.180014671 1.190339799 1.200755273 1.211261881 1.221860423 1.232551701 1.243336529 1.254215723 1.265190111 1.276260524 1.287427804 1.298692797 1.310056359 1.321519352 1.333082647 1.344747120 1.356513657 1.368383152 1.380356504 1.392434624 1.404618427 1.416908838 1.429306790

np = 0.010000 1.000% 1.010000000 1.020100000 1.030301000 1.040604010 1.051010050 1.061520151 1.072135352 1.082856706 1.093685273 1.104622125 1.115668347 1.126825030 1.138093280 1.149474213 1.160968955 1.172578645 1.184304431 1.196147476 1.208108950 1.220190040 1.232391940 1.244715860 1.257163018 1.269734649 1.282431995 1.295256315 1.308208878 1.321290967 1.334503877 1.347848915 1.361327404 1.374940679 1.388690085 1.402576986 1.416602756 1.430768784 1.445076471 1.459527236 1.474122509 1.488863734 1.503752371

1 0.0112500 1.125% 1.011250000 1.022626563 1.034131111 1.045765086 1.057529944 1.069427155 1.081458211 1.093624616 1.105927893 1.118369582 1.130951239 1.143674441 1.156540778 1.169551862 1.182709320 1.196014800 1.209469967 1.223076504 1.236836115 1.250750521 1.264821464 1.279050706 1.293440026 1.307991226 1.322706128 1.337586572 1.352634421 1.367851558 1.383239888 1.398801337 1.414537852 1.430451402 1.446543981 1.462817600 1.479274299 1.495916134 1.512745191 1.529763574 1.546973414 1.564376865 1.581976105

M= 0.0125000 1.250% 1.012500000 1.025156250 1.037970703 1.050945337 1.064082154 1.077383181 1.090850470 1.104486101 1.118292177 1.132270830 1.146424215 1.160754518 1.175263949 1.189954749 1.204829183 1.219889548 1.235138167 1.250577394 1.266209612 1.282037232 1.298062697 1.314288481 1.330717087 1.347351050 1.364192939 1.381245350 1.398510917 1.415992304 1.433692207 1.451613360 1.469758527 1.488130509 1.506732140 1.525566292 1.544635870 1.563943819 1.583493116 1.603286780 1.623327865 1.643619463 1.664164707

42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1.321900923 1.330713596 1.339585020 1.348515587 1.357505691 1.366555729 1.375666100 1.384837208 1.394069456 1.403363252 1.412719007 1.422137134 1.431618048 1.441162168 1.450769916 1.460441716 1.470177994 1.479979180 1.489845708

1.368649686 1.378914559 1.389256418 1.399675841 1.410173410 1.420749710 1.431405333 1.442140873 1.452956930 1.463854107 1.474833013 1.485894260 1.497038467 1.508266256 1.519578253 1.530975090 1.542457403 1.554025833 1.565681027

1.441813225 1.454429090 1.467155345 1.479992954 1.492942893 1.506006143 1.519183697 1.532476554 1.545885724 1.559412224 1.573057081 1.586821330 1.600706017 1.614712195 1.628840926 1.643093284 1.657470351 1.671973216 1.686602982

1.518789895 1.533977794 1.549317572 1.564810747 1.580458855 1.596263443 1.612226078 1.628348338 1.644631822 1.661078140 1.677688921 1.694465811 1.711410469 1.728524573 1.745809819 1.763267917 1.780900597 1.798709603 1.816696699

1.599773336 1.617770786 1.635970708 1.654375378 1.672987101 1.691808206 1.710841048 1.730088010 1.749551500 1.769233955 1.789137837 1.809265637 1.829619876 1.850203099 1.871017884 1.892066835 1.913352587 1.934877804 1.956645179

1.684966766 1.706028850 1.727354211 1.748946138 1.770807965 1.792943065 1.815354853 1.838046789 1.861022374 1.884285153 1.907838718 1.931686702 1.955832785 1.980280695 2.005034204 2.030097131 2.055473346 2.081166762 2.107181347

1.0050000 0.0137500 1.375% 1.013750000 1.027689063 1.041819787 1.056144809 1.070666800 1.085388469 1.100312560 1.115441858 1.130779184 1.146327397 1.162089399 1.178068128 1.194266565 1.210687730 1.227334687 1.244210538 1.261318433 1.278661562 1.296243158 1.314066502 1.332134916 1.350451771 1.369020483 1.387844515 1.406927377 1.426272628 1.445883877 1.465764780 1.485919046 1.506350433 1.527062751 1.548059864 1.569345687 1.590924190 1.612799398 1.634975390 1.657456301 1.680246326 1.703349713 1.726770771 1.750513869

0.0150000 1.500% 1.015000000 1.030225000 1.045678375 1.061363551 1.077284004 1.093443264 1.109844913 1.126492587 1.143389975 1.160540825 1.177948937 1.195618171 1.213552444 1.231755731 1.250232067 1.268985548 1.288020331 1.307340636 1.326950745 1.346855007 1.367057832 1.387563699 1.408377155 1.429502812 1.450945354 1.472709534 1.494800177 1.517222180 1.539980513 1.563080220 1.586526424 1.610324320 1.634479185 1.658996373 1.683881318 1.709139538 1.734776631 1.760798281 1.787210255 1.814018409 1.841228685

0.0162500 1.625% 1.016250000 1.032764063 1.049546479 1.066601609 1.083933885 1.101547811 1.119447962 1.137638992 1.156125625 1.174912667 1.194004998 1.213407579 1.233125452 1.253163741 1.273527652 1.294222476 1.315253591 1.336626462 1.358346642 1.380419775 1.402851596 1.425647935 1.448814714 1.472357953 1.496283769 1.520598381 1.545308104 1.570419361 1.595938676 1.621872679 1.648228110 1.675011817 1.702230759 1.729892009 1.758002754 1.786570299 1.815602066 1.845105600 1.875088566 1.905558755 1.936524085

0.0175000 1.750% 1.017500000 1.035306250 1.053424109 1.071859031 1.090616564 1.109702354 1.129122145 1.148881783 1.168987214 1.189444490 1.210259769 1.231439315 1.252989503 1.274916819 1.297227864 1.319929351 1.343028115 1.366531107 1.390445401 1.414778196 1.439536814 1.464728708 1.490361461 1.516442786 1.542980535 1.569982695 1.597457392 1.625412896 1.653857622 1.682800130 1.712249132 1.742213492 1.772702228 1.803724517 1.835289696 1.867407266 1.900086893 1.933338414 1.967171836 2.001597343 2.036625297

0.0187500 1.875% 1.018750000 1.037851563 1.057311279 1.077135866 1.097332163 1.117907141 1.138867900 1.160221673 1.181975830 1.204137877 1.226715462 1.249716377 1.273148559 1.297020094 1.321339221 1.346114331 1.371353975 1.397066862 1.423261866 1.449948026 1.477134551 1.504830824 1.533046402 1.561791022 1.591074604 1.620907253 1.651299263 1.682261125 1.713803521 1.745937337 1.778673662 1.812023793 1.845999239 1.880611725 1.915873195 1.951795817 1.988391989 2.025674338 2.063655732 2.102349277 2.141768326

0.0200000 2.000% 1.020000000 1.040400000 1.061208000 1.082432160 1.104080803 1.126162419 1.148685668 1.171659381 1.195092569 1.218994420 1.243374308 1.268241795 1.293606630 1.319478763 1.345868338 1.372785705 1.400241419 1.428246248 1.456811173 1.485947396 1.515666344 1.545979671 1.576899264 1.608437249 1.640605994 1.673418114 1.706886477 1.741024206 1.775844690 1.811361584 1.847588816 1.884540592 1.922231404 1.960676032 1.999889553 2.039887344 2.080685091 2.122298792 2.164744768 2.208039664 2.252200457

0.0212500 2.125% 1.021250000 1.042951563 1.065114283 1.087747962 1.110862606 1.134468436 1.158575891 1.183195628 1.208338535 1.234015729 1.260238563 1.287018633 1.314367779 1.342298094 1.370821929 1.399951895 1.429700872 1.460082016 1.491108759 1.522794820 1.555154210 1.588201237 1.621950513 1.656416961 1.691615822 1.727562658 1.764273365 1.801764174 1.840051662 1.879152760 1.919084756 1.959865307 2.001512445 2.044044585 2.087480532 2.131839493 2.177141083 2.223405331 2.270652694 2.318904064 2.368180775

1.774583435 1.798983957 1.823719986 1.848796136 1.874217083 1.899987568 1.926112397 1.952596443 1.979444644 2.006662008 2.034253610 2.062224597 2.090580185 2.119325663 2.148466391 2.178007804 2.207955411 2.238314798 2.269091626

1.868847115 1.896879822 1.925333019 1.954213014 1.983526210 2.013279103 2.043478289 2.074130464 2.105242421 2.136821057 2.168873373 2.201406473 2.234427570 2.267943984 2.301963144 2.336492591 2.371539980 2.407113079 2.443219776

1.967992601 1.999972481 2.032472034 2.065499704 2.099064074 2.133173865 2.167837941 2.203065307 2.238865119 2.275246677 2.312219435 2.349793001 2.387977137 2.426781766 2.466216970 2.506292995 2.547020256 2.588409336 2.630470987

2.072266239 2.108530899 2.145430189 2.182975218 2.221177284 2.260047886 2.299598724 2.339841702 2.380788932 2.422452738 2.464845661 2.507980460 2.551870118 2.596527845 2.641967083 2.688201507 2.735245033 2.783111821 2.831816278

2.181926482 2.222837604 2.264515809 2.306975480 2.350231271 2.394298107 2.439191196 2.484926031 2.531518395 2.578984364 2.627340321 2.676602952 2.726789258 2.777916556 2.830002492 2.883065038 2.937122508 2.992193555 3.048297184

2.297244466 2.343189355 2.390053142 2.437854205 2.486611289 2.536343515 2.587070385 2.638811793 2.691588029 2.745419790 2.800328185 2.856334749 2.913461444 2.971730673 3.031165286 3.091788592 3.153624364 3.216696851 3.281030788

2.418504616 2.469897840 2.522383169 2.575983811 2.630723467 2.686626341 2.743717150 2.802021140 2.861564089 2.922372326 2.984472738 3.047892783 3.112660505 3.178804541 3.246354137 3.315339163 3.385790120 3.457738160 3.531215096

0.0225000 2.250% 1.022500000 1.045506250 1.069030141 1.093083319 1.117677693 1.142825442 1.168539014 1.194831142 1.221714843 1.249203426 1.277310504 1.306049990 1.335436115 1.365483427 1.396206804 1.427621457 1.459742940 1.492587156 1.526170367 1.560509201 1.595620658 1.631522122 1.668231370 1.705766576 1.744146324 1.783389616 1.823515883 1.864544990 1.906497252 1.949393441 1.993254793 2.038103026 2.083960344 2.130849452 2.178793564 2.227816419 2.277942289 2.329195990 2.381602900 2.435188965 2.489980717

0.0237500 2.375% 1.023750000 1.048064063 1.072955584 1.098438279 1.124526188 1.151233685 1.178575485 1.206566653 1.235222611 1.264559148 1.294592428 1.325338998 1.356815799 1.389040174 1.422029879 1.455803088 1.490378411 1.525774899 1.562012053 1.599109839 1.637088698 1.675969554 1.715773831 1.756523459 1.798240892 1.840949113 1.884671654 1.929432606 1.975256630 2.022168975 2.070195489 2.119362631 2.169697494 2.221227809 2.273981970 2.327989042 2.383278781 2.439881652 2.497828842 2.557152277 2.617884643

0.0250000 2.500% 1.025000000 1.050625000 1.076890625 1.103812891 1.131408213 1.159693418 1.188685754 1.218402898 1.248862970 1.280084544 1.312086658 1.344888824 1.378511045 1.412973821 1.448298166 1.484505621 1.521618261 1.559658718 1.598650186 1.638616440 1.679581851 1.721571398 1.764610683 1.808725950 1.853944098 1.900292701 1.947800018 1.996495019 2.046407394 2.097567579 2.150006769 2.203756938 2.258850861 2.315322133 2.373205186 2.432535316 2.493348699 2.555682416 2.619574476 2.685063838 2.752190434

0.0262500 2.625% 1.026250000 1.053189063 1.080835275 1.109207201 1.138323890 1.168204893 1.198870271 1.230340616 1.262637057 1.295781279 1.329795538 1.364702671 1.400526116 1.437289927 1.475018787 1.513738030 1.553473654 1.594252337 1.636101461 1.679049124 1.723124164 1.768356173 1.814775523 1.862413380 1.911301731 1.961473402 2.012962079 2.065802333 2.120029644 2.175680422 2.232792034 2.291402824 2.351552149 2.413280392 2.476629003 2.541640514 2.608358578 2.676827990 2.747094725 2.819205962 2.893210118

0.0275000 2.750% 1.027500000 1.055756250 1.084789547 1.114621259 1.145273344 1.176768361 1.209129491 1.242380552 1.276546017 1.311651033 1.347721436 1.384783775 1.422865329 1.461994126 1.502198964 1.543509436 1.585955945 1.629569734 1.674382901 1.720428431 1.767740213 1.816353069 1.866302778 1.917626105 1.970360823 2.024545745 2.080220753 2.137426824 2.196206062 2.256601728 2.318658276 2.382421379 2.447937966 2.515256260 2.584425808 2.655497517 2.728523699 2.803558101 2.880655949 2.959873987 3.041270522

0.0287500 2.875% 1.028750000 1.058326563 1.088753451 1.120055113 1.152256697 1.185384077 1.219463870 1.254523456 1.290591005 1.327695497 1.365866742 1.405135411 1.445533054 1.487092129 1.529846028 1.573829101 1.619076688 1.665625143 1.713511866 1.762775332 1.813455123 1.865591957 1.919227726 1.974405523 2.031169682 2.089565811 2.149640828 2.211443001 2.275021988 2.340428870 2.407716200 2.476938041 2.548150009 2.621409322 2.696774840 2.774307117 2.854068446 2.936122914 3.020536448 3.107376871 3.196713956

0.0300000 3.000% 1.030000000 1.060900000 1.092727000 1.125508810 1.159274074 1.194052297 1.229873865 1.266770081 1.304773184 1.343916379 1.384233871 1.425760887 1.468533713 1.512589725 1.557967417 1.604706439 1.652847632 1.702433061 1.753506053 1.806111235 1.860294572 1.916103409 1.973586511 2.032794106 2.093777930 2.156591268 2.221289006 2.287927676 2.356565506 2.427262471 2.500080345 2.575082756 2.652335238 2.731905296 2.813862454 2.898278328 2.985226678 3.074783478 3.167026983 3.262037792 3.359898926

2.546005283 2.603290402 2.661864436 2.721756386 2.782995905 2.845613313 2.909639612 2.975106503 3.042046400 3.110492444 3.180478524 3.252039290 3.325210174 3.400027403 3.476528020 3.554749900 3.634731773 3.716513238 3.800134786

2.680059404 2.743710814 2.808873946 2.875584702 2.943879839 3.013796985 3.085374664 3.158652312 3.233670304 3.310469974 3.389093636 3.469584610 3.551987244 3.636346941 3.722710181 3.811124548 3.901638756 3.994302677 4.089167365

2.820995195 2.891520075 2.963808077 3.037903279 3.113850861 3.191697132 3.271489561 3.353276800 3.437108720 3.523036438 3.611112349 3.701390157 3.793924911 3.888773034 3.985992360 4.085642169 4.187783223 4.292477804 4.399789749

2.969156884 3.047097252 3.127083555 3.209169498 3.293410197 3.379862215 3.468583598 3.559633918 3.653074308 3.748967509 3.847377906 3.948371576 4.052016329 4.158381758 4.267539279 4.379562185 4.494525693 4.612506992 4.733585301

3.124905461 3.210840361 3.299138471 3.389864779 3.483086061 3.578870927 3.677289878 3.778415349 3.882321772 3.989085620 4.098785475 4.211502075 4.327318383 4.446319638 4.568593428 4.694229747 4.823321065 4.955962395 5.092251361

3.288619482 3.383167292 3.480433352 3.580495811 3.683435065 3.789333823 3.898277171 4.010352639 4.125650278 4.244262723 4.366285277 4.491815978 4.620955688 4.753808164 4.890480148 5.031081453 5.175725044 5.324527139 5.477607295

3.460695894 3.564516770 3.671452273 3.781595842 3.895043717 4.011895028 4.132251879 4.256219436 4.383906019 4.515423199 4.650885895 4.790412472 4.934124846 5.082148592 5.234613049 5.391651441 5.553400984 5.720003014 5.891603104

0.0312500 3.125% 1.031250000 1.063476563 1.096710205 1.130982399 1.166325599 1.202773274 1.240359939 1.279121187 1.319093724 1.360315403 1.402825259 1.446663548 1.491871784 1.538492778 1.586570677 1.636151011 1.687280730 1.740008252 1.794383510 1.850457995 1.908284807 1.967918708 2.029416167 2.092835422 2.158236529 2.225681421 2.295233965 2.366960027 2.440927528 2.517206513 2.595869216 2.676990129 2.760646071 2.846916261 2.935882394 3.027628719 3.122242116 3.219812182 3.320431313 3.424194791 3.531200879

0.0325000 3.250% 1.032500000 1.066056250 1.100703078 1.136475928 1.173411396 1.211547266 1.250922552 1.291577535 1.333553805 1.376894304 1.421643369 1.467846778 1.515551799 1.564807232 1.615663467 1.668172530 1.722388137 1.778365751 1.836162638 1.895837924 1.957452657 2.021069868 2.086754639 2.154574164 2.224597825 2.296897254 2.371546415 2.448621673 2.528201878 2.610368439 2.695205413 2.782799589 2.873240575 2.966620894 3.063036073 3.162584746 3.265368750 3.371493234 3.481066764 3.594201434 3.711012981

0.0337500 3.375% 1.033750000 1.068639063 1.104705631 1.141989446 1.180531590 1.220374531 1.261562171 1.304139895 1.348154616 1.393654834 1.440690685 1.489313996 1.539578343 1.591539112 1.645253557 1.700780865 1.758182219 1.817520869 1.878862198 1.942273797 2.007825538 2.075589650 2.145640800 2.218056177 2.292915573 2.370301474 2.450299149 2.532996745 2.618485385 2.706859267 2.798215767 2.892655549 2.990282674 3.091204714 3.195532873 3.303382108 3.414871254 3.530123159 3.649264815 3.772427503 3.899746931

0.0350000 3.500% 1.035000000 1.071225000 1.108717875 1.147523001 1.187686306 1.229255326 1.272279263 1.316809037 1.362897353 1.410598761 1.459969717 1.511068657 1.563956060 1.618694522 1.675348831 1.733986040 1.794675551 1.857489196 1.922501317 1.989788863 2.059431474 2.131511575 2.206114480 2.283328487 2.363244984 2.445958559 2.531567108 2.620171957 2.711877976 2.806793705 2.905031484 3.006707586 3.111942352 3.220860334 3.333590446 3.450266111 3.571025425 3.696011315 3.825371711 3.959259721 4.097833811

0.0362500 3.625% 1.036250000 1.073814063 1.112739822 1.153076641 1.194875669 1.238189912 1.283074296 1.329585740 1.377783223 1.427727864 1.479483000 1.533114258 1.588689650 1.646279650 1.705957287 1.767798239 1.831880925 1.898286609 1.967099498 2.038406855 2.112299104 2.188869946 2.268216482 2.350439329 2.435642755 2.523934805 2.615427441 2.710236686 2.808482766 2.910290266 3.015788288 3.125110614 3.238395873 3.355787724 3.477435029 3.603492049 3.734118635 3.869480436 4.009749102 4.155102507 4.305724973

0.0375000 3.750% 1.037500000 1.076406250 1.116771484 1.158650415 1.202099806 1.247178548 1.293947744 1.342470784 1.392813439 1.445043943 1.499233090 1.555454331 1.613783869 1.674300764 1.737087043 1.802227807 1.869811349 1.939929275 2.012676623 2.088151996 2.166457696 2.247699860 2.331988604 2.419438177 2.510167109 2.604298375 2.701959564 2.803283048 2.908406162 3.017471393 3.130626571 3.248025067 3.369826007 3.496194482 3.627301775 3.763325592 3.904450302 4.050867188 4.202774707 4.360378759 4.523892962

0.0387500 3.875% 1.038750000 1.079001563 1.120812873 1.164244372 1.209358841 1.256221496 1.304900079 1.355464957 1.407989225 1.462548807 1.519222573 1.578092448 1.639243530 1.702764217 1.768746331 1.837285251 1.908480054 1.982433656 2.059252961 2.139049013 2.221937162 2.308037227 2.397473670 2.490375774 2.586877836 2.687119352 2.791245227 2.899405979 3.011757961 3.128463582 3.249691546 3.375617093 3.506422255 3.642296118 3.783435092 3.930043202 4.082332376 4.240522756 4.404843013 4.575530679 4.752832493

3.641550906 3.755349372 3.872704040 3.993726041 4.118529980 4.247234042 4.379960105 4.516833859 4.657984917 4.803546945 4.953657788 5.108459593 5.268098956 5.432727048 5.602499768 5.777577886 5.958127195 6.144318670 6.336328628

3.831620903 3.956148582 4.084723411 4.217476922 4.354544922 4.496067632 4.642189830 4.793060999 4.948835482 5.109672635 5.275736995 5.447198448 5.624232397 5.807019950 5.995748099 6.190609912 6.391804734 6.599538388 6.814023385

4.031363390 4.167421905 4.308072394 4.453469837 4.603774444 4.759151832 4.919773206 5.085815552 5.257461826 5.434901163 5.618329077 5.807947684 6.003965918 6.206599768 6.416072510 6.632614957 6.856465712 7.087871430 7.327087090

4.241257995 4.389702025 4.543341595 4.702358551 4.866941101 5.037284039 5.213588981 5.396064595 5.584926856 5.780399296 5.982713271 6.192108235 6.408832024 6.633141145 6.865301085 7.105586623 7.354282154 7.611682030 7.878090901

4.461807503 4.623548025 4.791151641 4.964830888 5.144806007 5.331305225 5.524565040 5.724830522 5.932355629 6.147403520 6.370246898 6.601168348 6.840460700 7.088427401 7.345382894 7.611653024 7.887575446 8.173500056 8.469789433

4.693538949 4.869546659 5.052154659 5.241610458 5.438170851 5.642102258 5.853681092 6.073194133 6.300938913 6.537224122 6.782370027 7.036708903 7.300585487 7.574357443 7.858395847 8.153085691 8.458826404 8.776032395 9.105133609

4.937004752 5.128313687 5.327035842 5.533458481 5.747879997 5.970610347 6.201971498 6.442297893 6.691936937 6.951249493 7.220610411 7.500409064 7.791049915 8.092953100 8.406555032 8.732309040 9.070686015 9.422175098 9.787284383

0.0400000 4.000% 1.040000000 1.081600000 1.124864000 1.169858560 1.216652902 1.265319018 1.315931779 1.368569050 1.423311812 1.480244285 1.539454056 1.601032219 1.665073507 1.731676448 1.800943506 1.872981246 1.947900496 2.025816515 2.106849176 2.191123143 2.278768069 2.369918792 2.464715543 2.563304165 2.665836331 2.772469785 2.883368576 2.998703319 3.118651452 3.243397510 3.373133410 3.508058747 3.648381097 3.794316341 3.946088994 4.103932554 4.268089856 4.438813450 4.616365988 4.801020628 4.993061453

0.0412500 4.125% 1.041250000 1.084201563 1.128924877 1.175493028 1.223982116 1.274471378 1.327043322 1.381783859 1.438782443 1.498132219 1.559930173 1.624277293 1.691278731 1.761043979 1.833687043 1.909326633 1.988086357 2.070094919 2.155486335 2.244400146 2.336981652 2.433382145 2.533759159 2.638276724 2.747105639 2.860423747 2.978416226 3.101275895 3.229203526 3.362408172 3.501107509 3.645528193 3.795906231 3.952487363 4.115527467 4.285292975 4.462061310 4.646121339 4.837773845 5.037332016 5.245121961

0.0425000 4.250% 1.042500000 1.086806250 1.132995516 1.181147825 1.231346608 1.283678838 1.338235189 1.395110185 1.454402367 1.516214468 1.580653583 1.647831360 1.717864193 1.790873421 1.866985542 1.946332427 2.029051555 2.115286246 2.205185912 2.298906313 2.396609831 2.498465749 2.604650544 2.715348192 2.830750490 2.951057386 3.076477325 3.207227611 3.343534784 3.485635013 3.633774501 3.788209917 3.949208838 4.117050214 4.292024848 4.474435904 4.664599430 4.862844906 5.069515814 5.284970237 5.509581472

0.0437500 4.375% 1.043750000 1.089414063 1.137075928 1.186823000 1.238746506 1.292941665 1.349507863 1.408548832 1.470172844 1.534492906 1.601626970 1.671698150 1.744834944 1.821171473 1.900847725 1.984009813 2.070810242 2.161408190 2.255969799 2.354668477 2.457685223 2.565208952 2.677436844 2.794574705 2.916837349 3.044448983 3.177643626 3.316665534 3.461769652 3.613222074 3.771300540 3.936294938 4.108507842 4.288255060 4.475866219 4.671685366 4.876071600 5.089399733 5.312060971 5.544463639 5.787033923

0.0450000 4.500% 1.045000000 1.092025000 1.141166125 1.192518601 1.246181938 1.302260125 1.360861830 1.422100613 1.486095140 1.552969422 1.622853046 1.695881433 1.772196097 1.851944922 1.935282443 2.022370153 2.113376810 2.208478766 2.307860311 2.411714025 2.520241156 2.633652008 2.752166348 2.876013834 3.005434457 3.140679007 3.282009562 3.429699993 3.584036492 3.745318135 3.913857451 4.089981036 4.274030182 4.466361541 4.667347810 4.877378461 5.096860492 5.326219214 5.565899079 5.816364538 6.078100942

0.0462500 4.625% 1.046250000 1.094639063 1.145266119 1.198234677 1.253653031 1.311634484 1.372297579 1.435766342 1.502170535 1.571645922 1.644334546 1.720385019 1.799952826 1.883200644 1.970298674 2.061424987 2.156765893 2.256516316 2.360880195 2.470070904 2.584311684 2.703836099 2.828888519 2.959724613 3.096611876 3.239830175 3.389672321 3.546444666 3.710467731 3.882076864 4.061622919 4.249472979 4.446011104 4.651639118 4.866777427 5.091865883 5.327364680 5.573755297 5.831541479 6.101250272 6.383433097

5.192783911 5.400495268 5.616515078 5.841175681 6.074822709 6.317815617 6.570528242 6.833349371 7.106683346 7.390950680 7.686588707 7.994052256 8.313814346 8.646366920 8.992221596 9.351910460 9.725986879 10.115026354 10.519627408

5.461483242 5.686769426 5.921348665 6.165604297 6.419935474 6.684757813 6.960504073 7.247624866 7.546589391 7.857886204 8.182024010 8.519532500 8.870963216 9.236890448 9.617912179 10.014651057 10.427755413 10.857900324 11.305788712

5.743738684 5.987847578 6.242331100 6.507630172 6.784204454 7.072533144 7.373115802 7.686473224 8.013148336 8.353707140 8.708739694 9.078861131 9.464712729 9.866963020 10.286308948 10.723477078 11.179224854 11.654341911 12.149651442

6.040216657 6.304476136 6.580296967 6.868184959 7.168668051 7.482297278 7.809647784 8.151319875 8.507940119 8.880162499 9.268669609 9.674173904 10.097419013 10.539181094 11.000270267 11.481532091 11.983849120 12.508142519 13.055373755

6.351615484 6.637438181 6.936122899 7.248248430 7.574419609 7.915268491 8.271455573 8.643671074 9.032636273 9.439104905 9.863864626 10.307738534 10.771586768 11.256308172 11.762842040 12.292169932 12.845317579 13.423356870 14.027407929

6.678666878 6.987555221 7.310729650 7.648850897 8.002610251 8.372730975 8.759969782 9.165118385 9.589005110 10.032496596 10.496499564 10.981962669 11.489878442 12.021285320 12.577269766 13.158968493 13.767570786 14.404320935 15.070520778

0.0475000 4.750% 1.047500000 1.097256250 1.149375922 1.203971278 1.261159914 1.321065010 1.383815598 1.449546839 1.518400313 1.590524328 1.666074234 1.745212760 1.828110366 1.914945609 2.005905525 2.101186037 2.200992374 2.305539512 2.415052639 2.529767639 2.649931602 2.775803353 2.907654012 3.045767578 3.190441538 3.341987511 3.500731918 3.667016684 3.841199976 4.023656975 4.214780681 4.414982764 4.624694445 4.844367431 5.074474884 5.315512441 5.567999282 5.832479248 6.109522012 6.399724308 6.703711213

0.0487500 4.875% 1.048750000 1.099876563 1.153495545 1.209728453 1.268702715 1.330551972 1.395416381 1.463442929 1.534785772 1.609606579 1.688074899 1.770368551 1.856674017 1.947186876 2.042112236 2.141665207 2.246071386 2.355567366 2.470401276 2.590833338 2.717136463 2.849596866 2.988514713 3.134204805 3.286997289 3.447238407 3.615291279 3.791536729 3.976374145 4.170222384 4.373520726 4.586729861 4.810332942 5.044836673 5.290772460 5.548697618 5.819196627 6.102882462 6.400397982 6.712417384 7.039647731

0.0500000 5.000% 1.050000000 1.102500000 1.157625000 1.215506250 1.276281563 1.340095641 1.407100423 1.477455444 1.551328216 1.628894627 1.710339358 1.795856326 1.885649142 1.979931599 2.078928179 2.182874588 2.292018318 2.406619234 2.526950195 2.653297705 2.785962590 2.925260720 3.071523756 3.225099944 3.386354941 3.555672688 3.733456322 3.920129138 4.116135595 4.321942375 4.538039494 4.764941469 5.003188542 5.253347969 5.516015368 5.791816136 6.081406943 6.385477290 6.704751154 7.039988712 7.391988148

0.0512500 5.125% 1.051250000 1.105126563 1.161764299 1.221304719 1.283896586 1.349696286 1.418868221 1.491585217 1.568028959 1.648390444 1.732870454 1.821680065 1.915041168 2.013187028 2.116362863 2.224826460 2.338848816 2.458714817 2.584723952 2.717191054 2.856447096 3.002840010 3.156735560 3.318518257 3.488592318 3.667382675 3.855336037 4.052922008 4.260634261 4.478991767 4.708540095 4.949852775 5.203532730 5.470213782 5.750562239 6.045278553 6.355099079 6.680797907 7.023188800 7.383127226 7.761512496

0.0525000 5.250% 1.052500000 1.107756250 1.165913453 1.227123909 1.291547915 1.359354180 1.430720275 1.505833089 1.584889326 1.668096016 1.755671057 1.847843787 1.944855586 2.046960504 2.154425931 2.267533292 2.386578790 2.511874176 2.643747571 2.782544318 2.928627895 3.082380859 3.244205854 3.414526662 3.593789312 3.782463250 3.981042571 4.190047306 4.410024790 4.641551091 4.885232523 5.141707231 5.411646860 5.695758321 5.994785632 6.309511878 6.640761252 6.989401217 7.356344781 7.742552882 8.149036909

0.0537500 5.375% 1.053750000 1.110389063 1.170072475 1.232963870 1.299235678 1.369069596 1.442657087 1.520199905 1.601910650 1.688013347 1.778744065 1.874351558 1.975097955 2.081259470 2.193127166 2.311007751 2.435224418 2.566117730 2.704046558 2.849389061 3.002543723 3.163930448 3.333991710 3.513193764 3.702027929 3.901011930 4.110691321 4.331640980 4.564466682 4.809806766 5.068333880 5.340756826 5.627822506 5.930317965 6.249072556 6.584960206 6.938901817 7.311867790 7.704880683 8.119018020 8.555415239

7.022137495 7.355689026 7.705084255 8.071075757 8.454451856 8.856038319 9.276700139 9.717343395 10.178917207 10.662415774 11.168880523 11.699402348 12.255123960 12.837242348 13.447011359 14.085744399 14.754817258 15.455671078 16.189815454

7.382830558 7.742743548 8.120202296 8.516062158 8.931220188 9.366617172 9.823239759 10.302122698 10.804351179 11.331063299 11.883452635 12.462770951 13.070331035 13.707509673 14.375750769 15.076568619 15.811551340 16.582364467 17.390754735

7.761587555 8.149666933 8.557150280 8.985007793 9.434258183 9.905971092 10.401269647 10.921333129 11.467399786 12.040769775 12.642808264 13.274948677 13.938696111 14.635630916 15.367412462 16.135783085 16.942572240 17.789700852 18.679185894

8.159290012 8.577453625 9.017048123 9.479171839 9.964979396 10.475684590 11.012563425 11.576957301 12.170276363 12.794003026 13.449695681 14.138992585 14.863615955 15.625376273 16.426176807 17.268018368 18.153004309 19.083345780 20.061367251

8.576861346 9.027146567 9.501071762 9.999878029 10.524871626 11.077427386 11.658992324 12.271089421 12.915321616 13.593376000 14.307028240 15.058147223 15.848699952 16.680756700 17.556496426 18.478212489 19.448318645 20.469355373 21.543996530

9.015268808 9.499839506 10.010455879 10.548517883 11.115500719 11.712958883 12.342530423 13.005941433 13.705010785 14.441655115 15.217894077 16.035855884 16.897783138 17.806038981 18.763113576 19.771630931 20.834356094 21.954202734 23.134241131

0.0550000 5.500% 1.055000000 1.113025000 1.174241375 1.238824651 1.306960006 1.378842807 1.454679161 1.534686515 1.619094273 1.708144458 1.802092404 1.901207486 2.005773897 2.116091462 2.232476492 2.355262699 2.484802148 2.621466266 2.765646911 2.917757491 3.078234153 3.247537031 3.426151568 3.614589904 3.813392349 4.023128928 4.244401019 4.477843075 4.724124444 4.983951288 5.258068609 5.547262383 5.852361814 6.174241714 6.513825008 6.872085383 7.250050079 7.648802834 8.069486990 8.513308774 8.981540757

0.0562500 5.625% 1.056250000 1.115664063 1.178420166 1.244706300 1.314721030 1.388674088 1.466787005 1.549293774 1.636441549 1.728491386 1.825719027 1.928415722 2.036889106 2.151464118 2.272483975 2.400311199 2.535328704 2.677940943 2.828575121 2.987682472 3.155739611 3.333249964 3.520745274 3.718787196 3.927968976 4.148917231 4.382293825 4.628797853 4.889167732 5.164183417 5.454668734 5.761493850 6.085577879 6.427891635 6.789460539 7.171367695 7.574757127 8.000837216 8.450884309 8.926246552 9.428347920

0.0575000 5.750% 1.057500000 1.118306250 1.182608859 1.250608869 1.322518879 1.398563714 1.478981128 1.564022543 1.653953839 1.749056185 1.849626915 1.955980463 2.068449339 2.187385177 2.313159824 2.446166514 2.586821089 2.735563301 2.892858191 3.059197537 3.235101395 3.421119726 3.617834110 3.825859571 4.045846497 4.278482670 4.524495424 4.784653910 5.059771510 5.350708372 5.658374104 5.983730614 6.327795125 6.691643344 7.076412837 7.483306575 7.913596703 8.368628513 8.849824653 9.358689570 9.896814221

0.0587500 5.875% 1.058750000 1.120951563 1.186807467 1.256532405 1.330353684 1.408511963 1.491262041 1.578873686 1.671632515 1.769840925 1.873819080 1.983905951 2.100460425 2.223862475 2.354514396 2.492842116 2.639296591 2.794355265 2.958523637 3.132336901 3.316361694 3.511197943 3.717480823 3.935882821 4.167115937 4.411933998 4.671135120 4.945564309 5.236116212 5.543738039 5.869432649 6.214261817 6.579349699 6.965886494 7.375132325 7.808421349 8.267166103 8.752862112 9.267092761 9.811534461 10.387962110

0.0600000 6.000% 1.060000000 1.123600000 1.191016000 1.262476960 1.338225578 1.418519112 1.503630259 1.593848075 1.689478959 1.790847697 1.898298558 2.012196472 2.132928260 2.260903956 2.396558193 2.540351685 2.692772786 2.854339153 3.025599502 3.207135472 3.399563601 3.603537417 3.819749662 4.048934641 4.291870720 4.549382963 4.822345941 5.111686697 5.418387899 5.743491173 6.088100643 6.453386682 6.840589883 7.251025276 7.686086792 8.147252000 8.636087120 9.154252347 9.703507488 10.285717937 10.902861013

9.475525498 9.996679401 10.546496768 11.126554090 11.738514565 12.384132866 13.065260173 13.783849483 14.541961205 15.341769071 16.185566370 17.075772520 18.014940009 19.005761709 20.051078603 21.153887926 22.317351762 23.544806109 24.839770445

9.958692491 10.518868943 11.110555321 11.735524058 12.395647287 13.092902446 13.829378209 14.607280733 15.428940274 16.296818165 17.213514187 18.181774360 19.204499167 20.284752246 21.425769559 22.630969097 23.903961109 25.248558921 26.668790361

10.465881038 11.067669198 11.704060177 12.377043637 13.088723646 13.841325256 14.637201458 15.478840542 16.368873873 17.310084121 18.305413958 19.357975261 20.471058838 21.648144721 22.892913043 24.209255543 25.601287736 27.073361781 28.630080084

10.998254884 11.644402359 12.328510997 13.052811018 13.819663666 14.631568906 15.491173579 16.401280027 17.364855229 18.385040473 19.465161601 20.608739845 21.819503311 23.101399131 24.458606330 25.895549452 27.416912982 29.027656620 30.733031446

11.557032674 12.250454635 12.985481913 13.764610827 14.590487477 15.465916726 16.393871729 17.377504033 18.420154275 19.525363531 20.696885343 21.938698464 23.255020372 24.650321594 26.129340890 27.697101343 29.358927424 31.120463069 32.987690853

Tabla para Calcular Valor Presente con Interés Compuesto. M=

0.9950249 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

=1/(1+i/p)n 0.006667 0.667% 0.993377483 0.986798825 0.980263733 0.973771920 0.967323100 0.960916986 0.954553298 0.948231753 0.941952072 0.935713979 0.929517198 0.923361455 0.917246478 0.911171998 0.905137747 0.899143457 0.893188864 0.887273706 0.881397722 0.875560651 0.869762236 0.864002221 0.858280352 0.852596376 0.846950042 0.841341102 0.835769306 0.830234410 0.824736169 0.819274340 0.813848682 0.808458956 0.803104923 0.797786347 0.792502994 0.787254630 0.782041023 0.776861943 0.771717162 0.766606453 0.761529589

i/p = 0.007500 0.750% 0.992555831 0.985167078 0.977833328 0.970554172 0.963329203 0.956158018 0.949040216 0.941975401 0.934963177 0.928003153 0.921094941 0.914238155 0.907432412 0.900677332 0.893972538 0.887317655 0.880712313 0.874156142 0.867648776 0.861189852 0.854779010 0.848415891 0.842100139 0.835831404 0.829609334 0.823433582 0.817303804 0.811219656 0.805180800 0.799186898 0.793237616 0.787332622 0.781471585 0.775654178 0.769880078 0.764148961 0.758460507 0.752814399 0.747210321 0.741647962 0.736127009

0.500% 0.008750 0.875% 0.991325898 0.982727037 0.974202763 0.965752429 0.957375394 0.949071023 0.940838684 0.932677754 0.924587612 0.916567645 0.908617245 0.900735806 0.892922732 0.885177430 0.877499311 0.869887793 0.862342298 0.854862253 0.847447091 0.840096249 0.832809168 0.825585297 0.818424086 0.811324993 0.804287477 0.797311006 0.790395049 0.783539082 0.776742585 0.770005040 0.763325939 0.756704772 0.750141038 0.743634238 0.737183879 0.730789471 0.724450529 0.718166572 0.711937122 0.705761707 0.699639858

np = 0.010000 1.000% 0.990099010 0.980296049 0.970590148 0.960980344 0.951465688 0.942045235 0.932718055 0.923483222 0.914339824 0.905286955 0.896323718 0.887449225 0.878662599 0.869962970 0.861349475 0.852821262 0.844377487 0.836017314 0.827739915 0.819544470 0.811430169 0.803396207 0.795441789 0.787566127 0.779768443 0.772047963 0.764403924 0.756835568 0.749342147 0.741922918 0.734577146 0.727304105 0.720103075 0.712973341 0.705914199 0.698924950 0.692004901 0.685153367 0.678369670 0.671653139 0.665003108

1 0.0112500 1.125% 0.988875155 0.977874071 0.966995373 0.956237699 0.945599702 0.935080052 0.924677431 0.914390537 0.904218084 0.894158797 0.884211419 0.874374703 0.864647420 0.855028351 0.845516293 0.836110055 0.826808459 0.817610343 0.808514554 0.799519955 0.790625419 0.781829833 0.773132097 0.764531122 0.756025831 0.747615161 0.739298058 0.731073481 0.722940402 0.714897801 0.706944674 0.699080023 0.691302866 0.683612229 0.676007148 0.668486673 0.661049862 0.653695785 0.646423520 0.639232158 0.632120799

M= 0.0125000 1.250% 0.987654321 0.975461058 0.963418329 0.951524275 0.939777062 0.928174876 0.916715927 0.905398446 0.894220688 0.883180926 0.872277458 0.861508600 0.850872692 0.840368091 0.829993176 0.819746347 0.809626021 0.799630638 0.789758655 0.780008548 0.770378813 0.760867964 0.751474532 0.742197069 0.733034142 0.723984338 0.715046259 0.706218528 0.697499781 0.688888672 0.680383874 0.671984073 0.663687973 0.655494294 0.647401772 0.639409158 0.631515218 0.623718733 0.616018502 0.608413335 0.600902060

42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0.756486346 0.751476503 0.746499838 0.741556130 0.736645162 0.731766717 0.726920580 0.722106537 0.717324374 0.712573882 0.707854849 0.703167069 0.698510333 0.693884437 0.689289176 0.684724347 0.680189749 0.675685181 0.671210444

0.730647155 0.725208095 0.719809523 0.714451140 0.709132645 0.703853742 0.698614136 0.693413534 0.688251647 0.683128186 0.678042864 0.672995399 0.667985507 0.663012911 0.658077331 0.653178492 0.648316121 0.643489946 0.638699699

0.693571111 0.687555005 0.681591083 0.675678892 0.669817985 0.664007916 0.658248244 0.652538531 0.646878346 0.641267257 0.635704840 0.630190672 0.624724334 0.619305411 0.613933493 0.608608172 0.603329043 0.598095705 0.592907762

0.658418919 0.651899919 0.645445465 0.639054916 0.632727639 0.626463009 0.620260405 0.614119213 0.608038825 0.602018638 0.596058058 0.590156493 0.584313359 0.578528078 0.572800078 0.567128790 0.561513653 0.555954112 0.550449616

0.625088553 0.618134539 0.611257888 0.604457739 0.597733240 0.591083550 0.584507837 0.578005277 0.571575058 0.565216374 0.558928429 0.552710436 0.546561618 0.540481205 0.534468435 0.528522556 0.522642824 0.516828504 0.511078866

0.593483516 0.586156559 0.578920058 0.571772897 0.564713972 0.557742195 0.550856489 0.544055791 0.537339053 0.530705238 0.524153321 0.517682292 0.511291153 0.504978917 0.498744609 0.492587268 0.486505944 0.480499698 0.474567603

0.995024876 0.0137500 1.375% 0.986436498 0.973056965 0.959858905 0.946839857 0.933997393 0.921329117 0.908832668 0.896505715 0.884345958 0.872351130 0.860518994 0.848847343 0.837334000 0.825976819 0.814773681 0.803722496 0.792821205 0.782067773 0.771460195 0.760996493 0.750674716 0.740492938 0.730449261 0.720541811 0.710768741 0.701128228 0.691618474 0.682237705 0.672984173 0.663856151 0.654851937 0.645969851 0.637208238 0.628565463 0.620039914 0.611630001 0.603334157 0.595150833 0.587078503 0.579115663 0.571260827

0.0150000 1.500% 0.985221675 0.970661749 0.956316994 0.942184230 0.928260325 0.914542193 0.901026791 0.887711124 0.874592240 0.861667232 0.848933233 0.836387422 0.824027017 0.811849277 0.799851505 0.788031039 0.776385260 0.764911587 0.753607474 0.742470418 0.731497949 0.720687634 0.710037078 0.699543920 0.689205832 0.679020524 0.668985738 0.659099249 0.649358866 0.639762430 0.630307813 0.620992919 0.611815684 0.602774073 0.593866081 0.585089735 0.576443089 0.567924226 0.559531257 0.551262322 0.543115588

0.0162500 1.625% 0.984009840 0.968275365 0.952792487 0.937557183 0.922565494 0.907813524 0.893297441 0.879013472 0.864957906 0.851127091 0.837517432 0.824125395 0.810947498 0.797980318 0.785220485 0.772664684 0.760309652 0.748152179 0.736189106 0.724417325 0.712833776 0.701435450 0.690219385 0.679182666 0.668322427 0.657635844 0.647120142 0.636772588 0.626590492 0.616571210 0.606712138 0.597010714 0.587464417 0.578070767 0.568827323 0.559731683 0.550781484 0.541974400 0.533308143 0.524780460 0.516389137

0.0175000 1.750% 0.982800983 0.965897772 0.949285279 0.932958506 0.916912536 0.901142542 0.885643776 0.870411573 0.855441349 0.840728599 0.826268893 0.812057880 0.798091283 0.784364897 0.770874592 0.757616307 0.744586051 0.731779902 0.719194007 0.706824577 0.694667889 0.682720284 0.670978166 0.659438001 0.648096316 0.636949696 0.625994787 0.615228292 0.604646970 0.594247636 0.584027161 0.573982468 0.564110534 0.554408387 0.544873107 0.535501826 0.526291720 0.517240020 0.508344000 0.499600983 0.491008337

0.0187500 1.875% 0.981595092 0.963528925 0.945795263 0.928387989 0.911301093 0.894528680 0.878064962 0.861904258 0.846040989 0.830469682 0.815184964 0.800181560 0.785454292 0.770998078 0.756807930 0.742878949 0.729206331 0.715785355 0.702611392 0.689679894 0.676986399 0.664526526 0.652295977 0.640290529 0.628506041 0.616938445 0.605583750 0.594438037 0.583497459 0.572758242 0.562216679 0.551869133 0.541712033 0.531741872 0.521955212 0.512348675 0.502918944 0.493662768 0.484576950 0.475658356 0.466903907

0.0200000 2.000% 0.980392157 0.961168781 0.942322335 0.923845426 0.905730810 0.887971382 0.870560179 0.853490371 0.836755266 0.820348300 0.804263039 0.788493176 0.773032525 0.757875025 0.743014730 0.728445814 0.714162562 0.700159375 0.686430760 0.672971333 0.659775817 0.646839036 0.634155918 0.621721488 0.609530871 0.597579285 0.585862044 0.574374553 0.563112307 0.552070889 0.541245970 0.530633304 0.520228729 0.510028166 0.500027613 0.490223150 0.480610932 0.471187188 0.461948223 0.452890415 0.444010211

0.0212500 2.125% 0.979192166 0.958817299 0.938866388 0.919330613 0.900201334 0.881470095 0.863128612 0.845168775 0.827582644 0.810362442 0.793500555 0.776989528 0.760822059 0.744991000 0.729489352 0.714310259 0.699447010 0.684893033 0.670641893 0.656687288 0.643023048 0.629643131 0.616541622 0.603712726 0.591150773 0.578850206 0.566805587 0.555011591 0.543463002 0.532154714 0.521081727 0.510239146 0.499622174 0.489226119 0.479046384 0.469078466 0.459317960 0.449760548 0.440402005 0.431238194 0.422265061

0.563512529 0.555869326 0.548329792 0.540892519 0.533556123 0.526319233 0.519180501 0.512138596 0.505192203 0.498340027 0.491580792 0.484913235 0.478336113 0.471848200 0.465448286 0.459135178 0.452907697 0.446764682 0.440704989

0.535089249 0.527181526 0.519390666 0.511714942 0.504152653 0.496702121 0.489361695 0.482129749 0.475004679 0.467984905 0.461068872 0.454255047 0.447541918 0.440927998 0.434411820 0.427991941 0.421666937 0.415435406 0.409295967

0.508131992 0.500006880 0.492011690 0.484144344 0.476402799 0.468785042 0.461289094 0.453913008 0.446654866 0.439512783 0.432484904 0.425569401 0.418764478 0.412068367 0.405479328 0.398995649 0.392615645 0.386337658 0.380160057

0.482563476 0.474263859 0.466106986 0.458090404 0.450211700 0.442468501 0.434858477 0.427379339 0.420028834 0.412804751 0.405704915 0.398727189 0.391869474 0.385129704 0.378505851 0.371995923 0.365597958 0.359310033 0.353130253

0.458310584 0.449875420 0.441595504 0.433467979 0.425490041 0.417658936 0.409971962 0.402426466 0.395019843 0.387749540 0.380613045 0.373607897 0.366731678 0.359982015 0.353356579 0.346853084 0.340469285 0.334202979 0.328052004

0.435304128 0.426768753 0.418400739 0.410196803 0.402153728 0.394268361 0.386537609 0.378958440 0.371527882 0.364243022 0.357101002 0.350099021 0.343234335 0.336504250 0.329906127 0.323437379 0.317095470 0.310877912 0.304782266

0.413478640 0.404875045 0.396450473 0.388201197 0.380123572 0.372214024 0.364469056 0.356885245 0.349459236 0.342187746 0.335067561 0.328095531 0.321268573 0.314583670 0.308037866 0.301628265 0.295352034 0.289206398 0.283188640

0.0225000 2.250% 0.977995110 0.956474435 0.935427321 0.914843345 0.894712318 0.875024272 0.855769459 0.836938346 0.818521610 0.800510132 0.782894995 0.765667477 0.748819048 0.732341367 0.716226276 0.700465796 0.685052123 0.669977626 0.655234842 0.640816472 0.626715376 0.612924573 0.599437235 0.586246685 0.573346391 0.560729967 0.548391165 0.536323878 0.524522130 0.512980078 0.501692008 0.490652331 0.479855580 0.469296411 0.458969595 0.448870020 0.438992684 0.429332699 0.419885280 0.410645750 0.401609536

0.0237500 2.375% 0.976800977 0.954140148 0.932005029 0.910383423 0.889263416 0.868633374 0.848481928 0.828797976 0.809570673 0.790789424 0.772443882 0.754523938 0.737019720 0.719921582 0.703220105 0.686906085 0.670970535 0.655404674 0.640199926 0.625347913 0.610840452 0.596669550 0.582827399 0.569306373 0.556099021 0.543198067 0.530596403 0.518287084 0.506263330 0.494518516 0.483046169 0.471839970 0.460893743 0.450201459 0.439757225 0.429555287 0.419590024 0.409855945 0.400347687 0.391060012 0.381987802

0.0250000 2.500% 0.975609756 0.951814396 0.928599411 0.905950645 0.883854288 0.862296866 0.841265235 0.820746571 0.800728362 0.781198402 0.762144782 0.743555885 0.725420376 0.707727196 0.690465557 0.673624934 0.657195057 0.641165909 0.625527716 0.610270943 0.595386286 0.580864669 0.566697238 0.552875354 0.539390589 0.526234721 0.513399728 0.500877784 0.488661252 0.476742685 0.465114815 0.453770551 0.442702977 0.431905343 0.421371066 0.411093723 0.401067047 0.391284924 0.381741389 0.372430624 0.363346950

0.0262500 2.625% 0.974421437 0.949497137 0.925210365 0.901544814 0.878484593 0.856014220 0.834118607 0.812783052 0.791993229 0.771735181 0.751995304 0.732760345 0.714017389 0.695753850 0.677957467 0.660616289 0.643718674 0.627253275 0.611209038 0.595575189 0.580341232 0.565496937 0.551032338 0.536937723 0.523203628 0.509820831 0.496780347 0.484073420 0.471691517 0.459626326 0.447869746 0.436413881 0.425251041 0.414373731 0.403774646 0.393446671 0.383382871 0.373576488 0.364020939 0.354709806 0.345636839

0.0275000 2.750% 0.973236010 0.947188331 0.921837791 0.897165734 0.873153999 0.849784914 0.827041278 0.804906354 0.783363848 0.762397906 0.741993095 0.722134399 0.702807201 0.683997276 0.665690780 0.647874238 0.630534538 0.613658918 0.597234957 0.581250566 0.565693982 0.550553754 0.535818738 0.521478091 0.507521256 0.493937962 0.480718211 0.467852274 0.455330680 0.443144214 0.431283907 0.419741029 0.408507084 0.397573804 0.386933143 0.376577268 0.366498558 0.356689594 0.347143157 0.337852221 0.328809947

0.0287500 2.875% 0.972053463 0.944887935 0.918481589 0.892813209 0.867862172 0.843608430 0.820032495 0.797115427 0.774838811 0.753184749 0.732135844 0.711675182 0.691786326 0.672453293 0.653660553 0.635393004 0.617635970 0.600375183 0.583596776 0.567287267 0.551433552 0.536022894 0.521042910 0.506481565 0.492327159 0.478568320 0.465193993 0.452193432 0.439556191 0.427272118 0.415331342 0.403724269 0.392441574 0.381474191 0.370813308 0.360450360 0.350377021 0.340585197 0.331067020 0.321814843 0.312821233

0.0300000 3.000% 0.970873786 0.942595909 0.915141659 0.888487048 0.862608784 0.837484257 0.813091511 0.789409234 0.766416732 0.744093915 0.722421277 0.701379880 0.680951340 0.661117806 0.641861947 0.623166939 0.605016446 0.587394608 0.570286027 0.553675754 0.537549276 0.521892501 0.506691748 0.491933736 0.477605569 0.463694727 0.450189056 0.437076753 0.424346362 0.411986760 0.399987145 0.388337034 0.377026247 0.366044900 0.355383398 0.345032425 0.334982937 0.325226152 0.315753546 0.306556841 0.297628001

0.392772162 0.384129254 0.375676532 0.367409811 0.359324999 0.351418092 0.343685175 0.336122421 0.328726084 0.321492503 0.314418095 0.307499360 0.300732870 0.294115277 0.287643302 0.281313743 0.275123465 0.269069403 0.263148561

0.373126058 0.364469898 0.356014552 0.347755362 0.339687778 0.331807353 0.324109746 0.316590717 0.309246122 0.302071914 0.295064140 0.288218940 0.281532543 0.275001263 0.268621502 0.262389745 0.256302560 0.250356591 0.244548562

0.354484829 0.345838858 0.337403764 0.329174404 0.321145760 0.313312936 0.305671157 0.298215763 0.290942208 0.283846057 0.276922982 0.270168763 0.263579281 0.257150518 0.250878554 0.244759565 0.238789820 0.232965678 0.227283588

0.336795946 0.328181189 0.319786786 0.311607100 0.303636638 0.295870049 0.288302119 0.280927765 0.273742036 0.266740109 0.259917280 0.253268969 0.246790713 0.240478161 0.234327076 0.228333326 0.222492888 0.216801839 0.211256360

0.320009681 0.311444945 0.303109436 0.294997018 0.287101720 0.279417733 0.271939399 0.264661216 0.257577826 0.250684015 0.243974711 0.237444974 0.231089999 0.224905108 0.218885750 0.213027494 0.207326028 0.201777157 0.196376795

0.304078962 0.295581008 0.287320543 0.279290929 0.271485714 0.263898629 0.256523576 0.249354630 0.242386032 0.235612182 0.229027637 0.222627108 0.216405451 0.210357668 0.204478900 0.198764423 0.193209645 0.187810105 0.182561463

0.288959224 0.280542936 0.272371782 0.264438624 0.256736528 0.249258765 0.241998801 0.234950292 0.228107080 0.221463184 0.215012800 0.208750292 0.202670186 0.196767171 0.191036088 0.185471930 0.180069835 0.174825083 0.169733090

0.0312500 3.125% 0.969696970 0.940312213 0.911817904 0.884187058 0.857393511 0.831411889 0.806217590 0.781786754 0.758096246 0.735123632 0.712847159 0.691245730 0.670298889 0.649986802 0.630290232 0.611190528 0.592669603 0.574709918 0.557294466 0.540406755 0.524030793 0.508151072 0.492752554 0.477820659 0.463341245 0.449300601 0.435685431 0.422482842 0.409680332 0.397265777 0.385227420 0.373553861 0.362234048 0.351257258 0.340613099 0.330291490 0.320282657 0.310577122 0.301165694 0.292039461 0.283189780

0.0325000 3.250% 0.968523002 0.938036806 0.908510224 0.879913050 0.852216029 0.825390827 0.799410002 0.774246975 0.749876005 0.726272160 0.703411293 0.681270017 0.659825683 0.639056351 0.618940776 0.599458379 0.580589229 0.562314023 0.544614066 0.527471250 0.510868039 0.494787447 0.479213024 0.464128836 0.449519454 0.435369931 0.421665793 0.408393020 0.395538034 0.383087684 0.371029234 0.359350348 0.348039078 0.337083853 0.326473465 0.316197060 0.306244126 0.296604481 0.287268262 0.278225920 0.269468203

0.0337500 3.375% 0.967351874 0.935769649 0.905218523 0.875664835 0.847076020 0.819420575 0.792668029 0.766788904 0.741754683 0.717537783 0.694111519 0.671450079 0.649528492 0.628322604 0.607809049 0.587965223 0.568769260 0.550200010 0.532237011 0.514860470 0.498051241 0.481790801 0.466061234 0.450845209 0.436125958 0.421887262 0.408113434 0.394789295 0.381900165 0.369431840 0.357370583 0.345703103 0.334416545 0.323498471 0.312936853 0.302720051 0.292836809 0.283276236 0.274027798 0.265081304 0.256426896

0.0350000 3.500% 0.966183575 0.933510700 0.901942706 0.871442228 0.841973167 0.813500644 0.785990961 0.759411556 0.733730972 0.708918814 0.684945714 0.661783298 0.639404153 0.617781790 0.596890619 0.576705912 0.557203779 0.538361140 0.520155690 0.502565884 0.485570903 0.469150631 0.453285634 0.437957134 0.423146989 0.408837671 0.395012242 0.381654340 0.368748155 0.356278411 0.344230348 0.332589709 0.321342714 0.310476052 0.299976862 0.289832717 0.280031610 0.270561942 0.261412505 0.252572468 0.244031370

0.0362500 3.625% 0.965018094 0.931259922 0.898682675 0.867245042 0.836907158 0.807630550 0.779378094 0.752113963 0.725803583 0.700413591 0.675911788 0.652267106 0.629449559 0.607430214 0.586181147 0.565675414 0.545887010 0.526790842 0.508362694 0.490579198 0.473417803 0.456856746 0.440875026 0.425452377 0.410569242 0.396206748 0.382346680 0.368971465 0.356064140 0.343608338 0.331588263 0.319988674 0.308794860 0.297992627 0.287568277 0.277508591 0.267800811 0.258432629 0.249392163 0.240667949 0.232248926

0.0375000 3.750% 0.963855422 0.929017274 0.895438336 0.863073095 0.831877682 0.801809814 0.772828737 0.744895168 0.717971246 0.692020478 0.667007690 0.642898978 0.619661666 0.597264256 0.575676391 0.554868811 0.534813312 0.515482710 0.496850805 0.478892342 0.461582980 0.444899258 0.428818562 0.413319096 0.398379852 0.383980580 0.370101764 0.356724591 0.343830932 0.331403307 0.319424875 0.307879397 0.296751226 0.286025278 0.275687015 0.265722424 0.256117999 0.246860722 0.237938046 0.229337875 0.221048554

0.0387500 3.875% 0.962695548 0.926782717 0.892209595 0.858926205 0.826884433 0.796037962 0.766342202 0.737754226 0.710232708 0.683737866 0.658231399 0.633676437 0.610037485 0.587280370 0.565372198 0.544281297 0.523977182 0.504430500 0.485612996 0.467497469 0.450057732 0.433268575 0.417105728 0.401545827 0.386566380 0.372145733 0.358263040 0.344898233 0.332031994 0.319645722 0.307721513 0.296242131 0.285190980 0.274552087 0.264310072 0.254450129 0.244958006 0.235819982 0.227022847 0.218553884 0.210400851

0.274608272 0.266286809 0.258217512 0.250392738 0.242805080 0.235447350 0.228312582 0.221394019 0.214685109 0.208179500 0.201871030 0.195753726 0.189821795 0.184069619 0.178491752 0.173082911 0.167837974 0.162751975 0.157820097

0.260986153 0.252771093 0.244814618 0.237108589 0.229645122 0.222416583 0.215415577 0.208634941 0.202067740 0.195707254 0.189546977 0.183580607 0.177802041 0.172205367 0.166784859 0.161534972 0.156450336 0.151525749 0.146756174

0.248055038 0.239956506 0.232122376 0.224544015 0.217213074 0.210121474 0.203261402 0.196625298 0.190205851 0.183995986 0.177988862 0.172177859 0.166556575 0.161118815 0.155858588 0.150770097 0.145847736 0.141086081 0.136479885

0.235779102 0.227805895 0.220102314 0.212659241 0.205467866 0.198519677 0.191806451 0.185320243 0.179053375 0.172998429 0.167148241 0.161495885 0.156034672 0.150758137 0.145660036 0.140734334 0.135975202 0.131377007 0.126934306

0.224124416 0.216284117 0.208718086 0.201416730 0.194370788 0.187571328 0.181009725 0.174677660 0.168567103 0.162670304 0.156979787 0.151488335 0.146188984 0.141075015 0.136139942 0.131377507 0.126781672 0.122346607 0.118066690

0.213058848 0.205357925 0.197935350 0.190781060 0.183885359 0.177238900 0.170832675 0.164658000 0.158706506 0.152970126 0.147441086 0.142111890 0.136975315 0.132024400 0.127252434 0.122652949 0.118219709 0.113946708 0.109828152

0.202551962 0.194995872 0.187721658 0.180718804 0.173977188 0.167487064 0.161239051 0.155224117 0.149433566 0.143859029 0.138492446 0.133326061 0.128352406 0.123564290 0.118954791 0.114517248 0.110245245 0.106132606 0.102173388

0.0400000 4.000% 0.961538462 0.924556213 0.888996359 0.854804191 0.821927107 0.790314526 0.759917813 0.730690205 0.702586736 0.675564169 0.649580932 0.624597050 0.600574086 0.577475083 0.555264503 0.533908176 0.513373246 0.493628121 0.474642424 0.456386946 0.438833602 0.421955387 0.405726333 0.390121474 0.375116802 0.360689233 0.346816570 0.333477471 0.320651415 0.308318668 0.296460258 0.285057940 0.274094173 0.263552090 0.253415471 0.243668722 0.234296848 0.225285431 0.216620606 0.208289045 0.200277928

0.0412500 4.125% 0.960384154 0.922337723 0.885798533 0.850706875 0.817005402 0.784639041 0.753554902 0.723702186 0.695032112 0.667497826 0.641054335 0.615658425 0.591268596 0.567844990 0.545349330 0.523744855 0.502996259 0.483069636 0.463932424 0.445553348 0.427902375 0.410950661 0.394670502 0.379035296 0.364019492 0.349598552 0.335748910 0.322447932 0.309673885 0.297405892 0.285623905 0.274308673 0.263441702 0.253005236 0.242982220 0.233356274 0.224111667 0.215233294 0.206706645 0.198517786 0.190653336

0.0425000 4.250% 0.959232614 0.920127208 0.882616026 0.846634078 0.812119020 0.779011050 0.747252806 0.716789262 0.687567638 0.659537302 0.632649690 0.606858216 0.582118193 0.558386756 0.535622787 0.513786847 0.492841100 0.472749256 0.453476505 0.434989453 0.417256070 0.400245631 0.383928663 0.368276895 0.353263208 0.338861591 0.325047089 0.311795769 0.299084671 0.286891770 0.275195943 0.263976924 0.253215274 0.242892350 0.232990263 0.223491859 0.214380680 0.205640941 0.197257497 0.189215824 0.181501990

0.0437500 4.375% 0.958083832 0.917924630 0.879448747 0.842585626 0.807267666 0.773430099 0.741010873 0.709950537 0.680192131 0.651681084 0.624365110 0.598194118 0.573120113 0.549097114 0.526081067 0.504029765 0.482902769 0.462661336 0.443268345 0.424688235 0.406886932 0.389831791 0.373491536 0.357836202 0.342837080 0.328466664 0.314698600 0.301507641 0.288869596 0.276761289 0.265160517 0.254046004 0.243397369 0.233195084 0.223420440 0.214055511 0.205083125 0.196486826 0.188250851 0.180360097 0.172800093

0.0450000 4.500% 0.956937799 0.915729951 0.876296604 0.838561344 0.802451047 0.767895738 0.734828458 0.703185127 0.672904428 0.643927682 0.616198739 0.589663865 0.564271641 0.539972862 0.516720442 0.494469323 0.473176385 0.452800369 0.433301788 0.414642860 0.396787426 0.379700886 0.363350130 0.347703474 0.332730597 0.318402485 0.304691373 0.291570692 0.279015016 0.267000016 0.255502407 0.244499911 0.233971207 0.223895892 0.214254442 0.205028174 0.196199210 0.187750440 0.179665493 0.171928701 0.164525073

0.0462500 4.625% 0.955794504 0.913543134 0.873159507 0.834561058 0.797668873 0.762407525 0.728704922 0.696492160 0.665703378 0.636275631 0.608148751 0.581265234 0.555570116 0.531010863 0.507537265 0.485101328 0.463657184 0.443160988 0.423570837 0.404846678 0.386950230 0.369844903 0.353495726 0.337869272 0.322933593 0.308658154 0.295013767 0.281972537 0.269507801 0.257594075 0.246207001 0.235323299 0.224920716 0.214977984 0.205474776 0.196391661 0.187710071 0.179412254 0.171481246 0.163900833 0.156655515

0.0475000 4.750% 0.954653938 0.911364141 0.870037366 0.830584598 0.792920857 0.756965019 0.722639636 0.689870774 0.658587851 0.628723486 0.600213352 0.572996040 0.547012926 0.522208044 0.498527965 0.475921685 0.454340511 0.433737958 0.414069650 0.395293222 0.377368231 0.360256067 0.343919873 0.328324462 0.313436240 0.299223141 0.285654550 0.272701241 0.260335313 0.248530132 0.237260269 0.226501451 0.216230502 0.206425300 0.197064725 0.188128616 0.179597724 0.171453675 0.163678926 0.156256731 0.149171104

0.192574930 0.185168202 0.178046348 0.171198412 0.164613858 0.158282555 0.152194765 0.146341120 0.140712615 0.135300592 0.130096723 0.125093003 0.120281733 0.115655513 0.111207224 0.106930023 0.102817330 0.098862817 0.095060401

0.183100443 0.175846764 0.168880445 0.162190104 0.155764805 0.149594051 0.143667756 0.137976236 0.132510191 0.127260687 0.122219148 0.117377333 0.112727330 0.108261542 0.103972669 0.099853704 0.095897915 0.092098838 0.088450264

0.174102628 0.167004919 0.160196565 0.153665770 0.147401218 0.141392056 0.135627871 0.130098677 0.124794894 0.119707333 0.114827178 0.110145974 0.105655610 0.101348307 0.097216602 0.093253335 0.089451640 0.085804931 0.082306888

0.165556975 0.158617461 0.151968825 0.145598875 0.139495928 0.133648793 0.128046748 0.122679519 0.117537264 0.112610552 0.107890349 0.103367999 0.099035209 0.094884032 0.090906857 0.087096390 0.083445643 0.079947922 0.076596811

0.157440261 0.150660537 0.144172763 0.137964366 0.132023317 0.126338102 0.120897706 0.115691584 0.110709650 0.105942249 0.101380142 0.097014490 0.092836833 0.088839074 0.085013468 0.081352601 0.077849379 0.074497014 0.071289008

0.149730480 0.143111570 0.136785252 0.130738592 0.124959228 0.119435344 0.114155645 0.109109338 0.104286106 0.099676087 0.095269856 0.091058405 0.087033123 0.083185780 0.079508512 0.075993798 0.072634455 0.069423613 0.066354708

0.142406782 0.135949195 0.129784434 0.123899221 0.118280879 0.112917307 0.107796952 0.102908785 0.098242277 0.093787376 0.089534488 0.085474452 0.081598522 0.077898350 0.074365967 0.070993763 0.067774475 0.064701170 0.061767227

0.0487500 4.875% 0.953516091 0.909192935 0.866930093 0.826631793 0.788206716 0.751567786 0.716631977 0.683320121 0.651556731 0.621269827 0.592390776 0.564854137 0.538597509 0.513561391 0.489689050 0.466926388 0.445221824 0.424526173 0.404792537 0.385976197 0.368034515 0.350926832 0.334614381 0.319060196 0.304229031 0.290087276 0.276602886 0.263745302 0.251485389 0.239795365 0.228648739 0.218020252 0.207885818 0.198222473 0.189008317 0.180222472 0.171845027 0.163856998 0.156240284 0.148977625 0.142052563

0.0500000 5.000% 0.952380952 0.907029478 0.863837599 0.822702475 0.783526166 0.746215397 0.710681330 0.676839362 0.644608916 0.613913254 0.584679289 0.556837418 0.530321351 0.505067953 0.481017098 0.458111522 0.436296688 0.415520655 0.395733957 0.376889483 0.358942365 0.341849871 0.325571306 0.310067910 0.295302772 0.281240735 0.267848319 0.255093637 0.242946321 0.231377449 0.220359475 0.209866167 0.199872540 0.190354800 0.181290285 0.172657415 0.164435633 0.156605365 0.149147966 0.142045682 0.135281602

0.0512500 5.125% 0.951248514 0.904873735 0.860759795 0.818796476 0.778878931 0.740907425 0.704787087 0.670427669 0.637743324 0.606652389 0.577077183 0.548943813 0.522181986 0.496724838 0.472508764 0.449473259 0.427560770 0.406716547 0.386888511 0.368027121 0.350085252 0.333018075 0.316782949 0.301339309 0.286648570 0.272674026 0.259380762 0.246735565 0.234706839 0.223264532 0.212380054 0.202026211 0.192177133 0.182808212 0.173896040 0.165418349 0.157353959 0.149682720 0.142385465 0.135443962 0.128840867

0.0525000 5.250% 0.950118765 0.902725667 0.857696596 0.814913630 0.774264732 0.735643451 0.698948647 0.664084225 0.630958884 0.599485875 0.569582779 0.541171287 0.514176995 0.488529211 0.464160771 0.441007858 0.419009841 0.398109113 0.378250939 0.359383315 0.341456831 0.324424542 0.308241846 0.292866362 0.278257826 0.264377982 0.251190481 0.238660790 0.226756095 0.215445221 0.204698547 0.194487931 0.184786633 0.175569247 0.166811636 0.158490866 0.150585146 0.143073773 0.135937076 0.129156367 0.122713888

0.0537500 5.375% 0.948991696 0.900585240 0.854647914 0.811053774 0.769683297 0.730423057 0.693165416 0.657808224 0.624254543 0.592412377 0.562194427 0.533517843 0.506304003 0.480478294 0.455969912 0.432711660 0.410639772 0.389693734 0.369816118 0.350952425 0.333050937 0.316062574 0.299940758 0.284641289 0.270122219 0.256343743 0.243268084 0.230859391 0.219083645 0.207908560 0.197303497 0.187239381 0.177688617 0.168625022 0.160023746 0.151861206 0.144115024 0.136763961 0.129787863 0.123167604 0.116885034

0.0550000 5.500% 0.947867299 0.898452416 0.851613664 0.807216743 0.765134354 0.725245833 0.687436809 0.651598871 0.617629261 0.585430579 0.554910502 0.525981518 0.498560681 0.472569366 0.447933048 0.424581088 0.402446529 0.381465904 0.361579056 0.342728963 0.324861577 0.307925665 0.291872668 0.276656558 0.262233704 0.248562753 0.235604505 0.223321805 0.211679436 0.200644016 0.190183901 0.180269101 0.170871185 0.161963209 0.153519629 0.145516236 0.137930082 0.130739414 0.123923615 0.117463142 0.111339471

0.0562500 5.625% 0.946745562 0.896327159 0.848593760 0.803402377 0.760617635 0.720111370 0.681762244 0.645455379 0.611082016 0.578539186 0.547729407 0.518560385 0.490944744 0.464799757 0.440047107 0.416612646 0.394426174 0.373421230 0.353534892 0.334707590 0.316882926 0.300007503 0.284030772 0.268904873 0.254584495 0.241026741 0.228190998 0.216038814 0.204533789 0.193641457 0.183329190 0.173566097 0.164322932 0.155572007 0.147287107 0.139443415 0.132017434 0.124986920 0.118330812 0.112029171 0.106063120

0.135449404 0.129153186 0.123149641 0.117425165 0.111966784 0.106762130 0.101799409 0.097067374 0.092555303 0.088252971 0.084150628 0.080238978 0.076509156 0.072952712 0.069561584 0.066328090 0.063244901 0.060305031 0.057501817

0.128839621 0.122704401 0.116861334 0.111296509 0.105996675 0.100949214 0.096142109 0.091563913 0.087203727 0.083051169 0.079096351 0.075329858 0.071742722 0.068326402 0.065072764 0.061974061 0.059022915 0.056212300 0.053535524

0.122559683 0.116584717 0.110901038 0.105494448 0.100351437 0.095459155 0.090805379 0.086378482 0.082167403 0.078161620 0.074351125 0.070726397 0.067278380 0.063998459 0.060878439 0.057910524 0.055087300 0.052401713 0.049847051

0.116592767 0.110776976 0.105251284 0.100001220 0.095013035 0.090273668 0.085770706 0.081492357 0.077427418 0.073565242 0.069895717 0.066409233 0.063096658 0.059949319 0.056958973 0.054117789 0.051418327 0.048853517 0.046416643

0.110922927 0.105264936 0.099895550 0.094800048 0.089964458 0.085375524 0.081020663 0.076887937 0.072966013 0.069244141 0.065712115 0.062360251 0.059179361 0.056160722 0.053296059 0.050577517 0.047997644 0.045549365 0.043225969

0.105535044 0.100033217 0.094818215 0.089875085 0.085189654 0.080748488 0.076538851 0.072548674 0.068766515 0.065181531 0.061783442 0.058562504 0.055509483 0.052615623 0.049872629 0.047272634 0.044808184 0.042472212 0.040258021

0.100414788 0.095067255 0.090004502 0.085211363 0.080673480 0.076377259 0.072309831 0.068459012 0.064813265 0.061361671 0.058093890 0.055000133 0.052071131 0.049298113 0.046672769 0.044187237 0.041834071 0.039606221 0.037497014

0.0575000 5.750% 0.945626478 0.894209435 0.845588118 0.799610514 0.756132873 0.715019266 0.676141150 0.639376974 0.604611795 0.571736922 0.540649572 0.511252550 0.483453948 0.457166854 0.432309082 0.408802914 0.386574860 0.365555423 0.345678887 0.326883108 0.309109322 0.292301960 0.276408472 0.261379170 0.247167064 0.233727720 0.221019121 0.209001533 0.197637383 0.186891142 0.176729213 0.167119823 0.158032929 0.149440122 0.141314536 0.133630767 0.126364792 0.119493893 0.112996589 0.106852567 0.101042616

0.0587500 5.875% 0.944510035 0.892099207 0.842596654 0.795840995 0.751679807 0.709969121 0.670572959 0.633362890 0.598217605 0.565022532 0.533669451 0.504056152 0.476086094 0.449668094 0.424716027 0.401148550 0.378888831 0.357864303 0.338006426 0.319250461 0.301535264 0.284803083 0.268999370 0.254072605 0.239974125 0.226657969 0.214080726 0.202201395 0.190981246 0.180383704 0.170374218 0.160920159 0.151990705 0.143556746 0.135590788 0.128066860 0.120960434 0.114248344 0.107908707 0.101920857 0.096265272

0.0600000 6.000% 0.943396226 0.889996440 0.839619283 0.792093663 0.747258173 0.704960540 0.665057114 0.627412371 0.591898464 0.558394777 0.526787525 0.496969364 0.468839022 0.442300964 0.417265061 0.393646284 0.371364419 0.350343791 0.330513010 0.311804727 0.294155403 0.277505097 0.261797261 0.246978548 0.232998631 0.219810029 0.207367952 0.195630143 0.184556739 0.174110131 0.164254840 0.154957397 0.146186223 0.137911531 0.130105218 0.122740772 0.115793181 0.109238850 0.103055519 0.097222188 0.091719045

0.095548573 0.090353261 0.085440436 0.080794738 0.076401644 0.072247417 0.068319071 0.064604322 0.061091558 0.057769794 0.054628647 0.051658295 0.048849452 0.046193335 0.043681641 0.041306516 0.039060535 0.036936676 0.034928299

0.090923516 0.085878173 0.081112796 0.076611850 0.072360661 0.068345371 0.064552888 0.060970851 0.057587581 0.054392048 0.051373835 0.048523103 0.045830557 0.043287421 0.040885404 0.038616674 0.036473836 0.034449905 0.032538281

0.086527401 0.081629624 0.077009079 0.072650074 0.068537806 0.064658308 0.060998403 0.057545664 0.054288362 0.051215436 0.048316449 0.045581555 0.043001467 0.040567422 0.038271153 0.036104861 0.034061190 0.032133198 0.030314338

Tabla para Calcular Valor Futuro o Monto de una Anualidad Ordinaria. M=

1.00000000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

(1+i/p)np-1 i/p

0.00666667 0.6667% 1.0000000000 2.0066666667 3.0200444444 4.0401780741 5.0671125946 6.1008933452 7.1415659675 8.1891764073 9.2437709167 10.3053960561 11.3740986965 12.4499260211 13.5329255279 14.6231450315 15.7206326650 16.8254368828 17.9376064620 19.0571905051 20.1842384418 21.3188000314 22.4609253649 23.6106648673 24.7680692998 25.9331897618 27.1060776935 28.2867848782 29.4753634440 30.6718658670 31.8763449728 33.0888539392 34.3094462988 35.5381759408 36.7750971138 38.0202644279 39.2737328574 40.5355577431 41.8057947947 43.0845000933 44.3717300940

I/P

0.00750000 0.7500% 1.0000000000 2.0075000000 3.0225562500 4.0452254219 5.0755646125 6.1136313471 7.1594835822 8.2131797091 9.2747785569 10.3443393961 11.4219219416 12.5075863561 13.6013932538 14.7034037032 15.8136792310 16.9322818252 18.0592739389 19.1947184934 20.3386788821 21.4912189738 22.6524031161 23.8222961394 25.0009633605 26.1884705857 27.3848841151 28.5902707459 29.8046977765 31.0282330099 32.2609447574 33.5029018431 34.7541736069 36.0148299090 37.2849411333 38.5645781918 39.8538125282 41.1527161222 42.4613614931 43.7798217043 45.1081703671

0.005 np=

0.00875000 0.8750% 1.0000000000 2.0087500000 3.0263265625 4.0528069199 5.0882689805 6.1327913341 7.1864532582 8.2493347242 9.3215164031 10.4030796716 11.4941066187 12.5946800516 13.7048835021 14.8248012327 15.9545182435 17.0941202781 18.2436938306 19.4033261516 20.5731052554 21.7531199264 22.9434597258 24.1442149984 25.3554768796 26.5773373023 27.8098890037 29.0532255325 30.3074412559 31.5726313669 32.8488918913 34.1363196954 35.4350124927 36.7450688520 38.0665882045 39.3996708513 40.7444179712 42.1009316285 43.4693147802 44.8496712845 46.2421059083

0.01000000 1.0000% 1.0000000000 2.0100000000 3.0301000000 4.0604010000 5.1010050100 6.1520150601 7.2135352107 8.2856705628 9.3685272684 10.4622125411 11.5668346665 12.6825030132 13.8093280433 14.9474213238 16.0968955370 17.2578644924 18.4304431373 19.6147475687 20.8108950444 22.0190039948 23.2391940347 24.4715859751 25.7163018348 26.9734648532 28.2431995017 29.5256314967 30.8208878117 32.1290966898 33.4503876567 34.7848915333 36.1327404486 37.4940678531 38.8690085316 40.2576986170 41.6602756031 43.0768783592 44.5076471427 45.9527236142 47.4122508503

1

0.01125000 1.1250% 1.0000000000 2.0112500000 3.0338765625 4.0680076738 5.1137727602 6.1713027037 7.2407298591 8.3221880700 9.4158126858 10.5217405785 11.6401101601 12.7710613994 13.9147358401 15.0712766183 16.2408284803 17.4235378007 18.6195526009 19.8290225677 21.0520990716 22.2889351861 23.5396857070 24.8045071712 26.0835578768 27.3769979030 28.6849891294 30.0076952571 31.3452818287 32.6979162493 34.0657678071 35.4490076949 36.8478090315 38.2623468831 39.6927982855 41.1393422662 42.6021598667 44.0814341652 45.5773502996 47.0900954905 48.6198590647

40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

45.6675416279 46.9719919055 48.2851385182 49.6070394416 50.9377530379 52.2773380581 53.6258536452 54.9833593362 56.3499150651 57.7255811655 59.1104183733 60.5044878291 61.9078510813 63.3205700885 64.7427072224 66.1743252706 67.6154874390 69.0662573553 70.5266990710 71.9968770648 73.4768562452

46.4464816449 47.7948302572 49.1532914841 50.5219411703 51.9008557290 53.2901121470 54.6897879881 56.0999613980 57.5207111085 58.9521164418 60.3942573151 61.8472142450 63.3110683518 64.7859013645 66.2717956247 67.7688340919 69.2771003476 70.7966786002 72.3276536897 73.8701110924 75.4241369255

47.6467243350 49.0636331729 50.4929399632 51.9347531879 53.3891822783 54.8563376232 56.3363305774 57.8292734699 59.3352796128 60.8544633094 62.3869398634 63.9328255872 65.4922378111 67.0652948919 68.6521162222 70.2528222392 71.8675344338 73.4963753601 75.1394686445 76.7969389951 78.4689122113

48.8863733588 50.3752370924 51.8789894633 53.3977793580 54.9317571515 56.4810747231 58.0458854703 59.6263443250 61.2226077682 62.8348338459 64.4631821844 66.1078140062 67.7688921463 69.4465810678 71.1410468784 72.8524573472 74.5809819207 76.3267917399 78.0900596573 79.8709602539 81.6696698564

50.1668324792 51.7312093446 53.3131854497 54.9129587860 56.5307295724 58.1667002801 59.8210756582 61.4940627594 63.1858709654 64.8967120138 66.6268000239 68.3763515242 70.1455854788 71.9347233155 73.7439889528 75.5736088285 77.4238119278 79.2948298120 81.1868966474 83.1002492347 85.0351270386

m=

0.01250000 1.2500% 1.0000000000 2.0125000000 3.0376562500 4.0756269531 5.1265722900 6.1906544437 7.2680376242 8.3588880945 9.4633741957 10.5816663731 11.7139372028 12.8603614178 14.0211159356 15.1963798848 16.3863346333 17.5911638162 18.8110533639 20.0461915310 21.2967689251 22.5629785367 23.8450157684 25.1430784655 26.4573669463 27.7880840331 29.1354350836 30.4996280221 31.8808733724 33.2793842895 34.6953765932 36.1290688006 37.5806821606 39.0504406876 40.5385711962 42.0453033361 43.5708696278 45.1155054982 46.6794493169 48.2629424334 49.8662292138

1.0000000

0.01375000 1.3750% 1.0000000000 2.0137500000 3.0414390625 4.0832588496 5.1394036588 6.2100704591 7.2954589279 8.3957714882 9.5112133461 10.6419925296 11.7883199269 12.9504093259 14.1284774542 15.3227440191 16.5334317494 17.7607664360 19.0049769745 20.2662954079 21.5449569697 22.8412001280 24.1552666298 25.4874015460 26.8378533172 28.2068738003 29.5947183151 31.0016456919 32.4279183202 33.8738021971 35.3395669773 36.8254860232 38.3318364561 39.8588992073 41.4069590714 42.9763047587 44.5672289491 46.1800283471 47.8150037369 49.4724600383 51.1527063638

0.01500000 1.5000% 1.0000000000 2.0150000000 3.0452250000 4.0909033750 5.1522669256 6.2295509295 7.3229941935 8.4328391064 9.5593316929 10.7027216683 11.8632624934 13.0412114308 14.2368296022 15.4503820463 16.6821377770 17.9323698436 19.2013553913 20.4893757221 21.7967163580 23.1236671033 24.4705221099 25.8375799415 27.2251436407 28.6335207953 30.0630236072 31.5139689613 32.9866784957 34.4814786732 35.9987008533 37.5386813661 39.1017615865 40.6882880103 42.2986123305 43.9330915155 45.5920878882 47.2759692065 48.9851087446 50.7198853758 52.4806836564

0.01625000 1.6250% 1.0000000000 2.0162500000 3.0490140625 4.0985605410 5.1651621498 6.2490960347 7.3506438453 8.4700918078 9.6077307997 10.7638564252 11.9387690921 13.1327740898 14.3461816688 15.5793071209 16.8324708616 18.1059985131 19.4002209889 20.7154745800 22.0521010419 23.4104476839 24.7908674587 26.1937190549 27.6193669896 29.0681817032 30.5405396558 32.0368234253 33.5574218059 35.1027299103 36.6731492713 38.2690879470 39.8909606261 41.5391887363 43.2142005532 44.9164313122 46.6463233210 48.4043260750 50.1908963737 52.0064984398 53.8516040395

0.01750000 1.7500% 1.0000000000 2.0175000000 3.0528062500 4.1062303594 5.1780893907 6.2687059550 7.3784083092 8.5075304546 9.6564122376 10.8253994517 12.0148439421 13.2251037111 14.4565430261 15.7095325290 16.9844493483 18.2816772119 19.6016065631 20.9446346779 22.3111657848 23.7016111860 25.1163893818 26.5559261960 28.0206549044 29.5110163652 31.0274591516 32.5704396868 34.1404223813 35.7378797730 37.3632926690 39.0171502907 40.6999504208 42.4121995532 44.1544130453 45.9271152736 47.7308397909 49.5661294873 51.4335367533 53.3336236465 55.2669620603

0.01875000 1.8750% 1.0000000000 2.0187500000 3.0566015625 4.1139128418 5.1910487076 6.2883808708 7.4062880122 8.5451559124 9.7053775858 10.8873534155 12.0914912920 13.3182067538 14.5679231304 15.8410716891 17.1380917833 18.4594310042 19.8055453355 21.1768993106 22.5739661726 23.9972280384 25.4471760641 26.9243106153 28.4291414393 29.9621878413 31.5239788633 33.1150534670 34.7359607195 36.3872599830 38.0695211077 39.7833246285 41.5292619653 43.3079356271 45.1199594201 46.9659586593 48.8465703841 50.7624435788 52.7142393959 54.7026313846 56.7283057231

51.4895570790 53.1331765424 54.7973412492 56.4823080148 58.1883368650 59.9156910758 61.6646372143 63.4354451795 65.2283882442 67.0437430973 68.8817898860 70.7428122596 72.6270974128 74.5349361305 76.4666228321 78.4224556175 80.4027363127 82.4077705166 84.4378676481 86.4933409937 88.5745077561

52.8560560763 54.5828268474 56.3333407165 58.1079241514 59.9069081085 61.7306280950 63.5794242313 65.4536413144 67.3536288825 69.2797412797 71.2323377222 73.2117823659 75.2184443735 77.2526979836 79.3149225809 81.4055027664 83.5248284294 85.6732948203 87.8513026241 90.0592580352 92.2975728331

54.2678939113 55.7266926051 57.2341338963 58.7919614554 56.0819123199 57.6322513599 59.2357312395 60.8943107326 57.9231410047 59.5687754445 61.2723565362 63.0360790589 59.7919881198 61.5367680455 63.3446227756 65.2180055412 61.6888679416 63.5367405262 65.4531536742 67.4408431451 63.6142009607 65.5692125598 67.5985838635 69.7053589541 65.5684139751 67.6347122639 69.7815590811 72.0123344345 67.5519401848 69.7337763382 72.0027363650 74.3625657051 69.5652192875 71.8669502037 74.2627842514 76.7568638121 71.6086975768 74.0347881445 76.5623829758 79.1960550086 73.6828280405 76.2378534518 78.9022246779 81.6809810400 75.7880704611 78.4767185704 81.2830136097 84.2124994345 77.9248915180 80.7519652472 83.7054663479 86.7914837989 80.0937648908 83.0641846825 86.1703120090 89.4188241201 82.2951713642 85.4139776835 88.6782924692 92.0954270724 84.5295989346 87.8019548209 91.2301625874 94.8222163300 86.7975429186 90.2287365867 93.8266904326 97.6001328862 89.0995060624 92.6949535563 96.4686575152 100.4301353778 91.4359986534 95.2012465516 99.1568590217 103.3132004161 93.8075386332 97.7482668080 101.8921040546 106.2503229239 96.2146517126 100.3366761437 104.6752158756 109.2425164788

0.02000000 2.0000% 1.0000000000 2.0200000000 3.0604000000 4.1216080000 5.2040401600 6.3081209632 7.4342833825 8.5829690501 9.7546284311 10.9497209997 12.1687154197 13.4120897281 14.6803315227 15.9739381531 17.2934169162 18.6392852545 20.0120709596 21.4123123788 22.8405586264 24.2973697989 25.7833171949 27.2989835388 28.8449632096 30.4218624738 32.0302997232 33.6709057177 35.3443238321 37.0512103087 38.7922345149 40.5680792052 42.3794407893 44.2270296051 46.1115701972 48.0338016011 49.9944776331 51.9943671858 54.0342545295 56.1149396201 58.2372384125

0.02125000 2.1250% 1.0000000000 2.0212500000 3.0642015625 4.1293158457 5.2170638074 6.3279264133 7.4623948496 8.6209707402 9.8041663684 11.0125049037 12.2465206329 13.5067591964 14.7937778293 16.1081456082 17.4504437024 18.8212656310 20.2212175257 21.6509183981 23.1110004141 24.6021091729 26.1249039928 27.6800582026 29.2682594394 30.8902099525 32.5466269140 34.2382427359 35.9658053941 37.7300787587 39.5318429323 41.3718945946 43.2510473548 45.1701321111 47.1299974184 49.1315098636 51.1755544482 53.2630349802 55.3948744735 57.5720155561 59.7954208866

0.02250000 2.2500% 1.0000000000 2.0225000000 3.0680062500 4.1370363906 5.2301197094 6.3477974029 7.4906228444 8.6591618584 9.8539930003 11.0757078428 12.3249112692 13.6022217728 14.9082717627 16.2437078773 17.6091913046 19.0053981089 20.4330195664 21.8927625066 23.3853496630 24.9115200304 26.4720292311 28.0676498888 29.6991720113 31.3674033816 33.0731699577 34.8173162817 36.6007058980 38.4242217807 40.2887667708 42.1952640232 44.1446574637 46.1379122566 48.1760152824 50.2599756262 52.3908250778 54.5696186421 56.7974350615 59.0753773504 61.4045733408

0.02375000 2.3750% 1.0000000000 2.0237500000 3.0718140625 4.1447696465 5.2432079256 6.3677341138 7.5189677990 8.6975432843 9.9041099373 11.1393325483 12.4038916963 13.6984841241 15.0238231220 16.3806389212 17.7696790955 19.1917089741 20.6475120622 22.1378904737 23.6636653724 25.2256774250 26.8247872639 28.4618759614 30.1378455155 31.8536193465 33.6101428059 35.4083836976 37.2493328104 39.1340044646 41.0634370707 43.0386937011 45.0608626765 47.1310581651 49.2504207965 51.4201182904 53.6413460998 55.9153280697 58.2433171113 60.6265958927 63.0664775452

0.02500000 2.5000% 1.0000000000 2.0250000000 3.0756250000 4.1525156250 5.2563285156 6.3877367285 7.5474301467 8.7361159004 9.9545187979 11.2033817679 12.4834663121 13.7955529699 15.1404417941 16.5189528390 17.9319266599 19.3802248264 20.8647304471 22.3863487083 23.9460074260 25.5446576116 27.1832740519 28.8628559032 30.5844273008 32.3490379833 34.1577639329 36.0117080312 37.9120007320 39.8598007503 41.8562957690 43.9027031633 46.0002707424 48.1502775109 50.3540344487 52.6128853099 54.9282074426 57.3014126287 59.7339479444 62.2272966430 64.7829790591

0.02625000 2.6250% 1.0000000000 2.0262500000 3.0794390625 4.1602743379 5.2694815393 6.4078054297 7.5760103222 8.7748805932 10.0052212087 11.2678582655 12.5636395449 13.8934350830 15.2581377539 16.6586638699 18.0959537965 19.5709725837 21.0847106140 22.6381842676 24.2324366047 25.8685380655 27.5475871897 29.2707113535 31.0390675265 32.8538430491 34.7162564291 36.6275581604 38.5890315621 40.6019936406 42.6677959737 44.7878256180 46.9635060404 49.1962980740 51.4877008984 53.8392530470 56.2525334395 58.7291624423 61.2708029564 63.8791615340 66.5559895243

60.4019831807 62.6100228444 64.8622233012 67.1594677673 69.5026571226 71.8927102651 74.3305644704 76.8171757598 79.3535192750 81.9405896605 84.5794014537 87.2709894828 90.0164092724 92.8167374579 95.6730722070 98.5865336512 101.5582643242 104.5894296107 107.6812182029 110.8348425669 114.0515394183

62.0660735805 64.3849776441 66.7531584190 69.1716630354 71.6415608749 74.1639440435 76.7399278544 79.3706513213 82.0572776619 84.8009948122 87.6030159520 90.4645800410 93.3869523668 96.3714251046 99.4193178881 102.5319783932 105.7107829341 108.9571370714 112.2724762342 115.6582663542 119.1160045142

63.7861762410 66.2213652064 68.7113459235 71.2573512068 73.8606416090 76.5225060452 79.2442624312 82.0272583359 84.8728716484 87.7825112605 90.7576177639 93.7996641636 96.9101566073 100.0906351309 103.3426744214 106.6678845958 110.0679119993 113.5444400192 117.0991899197 120.7339216929 124.4504349310

65.5643063869 68.1214586636 70.7393433068 73.4194027104 76.1631135247 78.9719874709 81.8475721734 84.7914520125 87.8052489978 90.8906236615 94.0492759734 97.2829462778 100.5934162519 103.9825098879 107.4520944977 111.0040817421 114.6404286834 118.3631388647 122.1742634127 126.0759021687 130.0702048453

67.4025535356 70.0876173740 72.8398078083 75.6608030035 78.5523230786 81.5161311556 84.5540344345 87.6678852954 90.8595824277 94.1310719884 97.4843487881 100.9214575078 104.4444939455 108.0556062942 111.7569964515 115.5509213628 119.4396943969 123.4256867568 127.5113289257 131.6991121489 135.9915899526

69.3030842493 72.1222902108 75.0155003289 77.9846572125 81.0317544643 84.1588380190 87.3680075170 90.6614177143 94.0412799293 97.5098635275 101.0694974451 104.7225717530 108.4715392615 112.3189171672 116.2672887428 120.3193050723 124.4776868304 128.7452261097 133.1247882951 137.6193139879 142.2318209800

0.02750000 2.7500% 1.0000000000 2.0275000000 3.0832562500 4.1680457969 5.2826670563 6.4279404003 7.6047087613 8.8138382523 10.0562188042 11.3327648213 12.6444158539 13.9921372899 15.3769210654 16.7997863947 18.2617805205 19.7639794848 21.3074889207 22.8934448660 24.5230145998 26.1973975013 27.9178259326 29.6855661457 31.5019192147 33.3682219932 35.2858480980 37.2562089207 39.2807546660 41.3609754193 43.4984022433 45.6946083050 47.9512100334 50.2698683093 52.6522896878 55.1002276542 57.6154839147 60.1999097224 62.8554072398 65.5839309388 68.3874890397

0.02875000 2.8750% 1.0000000000 2.0287500000 3.0870765625 4.1758300137 5.2958851266 6.4481418240 7.6335259014 8.8529897711 10.1075132270 11.3981042323 12.7257997289 14.0916664711 15.4968018822 16.9423349363 18.4294270657 19.9592730939 21.5331021953 23.1521788834 24.8178040263 26.5313158921 28.2940912240 30.1075463467 31.9731383041 33.8923660304 35.8667715537 37.8979412359 39.9875070464 42.1371478740 44.3485908754 46.6236128631 48.9640417329 51.3717579327 53.8486959733 56.3968459825 59.0182553045 61.7150301445 64.4893372612 67.3434057074 70.2795286215

0.03000000 3.0000% 1.0000000000 2.0300000000 3.0909000000 4.1836270000 5.3091358100 6.4684098843 7.6624621808 8.8923360463 10.1591061276 11.4638793115 12.8077956908 14.1920295615 15.6177904484 17.0863241618 18.5989138867 20.1568813033 21.7615877424 23.4144353747 25.1168684359 26.8703744890 28.6764857236 30.5367802954 32.4528837042 34.4264702153 36.4592643218 38.5530422515 40.7096335190 42.9309225246 45.2188502003 47.5754157063 50.0026781775 52.5027585228 55.0778412785 57.7301765169 60.4620818124 63.2759442668 66.1742225948 69.1594492726 72.2342327508

0.03125000 3.1250% 1.0000000000 2.0312500000 3.0947265625 4.1914367676 5.3224191666 6.4887447655 7.6915180394 8.9318779782 10.2109991650 11.5300928889 12.8904082917 14.2932335508 15.7398970993 17.2317688836 18.7702616612 20.3568323381 21.9929833487 23.6802640783 25.4202723308 27.2146558411 29.0651138362 30.9733986435 32.9413173512 34.9707335184 37.0635689408 39.2218054702 41.4474868912 43.7427208565 46.1096808833 48.5506084109 51.0678149237 53.6636841401 56.3406742695 59.1013203404 61.9482366010 64.8841189948 67.9117477134 71.0339898295 74.2538020116

0.03250000 3.2500% 1.0000000000 2.0325000000 3.0985562500 4.1992593281 5.3357352563 6.5091466521 7.7206939183 8.9716164707 10.2631940060 11.5967478111 12.9736421150 14.3952854837 15.8631322620 17.3786840605 18.9434912924 20.5591547595 22.2273272891 23.9497154260 25.7280811774 27.5642438156 29.4600817397 31.4175343962 33.4386042641 35.5253589026 37.6799330670 39.9045308917 42.2014281456 44.5729745604 47.0215962336 49.5497981112 52.1601665498 54.8553719627 57.6381715514 60.5114121269 63.4780330210 66.5410690942 69.7036538397 72.9690225895 76.3405158237

0.03375000 3.3750% 1.0000000000 2.0337500000 3.1023890625 4.2070946934 5.3490841393 6.5296157290 7.7499902598 9.0115524311 10.3156923256 11.6638469416 13.0575017759 14.4981924608 15.9875064564 17.5270847993 19.1186239113 20.7638774683 22.4646583328 24.2228405516 26.0403614202 27.9192236181 29.8614974152 31.8693229530 33.9449126026 36.0905534030 38.3086095803 40.6015251537 42.9718266276 45.4221257763 47.9551225212 50.5736079063 53.2804671732 56.0786829403 58.9713384895 61.9616211635 65.0528258778 68.2483587512 71.5517408590 74.9666121130 78.4967352718

71.2681449883 74.2280189754 77.2692894973 80.3941949584 83.6050353198 86.9041737911 90.2940385703 93.7771246310 97.3559955584 101.0332854362 104.8117007857 108.6940225573 112.6831081777 116.7818936525 120.9933957280 125.3207141105 129.7670337486 134.3356271766 139.0298569240 143.8531779894 148.8091403841

73.3000650694 76.4074419401 79.6041558959 82.8927753779 86.2759426700 89.7563760218 93.3368718324 97.0203068976 100.8096407209 104.7079178916 108.7182705310 112.8439208088 117.0881835320 121.4544688086 125.9462847868 130.5672404744 135.3210486381 140.2115287864 145.2426102390 150.4183352834 155.7428624228

75.4012597333 78.6632975253 82.0231964511 85.4838923446 89.0484091149 92.7198613884 96.5014572300 100.3965009469 104.4083959753 108.5406478546 112.7968672902 117.1807733089 121.6961965082 126.3470824035 131.1374948756 136.0716197218 141.1537683135 146.3883813629 151.7800328038 157.3334337879 163.0534368015

77.5742333245 80.9984281159 84.5296289945 88.1711799006 91.9265292725 95.7992333122 99.7929593532 103.9114893330 108.1587233747 112.5386834801 117.0555173389 121.7135022557 126.5170492012 131.4707069888 136.5791665822 141.8472655379 147.2799925859 152.8824923542 158.6600702403 164.6181974353 170.7625161052

79.8215825880 83.4157840221 87.1267970028 90.9584179054 94.9145664873 98.9992898981 103.2167668198 107.5713117415 112.0673793731 116.7095692027 121.5026302018 126.4514656833 131.5611383180 136.8368753134 142.2840737611 147.9083061583 153.7153261084 159.7110742070 165.9016841187 172.2934888526 178.8930272403

82.1460000872 85.9184275902 89.8181745214 93.8495379115 98.0169598160 102.3250322098 106.7785020468 111.3822764909 116.1414283225 121.0612015284 126.1470170800 131.4044789064 136.8393800695 142.4577091468 148.2656568305 154.2696227486 160.4762225163 166.8922950263 173.5249099834 180.3813756953 187.4692471251

0.03500000 3.5000% 1.0000000000 2.0350000000 3.1062250000 4.2149428750 5.3624658756 6.5501521813 7.7794075076 9.0516867704 10.3684958073 11.7313931606 13.1419919212 14.6019616385 16.1130302958 17.6769863562 19.2956808786 20.9710297094 22.7050157492 24.4996913004 26.3571804960 28.2796818133 30.2694706768 32.3289021505 34.4604137257 36.6665282061 38.9498566933 41.3131016776 43.7590602363 46.2906273446 48.9107993017 51.6226772772 54.4294709819 57.3345024663 60.3412100526 63.4531524044 66.6740127386 70.0076031845 73.4578692959 77.0288947213 80.7249060365

0.03625000 3.6250% 1.0000000000 2.0362500000 3.1100640625 4.2228038848 5.3758805256 6.5707561946 7.8089461067 9.0920204031 10.4216061427 11.7993893653 13.2271172298 14.7066002294 16.2397144877 17.8284041379 19.4746837879 21.1806410752 22.9484393142 24.7803202393 26.6786068480 28.6457063463 30.6841132013 32.7964123049 34.9852822509 37.2534987325 39.6039380616 42.0395808163 44.5635156209 47.1789430621 49.8891797482 52.6976625140 55.6079527802 58.6237410684 61.7488516822 64.9872475556 68.3430352795 71.8204703084 75.4239623571 79.1580809925 83.0275614285

0.03750000 3.7500% 1.0000000000 2.0375000000 3.1139062500 4.2306777344 5.3893281494 6.5914279550 7.8386065033 9.1325542472 10.4750250315 11.8678384702 13.3128824128 14.8121155033 16.3675698346 17.9813537034 19.6556544673 21.3927415098 23.1949693165 25.0647806658 27.0047099408 29.0173865636 31.1055385597 33.2719962557 35.5196961153 37.8516847196 40.2711228966 42.7812900052 45.3855883804 48.0875479447 50.8908309926 53.7992371548 56.8167085481 59.9473351187 63.1953601856 66.5651861926 70.0613806748 73.6886824501 77.4520080420 81.3564583436 85.4073255315

0.03875000 3.8750% 1.0000000000 2.0387500000 3.1177515625 4.2385644355 5.4028088074 6.6121676487 7.8683891451 9.1732892245 10.5287541819 11.9367434065 13.3992922135 14.9185147867 16.4966072347 18.1358507651 19.8386149822 21.6073613128 23.4446465637 25.3531266180 27.3355602744 29.3948132351 31.5338622479 33.7557994100 36.0638366372 38.4613103069 40.9516860813 43.5385639169 46.2256832687 49.0169284954 51.9163344746 54.9280924354 58.0565560173 61.3062475630 64.6818646560 68.1882869115 71.8305830293 75.6140181217 79.5440613239 83.6263937002 87.8669164561

0.04000000 4.0000% 1.0000000000 2.0400000000 3.1216000000 4.2464640000 5.4163225600 6.6329754624 7.8982944809 9.2142262601 10.5827953105 12.0061071230 13.4863514079 15.0258054642 16.6268376828 18.2919111901 20.0235876377 21.8245311432 23.6975123889 25.6454128845 27.6712293998 29.7780785758 31.9692017189 34.2479697876 36.6178885791 39.0826041223 41.6459082872 44.3117446187 47.0842144034 49.9675829796 52.9662862987 56.0849377507 59.3283352607 62.7014686711 66.2095274180 69.8579085147 73.6522248553 77.5983138495 81.7022464035 85.9703362596 90.4091497100

0.04125000 4.1250% 1.0000000000 2.0412500000 3.1254515625 4.2543764395 5.4298694676 6.6538515831 7.9283229609 9.2553662831 10.6371501422 12.0759325856 13.5740648048 15.1339949780 16.7582722708 18.4495510020 20.2105949808 22.0442820238 23.9536086572 25.9416950143 28.0117899337 30.1672762685 32.4116764145 34.7486580666 37.1820402119 39.7157993706 42.3540760947 45.1011817336 47.9616054801 50.9400217061 54.0412976015 57.2705011276 60.6329092991 64.1340168077 67.7795450010 71.5754512323 75.5279385956 79.6434660627 83.9287590377 88.3908203481 93.0369416874

84.5502777478 88.5095374690 92.6073712804 96.8486292752 101.2383312998 105.7816728953 110.4840314467 115.3509725473 120.3882565864 125.6018455670 130.9979101618 136.5828370175 142.3632363131 148.3459495840 154.5380578195 160.9468898432 167.5800309877 174.4453320722 181.5509186948 188.9052008491 196.5168828788

87.0373105303 91.1924130370 95.4981380096 99.9599455125 104.5834935373 109.3746451780 114.3394760657 119.4842820731 124.8155872983 130.3401523378 136.0649828601 141.9973384887 148.1447420090 154.5149889068 161.1161572547 167.9566179551 175.0450453560 182.3904282502 190.0020812742 197.8896567204 206.0631567765

89.6101002389 93.9704789979 98.4943719603 103.1879109088 108.0574575679 113.1096122267 118.3512226852 123.7893935359 129.4314957935 135.2851768857 141.3583710189 147.6593099321 154.1965340546 160.9789040816 168.0156129847 175.3161984716 182.8905559143 190.7489517611 198.9020374521 207.3608638566 216.1368962512

92.2717594687 96.8472901482 101.6001226414 106.5371273938 111.6654410803 116.9924769221 122.5259354029 128.2738153997 134.2444257465 140.4463972441 146.8886951373 153.5806320739 160.5318815668 167.7524919775 175.2529010416 183.0439509570 191.1369040566 199.5434590888 208.2757681284 217.3464541434 226.7686292415

95.0255156984 99.8265363264 104.8195977794 110.0123816906 115.4128769582 121.0293920365 126.8705677180 132.9453904267 139.2632060438 145.8337342855 152.6670836570 159.7737670032 167.1647176834 174.8513063907 182.8453586463 191.1591729922 199.8055399119 208.7977615083 218.1496719687 227.8756588474 237.9906852013

97.8747155320 102.9120475477 108.1571695091 113.6186527513 119.3054221773 125.2267708421 131.3923751393 137.8123106138 144.4970684267 151.4575724993 158.7051973649 166.2517867562 174.1096729599 182.2916969694 190.8112294694 199.6821926850 208.9190831333 218.5369953126 228.5516463692 238.9794017819 249.8373021054

0.04250000 4.2500% 1.0000000000 2.0425000000 3.1293062500 4.2623017656 5.4434495907 6.6747961983 7.9584750367 9.2967102258 10.6918204103 12.1462227778 13.6624372458 15.2430908288 16.8909221890 18.6087863820 20.3996598033 22.2666453449 24.2129777721 26.2420293274 28.3573155738 30.5625014857 32.8614077988 35.2580176303 37.7564833796 40.3611339232 43.0764821149 45.9072326048 48.8582899905 51.9347673151 55.1419949260 58.4855297104 61.9711647231 65.6049392238 69.3931491408 73.3423579793 77.4594081934 81.7514330416 86.2258689459 90.8904683761 95.7533132821

0.04375000 0.04500000 0.04625000 0.04750000 0.04875000 4.3750% 4.5000% 4.6250% 4.7500% 4.8750% 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000 2.0437500000 2.0450000000 2.0462500000 2.0475000000 2.0487500000 3.1331640625 3.1370250000 3.1408890625 3.1447562500 3.1486265625 4.2702399902 4.2781911250 4.2861551816 4.2941321719 4.3021221074 5.4570629898 5.4707097256 5.4843898588 5.4981034500 5.5118505602 6.6958094956 6.7168916633 6.7380428898 6.7592633639 6.7805532750 7.9887511610 8.0191517881 8.0496773734 8.0803283737 8.1111052471 9.3382590243 9.3800136186 9.4219749519 9.4641439715 9.5065216279 10.7468078567 10.8021142314 10.8577412935 10.9136908101 10.9699645573 12.2169807004 12.2882093718 12.3599118283 12.4320911236 12.5047503294 13.7514736060 13.8411787936 13.9315577503 14.0226154519 14.1143569080 15.3531005763 15.4640318393 15.5758922963 15.6886896859 15.8024318073 17.0247987265 17.1599132721 17.2962773150 17.4339024460 17.5728003579 18.7696336708 18.9321093693 19.0962301408 19.2620128122 19.4294743753 20.5908051439 20.7840542909 20.9794307848 21.1769584208 21.3766612511 22.4916528689 22.7193367340 22.9497294586 23.1828639457 23.4187734871 24.4756626819 24.7417068870 25.0111544461 25.2840499832 25.5604386946 26.5464729243 26.8550836970 27.1679203392 27.4850423574 27.8065100810 28.7078811147 29.0635624633 29.4244366549 29.7905818693 30.1620774474 30.9638509135 31.3714227742 31.7853168502 32.2056345081 32.6324787230 33.3185193909 33.7831367990 34.2553877545 34.7354021473 35.2233120607 35.7762046143 36.3033779550 36.8396994382 37.3853337493 37.9404485237 38.3414135662 38.9370299629 39.5435355372 40.1611371024 40.7900453892 41.0188504097 41.6891963113 42.3724240558 43.0687911147 43.7785601019 43.8134251151 44.5652101453 45.3321486684 46.1145586927 46.9127649069 46.7302624639 47.5706446018 48.4287605443 49.3050002306 50.1997621961 49.7747114467 50.7113236089 51.6685907194 52.6469877415 53.6470006032 52.9523550725 53.9933331713 55.0582630402 56.1477196592 57.2622918826 56.2690206069 57.4230331640 58.6047077058 59.8147363431 61.0538286119 59.7307902585 61.0070696564 62.3151754372 63.6559363194 65.0302027567 63.3440123323 64.7523877909 66.1972523012 67.6795932945 69.2004251411 67.1153128718 68.6662452415 70.2588752201 71.8943739760 73.5739458667 71.0516078100 72.7562262774 74.5083481990 76.3093567399 78.1606757277 75.1601156516 77.0302564599 78.9543593033 80.9340511850 82.9710086694 79.4483707114 81.4966180005 83.6059984210 85.7784186163 88.0158453421 83.9242369300 86.1639658106 88.4727758480 90.8528935006 93.3066178025 88.5959222957 91.0413442720 93.5646417310 96.1684059419 98.8553154204 93.4719938962 96.1382047643 98.8920064110 101.7364052241 104.6745120471 98.5613936291 101.4644239787 104.4657617075 107.5688844722 110.7773945094

100.8228290966 106.1077993332 111.6173808049 117.3611194891 123.3489670674 129.5912981677 136.0989283398 142.8831327943 149.9556659380 157.3287817404 165.0152549644 173.0284033004 181.3821104406 190.0908501344 199.1697112651 208.6344239938 218.5013870136 228.7876959616 239.5111730400 250.6903978942 262.3447398047

103.8734546004 109.4179182392 115.2049521621 121.2451688192 127.5496449551 134.1299419218 140.9981268809 148.1667949320 155.6490922102 163.4587399944 171.6100598692 180.1179999885 188.9981624880 198.2668320968 207.9410060010 218.0384250136 228.5776061079 239.5778763751 251.0594084666 263.0432575870 275.5514001064

107.0303230577 112.8466875953 118.9247885371 125.2764040213 131.9138422022 138.8499651013 146.0982135309 153.6726331398 161.5879016311 169.8593572045 178.5030282787 187.5356645512 196.9747694560 206.8386340815 217.1463726152 227.9179593829 239.1742675551 250.9371095951 263.2292795269 276.0745971056 289.4979539753

110.2973031865 116.3985534589 122.7819865564 129.4606534346 136.4482086559 143.7589383063 151.4077892029 159.4103994536 167.7831304283 176.5431002106 185.7082185954 195.2972237054 205.3297203018 215.8262198657 226.8081825345 238.2980609767 250.3193462969 262.8966160631 276.0555845561 289.8231553418 304.2274762763

113.6784064847 120.0781307927 126.7818420054 133.8039795006 141.1596685269 148.8647527819 156.9358285391 165.3902803947 174.2463187134 183.5230188523 193.2403622478 203.4192794545 214.0816952286 225.2505757520 236.9499781002 249.2051020600 262.0423444078 275.4893557672 289.5751001661 304.3299174240 319.7855885017

117.1777924917 123.8902098757 130.9298576072 138.3126881655 146.0554317136 154.1756340096 162.6916961676 171.6229163557 180.9895335281 190.8127732876 201.1148959854 211.9192471646 223.2503104639 235.1337630990 247.5965340501 260.6668650851 274.3743747580 288.7501255274 303.8266941469 319.6382454865 336.2206099540

0.05000000 0.05125000 0.05250000 0.05375000 5.0000% 5.1250% 5.2500% 5.3750% 1.0000000000 1.0000000000 1.0000000000 1.0000000000 2.0500000000 2.0512500000 2.0525000000 2.0537500000 3.1525000000 3.1563765625 3.1602562500 3.1641390625 4.3101250000 4.3181408613 4.3261697031 4.3342115371 5.5256312500 5.5394455805 5.5532936125 5.5671754072 6.8019128125 6.8233421665 6.8448415272 6.8664110854 8.1420084531 8.1730384525 8.2041957074 8.2354806812 9.5491088758 9.5919066732 9.6349159820 9.6781377678 11.0265643196 11.0834918902 11.1407490711 11.1983376728 12.5778925355 12.6515208496 12.7256383973 12.8002483228 14.2067871623 14.2999112931 14.3937344132 14.4882616701 15.9171265204 16.0327817469 16.1494054698 16.2670057349 17.7129828465 17.8544618114 17.9972492570 18.1413572931 19.5986319888 19.7695029792 19.9421048430 20.1164552476 21.5785635882 21.7826900069 21.9890653473 22.1977147172 23.6574917676 23.8990528698 24.1434912780 24.3908418832 25.8403663560 26.1238793294 26.4110245701 26.7018496345 28.1323846738 28.4627281450 28.7976033600 29.1370740523 30.5390039075 30.9214429624 31.3094775364 31.7031917826 33.0659541029 33.5061669142 33.9532251071 34.4072383409 35.7192518080 36.2233579686 36.7357694252 37.2566274018 38.5052143984 39.0798050645 39.6643973200 40.2591711246 41.4304751184 42.0826450740 42.7467781793 43.4231015726 44.5019988743 45.2393806341 45.9909840337 46.7570932821 47.7270988180 48.5578988916 49.4055106955 50.2702870460 51.1134537589 52.0464912098 52.9993000070 53.9723149747 54.6691264468 55.7138738843 56.7817632574 57.8733269046 58.4025827692 59.5692099208 60.7628058284 61.9840182257 62.3227119076 63.6221319293 64.9528531344 66.3156592054 66.4388475030 67.8827661907 69.3628779240 70.8801258877 70.7607898782 72.3617579579 74.0044290150 75.6899326541 75.2988293721 77.0702980533 78.8896615383 80.7582665343 80.0637708407 82.0201508285 84.0313687690 86.0990233605 85.0669593827 87.2236835585 89.4430156294 91.7268458661 90.3203073518 92.6938973408 95.1387739499 97.6571638314 95.8363227194 98.4444595796 101.1335595823 103.9062363874 101.6281388554 104.4897381330 107.4430714604 110.4911965932 107.7095457982 110.8448372123 114.0838327120 117.4300984101 114.0950230881 117.5256351195 121.0732339294 124.7419661996

0.05500000 5.5000% 1.0000000000 2.0550000000 3.1680250000 4.3422663750 5.5810910256 6.8880510320 8.2668938388 9.7215729999 11.2562595149 12.8753537882 14.5834982466 16.3855906502 18.2867981359 20.2925720334 22.4086634952 24.6411399875 26.9964026868 29.4812048346 32.1026711005 34.8683180110 37.7860755016 40.8643096542 44.1118466852 47.5379982528 51.1525881567 54.9659805054 58.9891094332 63.2335104520 67.7113535268 72.4354779708 77.4194292592 82.6774978685 88.2247602512 94.0771220651 100.2513637786 106.7651887865 113.6372741697 120.8873242490 128.5361270827

0.05625000 5.6250% 1.0000000000 2.0562500000 3.1719140625 4.3503342285 5.5950405289 6.9097615586 8.2984356463 9.7652226514 11.3145164255 12.9509579745 14.6794493605 16.5051683871 18.4335841088 20.4704732150 22.6219373333 24.8944213083 27.2947325069 29.8300612104 32.5080021535 35.3365772746 38.3242597463 41.4799993571 44.8132493209 48.3339945952 52.0527817912 55.9807507669 60.1296679976 64.5119618224 69.1407596749 74.0299274066 79.1941108233 84.6487795571 90.4102734072 96.4958512863 102.9237429212 109.7132034605 116.8845711551 124.4593282826 132.4601654985

120.7997742425 127.8397629546 135.2317511023 142.9933386575 151.1430055903 159.7001558699 168.6851636633 178.1194218465 188.0253929388 198.4266625858 209.3479957151 220.8153955008 232.8561652759 245.4989735397 258.7739222166 272.7126183275 287.3482492439 302.7156617060 318.8514447913 335.7940170309 353.5837178825

124.5488239193 131.9319511452 139.6934636414 147.8527536530 156.4302072777 165.4472554007 174.9264272400 184.8914066361 195.3670912262 206.3796546515 217.9566119524 230.1268883149 242.9208913411 256.3705870223 270.5095796072 285.3731955621 300.9985718346 317.4247486412 334.6927670090 352.8457713182 371.9291170983

128.4295787107 136.1721315930 144.3211685017 152.8980298480 161.9251764150 171.4262481768 181.4261262061 191.9509978319 203.0284252181 214.6874175421 226.9585069630 239.8738285786 253.4672045789 267.7742328193 282.8323800424 298.6810799946 315.3618366943 332.9183331207 351.3965456096 370.8448642541 391.3142196274

132.4468468828 140.5658649028 149.1212801413 158.1365489489 167.6363884549 177.6468443344 188.1953622173 199.3108629365 211.0238218194 223.3663522421 236.3722936752 250.0773044602 264.5189595749 279.7368536521 295.7727095359 312.6704926734 330.4765316546 349.2396452311 369.0112761622 389.8456322560 411.7998349897

136.6056140723 145.1189228463 154.1004636028 163.5759891010 173.5726685015 184.1191652691 195.2457193589 206.9842339237 219.3683667895 232.4336269629 246.2174764458 260.7594376503 276.1012067211 292.2867730908 309.3625456108 327.3774856194 346.3832473284 366.4343259315 387.5882138577 409.9055656199 433.4503717290

140.9110498078 149.8372963595 159.2656442797 169.2243367705 179.7432057138 190.8537610352 202.5892850934 214.9849323799 228.0778348263 241.9072130353 256.5144937685 271.9434340430 288.2402522079 305.4537663946 323.6355407543 342.8400399217 363.1247921673 384.5505617267 407.1815308239 431.0854919327 456.3340508539

0.05750000 5.7500% 1.0000000000 2.0575000000 3.1758062500 4.3584151094 5.6090239782 6.9315428569 8.3301065712 9.8090876990 11.3731102417 13.0270640806 14.7761202653 16.6257471805 18.5817276434 20.6501769829 22.8375621594 25.1507219836 27.5968884976 30.1837095862 32.9192728874 35.8121310785 38.8713286155 42.1064300109 45.5275497365 49.1453838463 52.9712434175 57.0170899140 61.2955725841 65.8200680076 70.6047219181 75.6644934284 81.0152018005 86.6735759040 92.6573065185 98.9851016433 105.6767449878 112.7531578246 120.2364643995 128.1500611025 136.5186896159

0.05875000 5.8750% 1.0000000000 2.0587500000 3.1797015625 4.3665090293 5.6230414348 6.9533951191 8.3619070823 9.8531691234 11.4320428094 13.1036753244 14.8735162498 16.7473353294 18.7312412800 20.8317017052 23.0555641804 25.4100785760 27.9029206924 30.5422172830 33.3365725484 36.2950961856 39.4274330865 42.7437947804 46.2549927237 49.9724735462 53.9083563671 58.0754723036 62.4874063015 67.1585414217 72.1041057302 77.3402219419 82.8839599809 88.7533926298 94.9676544468 101.5470041456 108.5128906391 115.8880229642 123.6964443133 131.9636104167 140.7164725287

0.06000000 6.0000% 1.0000000000 2.0600000000 3.1836000000 4.3746160000 5.6370929600 6.9753185376 8.3938376499 9.8974679088 11.4913159834 13.1807949424 14.9716426389 16.8699411973 18.8821376691 21.0150659292 23.2759698850 25.6725280781 28.2128797628 30.9056525485 33.7599917015 36.7855912035 39.9927266758 43.3922902763 46.9958276929 50.8155773545 54.8645119957 59.1563827155 63.7057656784 68.5281116191 73.6397983162 79.0581862152 84.8016773881 90.8897780314 97.3431647133 104.1837545961 111.4347798719 119.1208666642 127.2681186640 135.9042057839 145.0584581309

0.06125000 6.1250% 1.0000000000 2.0612500000 3.1875015625 4.3827360332 5.6511786152 6.9973133054 8.4258987454 9.9419850435 11.5509316274 13.2584261896 15.0705047937 16.9935732124 19.0344295716 21.2002883829 23.4988060463 25.9381079167 28.5268170266 31.2740845694 34.1896222493 37.2837366121 40.5673654796 44.0521166152 47.7503087579 51.6750151693 55.8401098484 60.2603165766 64.9512609670 69.9295257012 75.2127091504 80.8194875858 86.7696812005 93.0843241740 99.7857390297 106.8976155452 114.4450944974 122.4548565353 130.9552164981 139.9762235086 149.5497671986

0.06250000 6.2500% 1.0000000000 2.0625000000 3.1914062500 4.3908691406 5.6652984619 7.0193796158 8.4580908418 9.9867215194 11.6108916143 13.3365723402 15.1701081115 17.1182398685 19.1881298603 21.3873879765 23.7240997251 26.2068559579 28.8447844552 31.6475834837 34.6255574514 37.7896547921 41.1515082166 44.7234774802 48.5186948227 52.5511132491 56.8355578272 61.3877801914 66.2245164533 71.3635487317 76.8237705274 82.6252561854 88.7893346969 95.3386681155 102.2973348727 109.6909183023 117.5466006962 125.8932632397 134.7615921921 144.1841917042 154.1957036857

0.06375000 6.3750% 1.0000000000 2.0637500000 3.1953140625 4.3990153340 5.6794525615 7.0415176623 8.4904144133 10.0316783321 11.6711978258 13.4152366872 15.2704580260 17.2439497252 19.3432515202 21.5763838046 23.9518782721 26.4788105120 29.1668346821 32.0262203931 35.0678919431 38.3034700545 41.7453162705 45.4065801827 49.3012496694 53.4442043358 57.8512723622 62.5392909753 67.5261707750 72.8309641619 78.4739381272 84.4766516828 90.8620382276 97.6544931646 104.8799671039 112.5660650067 120.7421516509 129.4394638187 138.6912296371 148.5327955265 159.0017612413

145.3685142688 154.7272038393 164.6240180600 175.0898990985 186.1575682966 197.8616284737 210.2386721109 223.3273957573 237.1687210134 251.8059224716 267.2847630138 283.6536368870 300.9637210081 319.2691349660 338.6271102266 359.0981690646 380.7463137858 403.6392268285 427.8484823711 453.4497701075 480.5231318886

149.9835652898 159.7950997506 170.1830618609 181.1813167452 192.8257191040 205.1542301014 218.2070411198 232.0267047856 246.6582736918 262.1494472712 278.5507272983 295.9155825271 314.3006230006 333.7657846019 354.3745244472 376.1940277585 399.2954268893 423.7540332191 449.6495826707 477.0664956526 506.0941522722

154.7619656188 165.0476835559 175.9505445692 187.5075772434 199.7580318780 212.7435137907 226.5081246181 241.0986120952 256.5645288209 272.9584005502 290.3359045832 308.7560588582 328.2814223897 348.9783077331 370.9170061970 394.1720265689 418.8223481630 444.9516890528 472.6487903959 502.0077178197 533.1281808889

159.7096904395 170.4919089789 181.9345384038 194.0780288811 206.9653081500 220.6419332742 235.1562516873 250.5595721031 266.9063458944 284.2543595805 302.6649391048 322.2031666249 342.9381105807 364.9430698538 388.2958328823 413.0789526464 439.3800384960 467.2920658538 496.9137048874 528.3496693117 561.7110865571

164.8329351660 176.1349936139 188.1434307148 200.9023951344 214.4587948303 228.8624695072 244.1663738514 260.4267722172 277.7034454807 296.0599108233 315.5636552497 336.2863837028 358.3042826843 381.6983003520 406.5544441240 432.9640968818 461.0243529369 490.8383749954 522.5157734327 556.1730092722 591.9338223517

170.1381235204 181.9844288948 194.5859362369 207.9907896720 222.2502025136 237.4186529238 253.5540920477 270.7181654157 288.9764484610 308.3986970504 329.0591139873 351.0366325040 374.4152178261 399.2841879626 425.7385549452 453.8793878229 483.8141987966 515.6573539699 549.5305102855 585.5630803162 623.8927266864

0.06500000 6.5000% 1.0000000000 2.0650000000 3.1992250000 4.4071746250 5.6936409756 7.0637276390 8.5228699356 10.0768564814 11.7318521527 13.4944225426 15.3715600079 17.3707114084 19.4998076499 21.7672951472 24.1821693317 26.7540103383 29.4930210103 32.4100673760 35.5167217554 38.8253086695 42.3489537330 46.1016357257 50.0982420478 54.3546277809 58.8876785867 63.7153776948 68.8568772450 74.3325742659 80.1641915932 86.3748640468 92.9892302098 100.0335301735 107.5357096347 115.5255307610 124.0346902605 133.0969451274 142.7482465607 153.0268825871 163.9736299553

0.06625000 6.6250% 1.0000000000 2.0662500000 3.2031390625 4.4153470254 5.7078637658 7.0860097403 8.5554578856 10.1222569705 11.7928564948 13.5741332376 15.4734195646 17.4985336108 19.6578114625 21.9601414719 24.4150008444 27.0324946503 29.8233974209 32.7991975000 35.9721443344 39.3552988965 42.9625874484 46.8088588669 50.9099457668 55.2827296739 59.9452105148 64.9165807114 70.2173041835 75.8692005857 81.8955351245 88.3211143265 95.1723881506 102.4775588656 110.2666971404 118.5718658260 127.4272519369 136.8693073778 146.9368989915 157.6714685497 169.1172033411

0.06750000 6.7500% 1.0000000000 2.0675000000 3.2070562500 4.4235325469 5.7221209938 7.1083641609 8.5881787417 10.1678808068 11.8542127613 13.6543721226 15.5760422409 17.6274250922 19.8172762859 22.1549424352 24.6504010496 27.3143031204 30.1580185810 33.1936848353 36.4342585617 39.8935710146 43.5863870580 47.5284681845 51.7366397869 56.2288629725 61.0243112232 66.1434522307 71.6081352563 77.4416843861 83.6689980822 90.3166554527 97.4130296958 104.9884092003 113.0751268213 121.7076978817 130.9229674887 140.7602677942 151.2615858703 162.4717429166 174.4385855634

0.06875000 6.8750% 1.0000000000 2.0687500000 3.2109765625 4.4317312012 5.7364127213 7.1307910958 8.6210329837 10.2137290013 11.9159228701 13.7351425675 15.6794336190 17.7573946803 19.9782155646 22.3517178846 24.8883984892 27.5994758853 30.4969398524 33.5936044673 36.9031647744 40.4402573527 44.2205250457 48.2606861425 52.5786083148 57.1933876365 62.1254330365 67.3965565578 73.0300698211 79.0508871213 85.4856356109 92.3627730591 99.7127137069 107.5679627743 115.9632602150 124.9357343548 134.5250660917 144.7736643855 155.7268538120 167.4330750116 179.9440989186

0.07000000 7.0000% 1.0000000000 2.0700000000 3.2149000000 4.4399430000 5.7507390100 7.1532907407 8.6540210925 10.2598025690 11.9779887489 13.8164479613 15.7835993186 17.8884512709 20.1406428598 22.5504878600 25.1290220102 27.8880535509 30.8402172995 33.9990325105 37.3789647862 40.9954923212 44.8651767837 49.0057391586 53.4361408997 58.1766707627 63.2490377160 68.6764703562 74.4838232811 80.6976909108 87.3465292745 94.4607863237 102.0730413664 110.2181542621 118.9334250604 128.2587648146 138.2368783516 148.9134598363 160.3374020248 172.5610201665 185.6402915782

0.07125000 7.1250% 1.0000000000 2.0712500000 3.2188265625 4.4481679551 5.7650999219 7.1758632913 8.6871435508 10.3061025288 12.0404123340 13.8982917128 15.8885449973 18.0206038284 20.3045718512 22.7512725956 25.3723007680 28.1800771977 31.1879076980 34.4100461215 37.8617619077 41.5594124436 45.5205205802 49.7638576716 54.3095325306 59.1790867235 64.3955966525 69.9837829140 75.9701274466 82.3829990272 89.2527877079 96.6120488321 104.4956573113 112.9409728948 121.9880172135 131.6796634400 142.0618394601 153.1837455216 165.0980873900 177.8613261166 191.5339456024

175.6319159024 188.0479904360 201.2711098144 215.3537319523 230.3517245292 246.3245866236 263.3356847541 281.4525042631 300.7469170402 321.2954666479 343.1796719800 366.4863506587 391.3079634515 417.7429810758 445.8962748458 475.8795327107 507.8117023369 541.8194629888 578.0377280831 616.6101804085 657.6898421351

181.3212180625 194.3337487591 208.2083596144 223.0021634389 238.7760567667 255.5949705275 273.5281373250 292.6493764227 313.0373976107 334.7761252025 357.9550434971 382.6695651288 409.0214238186 437.1190931466 467.0782330675 499.0221660083 533.0823845063 569.3990924798 608.1217823566 649.4098504378 693.4332530293

187.2131900890 200.8500804200 215.4074608483 230.9474644556 247.5364183063 265.2451265420 284.1491725836 304.3292417330 325.8714655500 348.8677894746 373.4163652641 399.6219699194 427.5964528890 457.4592134590 489.3377103675 523.3680058173 559.6953462100 598.4747820792 639.8718298695 684.0631783857 731.2374429267

193.3152557193 207.6056795500 222.8785700191 239.2014717079 256.6465728878 275.2910247738 295.2172827270 316.5134709145 339.2737720399 363.5988438676 389.5962643835 417.3810075599 447.0759518296 478.8124235179 512.7307776348 548.9810185972 587.7234636257 629.1294517500 673.3821015578 720.6771210399 771.2236731114

199.6351119887 214.6095698279 230.6322397158 247.7764964959 266.1208512507 285.7493108382 306.7517625969 329.2243859787 353.2700929972 378.9989995070 406.5289294724 435.9859545355 467.5049713530 501.2303193477 537.3164417021 575.9285926212 617.2435941047 661.4506456920 708.7521908905 759.3648442528 813.5203833505

206.1807392266 221.8711168965 238.6794339753 256.6853436461 275.9741743809 296.6373343055 318.7727443748 342.4853024115 367.8873802083 395.0993560481 424.2501851665 455.4780108597 488.9308191334 524.7671399967 563.1567987214 604.2817206303 648.3367932252 695.5307897425 746.0873585117 800.2460828056 858.2636162056

0.07250000 7.2500% 1.0000000000 2.0725000000 3.2227562500 4.4564060781 5.7794955188 7.1985089439 8.7204008423 10.3526299034 12.1031955714 13.9806772503 15.9942763510 18.1538613864 20.4700163369 22.9540925214 25.6182642292 28.4755883858 31.5400685437 34.8267235132 38.3516609679 42.1321563880 46.1867377262 50.5352762113 55.1990837366 60.2010173076 65.5655910624 71.3190964144 77.4897309044 84.1077363950 91.2055472836 98.8179494617 106.9822507977 115.7384639805 125.1295026191 135.2013915590 146.0034924470 157.5887456494 170.0139297090 183.3399396129 197.6320852348

0.07375000 7.3750% 1.0000000000 2.0737500000 3.2266890625 4.4646573809 5.7939258627 7.2212278951 8.7537934523 10.3993857194 12.1663404163 14.0636080220 16.1007991136 18.2882330482 20.6369902355 23.1589682654 25.8669421749 28.7746291603 31.8967580609 35.2491439679 38.8487683355 42.7138650003 46.8640125441 51.3202334692 56.1051006875 61.2428518632 66.7595121882 72.6830262120 79.0433993952 85.8728501006 93.2059727955 101.0799132891 109.5345568942 118.6127304652 128.3604193370 138.8270002631 150.0654915325 162.1328215330 175.0901171211 189.0030132587 203.9419854866

0.07500000 7.5000% 1.0000000000 2.0750000000 3.2306250000 4.4729218750 5.8083910156 7.2440203418 8.7873218674 10.4463710075 12.2298488331 14.1470874955 16.2081190577 18.4237279870 20.8055075860 23.3659206550 26.1183647041 29.0772420569 32.2580352112 35.6773878520 39.3531919410 43.3046813365 47.5525324368 52.1189723695 57.0278952972 62.3049874445 67.9778615029 74.0762011156 80.6319161992 87.6793099142 95.2552581578 103.3994025196 112.1543577086 121.5659345367 131.6833796269 142.5596330990 154.2516055814 166.8204760000 180.3320117000 194.8569125775 210.4711810208

0.07625000 7.6250% 1.0000000000 2.0762500000 3.2345640625 4.4811995723 5.8228910397 7.2668864814 8.8209865756 10.4935868020 12.2937227957 14.2311191588 16.3162419947 18.5603554468 20.9755825496 23.5749707190 26.3725622364 29.3834701069 32.6239597025 36.1115366299 39.8650412979 43.9047506968 48.2524879375 52.9317401427 57.9677853286 63.3878289599 69.2211509181 75.4992636756 82.2560825309 89.5281088238 97.3546271217 105.7779174397 114.8434836445 124.6002992723 135.1010720919 146.4025288389 158.5657216628 171.6563579396 185.7451552325 200.9082233190 217.2274753471

0.07750000 7.7500% 1.0000000000 2.0775000000 3.2385062500 4.4894904844 5.8374259969 7.2898265117 8.8547880663 10.5410341415 12.3579642874 14.3157065197 16.4251737750 18.6981247425 21.1472294101 23.7861396894 26.6295655153 29.6933568427 32.9945919981 36.5516728779 40.3844275259 44.5142206592 48.9640727603 53.7587883992 58.9250945002 64.4917893239 70.4899029965 76.9528704787 83.9167179409 91.4202635813 99.5053340088 108.2169973945 117.6038146926 127.7181103312 138.6162638819 150.3590243328 163.0118487186 176.6452669942 191.3352751863 207.1637590132 224.2189503368

212.9604114143 229.4000412419 247.0315442319 265.9413311887 286.2220776999 307.9731783331 331.3012337623 356.3205732100 383.1538147678 411.9324663384 442.7975701480 475.9003939837 511.4031725475 549.4799025572 590.3171954926 634.1151921658 681.0885435978 731.4674630087 785.4988540768 843.4475209974 905.5974662697

219.9827069162 227.2565195974 234.7910703423 242.5959189879 237.2064315513 245.3007585672 253.6938894559 262.3971027094 255.7004058782 264.6983154597 274.0380485269 283.7328781694 275.5583108117 285.5506891192 295.9334497271 306.7221762275 296.8807362341 307.9669908031 319.4983752688 331.4931448852 319.7756905313 332.0645151134 344.8601263830 358.1838636138 344.3591477080 357.9693537469 372.1557110197 386.9431130438 370.7556348515 385.8170552779 401.5325839850 417.9312043047 399.0988629218 415.7533344237 433.1494435138 451.3208726383 429.5324040622 447.9348345055 467.1770885817 487.2982402678 462.2104188618 482.5299470934 503.7993415861 526.0638538886 497.2984372529 519.7196931254 543.2140413820 567.8338025649 534.9741970003 559.6986701098 585.6341120374 612.8409222637 575.4285440291 602.6760703681 631.2887130803 661.3360937391 618.8663991512 648.8767756457 680.4244774527 713.5896410039 665.5077960886 698.5425338191 733.3068438584 769.8928381817 715.5889960501 751.9332238555 790.2214907026 830.5595331408 769.3636845088 809.3282156447 851.4758793687 895.9278969592 827.1042562414 871.0278318180 917.4009151706 966.3623089736 889.1031951392 937.3549192044 988.3527349523 1042.2553879190 955.6745557807 1008.6565381447 1064.7146309924 1124.0301804828

0.07875000 7.8750% 1.0000000000 2.0787500000 3.2424515625 4.4977946230 5.8519959496 7.3128406306 8.8887268303 10.5887140682 12.4225753011 14.4008531060 16.5349202881 18.8370452608 21.3204625751 23.9994490029 26.8894056119 30.0069463038 33.3699933252 36.9978802996 40.9114633732 45.1332411138 49.6874838515 54.6003732048 59.9001525947 65.6172896116 71.7846511685 78.4376924480 85.6146607283 93.3568152606 101.7086644624 110.7182217888 120.4372817547 130.9217176928 142.2318029612 154.4325574443 167.5941213431 181.7921583989 197.1082908728 213.6305687790 231.4539760703

0.08000000 8.0000% 1.0000000000 2.0800000000 3.2464000000 4.5061120000 5.8666009600 7.3359290368 8.9228033597 10.6366276285 12.4875578388 14.4865624659 16.6454874632 18.9771264602 21.4952965771 24.2149203032 27.1521139275 30.3242830417 33.7502256850 37.4502437398 41.4462632390 45.7619642981 50.4229214420 55.4567551573 60.8932955699 66.7647592155 73.1059399527 79.9544151490 87.3507683609 95.3388298297 103.9659362161 113.2832111134 123.3458680025 134.2135374427 145.9506204381 158.6266700732 172.3168036790 187.1021479733 203.0703198112 220.3159453961 238.9412210278

0.08125000 8.1250% 1.0000000000 2.0812500000 3.2503515625 4.5144426270 5.8812410904 7.3590919290 8.9570181482 10.6847758728 12.5529139124 14.5728381678 16.7568812689 19.1183778720 21.6717460741 24.4325754427 27.4177221974 30.6454121259 34.1353518612 37.9088491999 41.9889431974 46.4005448322 51.1705890998 56.3281994641 61.9048656706 67.9346360063 74.4543251818 81.5037391028 89.1259179050 97.3673987347 106.2784998819 115.9136279973 126.3316102721 137.5960536067 149.7757329623 162.9450112655 177.1842934308 192.5805172720 209.2276843004 227.2274336498 246.6896626338

0.08250000 8.2500% 1.0000000000 2.0825000000 3.2543062500 4.5227865156 5.8959164032 7.3823295064 8.9913716907 10.7331598552 12.6186455432 14.6596838006 16.8691077141 19.2608091005 21.8498258513 24.6524364840 27.6862624940 30.9703791497 34.5254354296 38.3737838525 42.5396210204 47.0491397545 51.9306937843 57.2149760215 62.9352115433 69.1273664956 75.8303742315 83.0863801056 90.9410064643 99.4436394976 108.6477397561 118.6111782860 129.3966004946 141.0718200354 153.7102451883 167.3913404164 182.2011260007 198.2327188958 215.5869182047 234.3728389566 254.7085981705

0.08375000 8.3750% 1.0000000000 2.0837500000 3.2582640625 4.5311436777 5.9106269607 7.4056419687 9.0258644836 10.7817806341 12.6847547622 14.7471029735 16.9821728476 19.4044298235 22.0295508213 24.8745257025 27.9577672301 31.2992302357 34.9205407679 38.8451360572 43.0984162020 47.7079085589 52.7034459007 58.1173594949 63.9846883526 70.3434060021 77.2346662548 84.7030695536 92.7969516288 101.5686963277 111.0750746451 121.3776121466 132.5429871639 144.6434623389 157.7573523098 171.9695305657 187.3719787506 204.0643819710 222.1547739611 241.7602362803 263.0076560688

250.6809766859 259.0565187100 267.7331977228 276.7220575195 271.4221035999 280.7810402068 290.4865200378 300.5516272649 293.7965942584 304.2435234233 315.0885497909 326.3471365143 317.9330760562 329.5830052972 341.6894944614 354.2707752767 343.9703057957 356.9496457210 370.4517658864 384.4981142370 372.0579673771 386.5056173787 401.5509718647 417.2192086616 402.3575323080 418.4260667690 435.1769883287 452.6397933761 435.0431879773 452.9001521105 471.5351186304 490.9825763297 470.3028390305 490.1321642793 510.8473470191 532.4886388769 508.3391876041 530.3427374217 553.3536939644 577.4189515842 549.3708986280 573.7701564154 599.3136815990 626.0560150899 593.6338568949 620.6717689286 649.0079182289 678.7056363348 641.3825231254 671.3255104429 702.7398115850 735.6988513325 692.8913968215 726.0315512783 760.8374212763 797.3940065674 748.4565943212 785.1140753806 823.6554617550 864.1790121092 808.3975511240 848.9232014111 891.5774680226 936.4737806082 873.0588582750 917.8370575239 965.0181372994 1014.7328675084 942.8122433642 992.2640221259 1044.4258609550 1099.4483290778 1018.0587075291 1072.6451438959 1130.2854621576 1191.1528162267 1099.2308307470 1159.4567554076 1223.1211559579 1290.4229235655 1186.7952586684 1253.2132958402 1323.4997498795 1397.8828147596

286.0345472645 310.9899405979 338.0353481230 367.3458085283 399.1110199925 433.5365679169 470.8452554800 511.2785456264 555.0981238226 602.5875916928 654.0543024970 709.8313503312 770.2797259214 835.7906529673 906.7881201533 983.7316252162 1067.1191488280 1157.4903775424 1255.4301966616 1361.5724756320 1476.6041704661

0.08500000 8.5000% 1.0000000000 2.0850000000 3.2622250000 4.5395141250 5.9253728256 7.4290295158 9.0604970246 10.8306392717 12.7512436098 14.8350993167 17.0960827586 19.5492497931 22.2109360255 25.0988655877 28.2322691626 31.6320120414 35.3207330649 39.3229953755 43.6654499824 48.3770132309 53.4890593555 59.0356294007 65.0536578998 71.5832188213 78.6677924211 86.3545547769 94.6946919329 103.7437407472 113.5619587107 124.2147252011 135.7729768432 148.3136798749 161.9203426642 176.6835717907 192.7016753929 210.0813178013 228.9382298144 249.3979793487 271.5968075933

0.08625000 8.6250% 1.0000000000 2.0862500000 3.2661890625 4.5478978691 5.9401540604 7.4524923481 9.0952698131 10.8797368345 12.8181141364 14.9236764807 17.2108435772 19.6952788357 22.3939966353 25.3254788451 28.5098013954 31.9687717658 35.7260783306 39.8074525866 44.2408453722 49.0566182856 54.2877516127 59.9700701893 66.1424887431 72.8472783972 80.1303561590 88.0415993777 96.6351873240 105.9699722307 116.1098823356 127.1243596870 139.0888357100 152.0852477900 166.2026004119 181.5375746975 198.1951905151 216.2895256970 235.9444972884 257.2947101795 280.4863789325

0.08750000 8.7500% 1.0000000000 2.0875000000 3.2701562500 4.5562949219 5.9549707275 7.4760306662 9.1301833495 10.9290743926 12.8853684019 15.0128381371 17.3264614741 19.8425268531 22.5787479527 25.5543883986 28.7903973834 32.3095571545 36.1366434055 40.2985997035 44.8247271776 49.7468908056 55.0997437511 60.9209713293 67.2515563206 74.1360674987 81.6229734048 89.7649835777 98.6194196408 108.2486188593 118.7203730095 130.1084056479 142.4928911421 155.9610191170 170.6076082897 186.5357740151 203.8576542414 222.6951989875 243.1810288989 265.4593689276 289.6870637087

0.08875000 8.8750% 1.0000000000 2.0887500000 3.2741265625 4.5647052949 5.9698228898 7.4996446713 9.1652381359 10.9786530205 12.9530084760 15.1025879783 17.4429426613 19.9910038225 22.7652054118 25.7856173921 29.0740909356 32.6544165062 36.5524959711 40.7965299885 45.4172220250 50.4480004797 55.9252605223 61.8886273937 68.3812430749 75.4500783977 83.1462728555 91.5255045715 100.6483931022 110.5809379900 121.3949962366 133.1688021526 145.9875333437 159.9439269279 175.1389504428 191.6825322946 209.6943570357 229.3047312226 250.6555261186 273.9012040617 299.2099359221

0.09000000 9.0000% 1.0000000000 2.0900000000 3.2781000000 4.5731290000 5.9847106100 7.5233345649 9.2004346757 11.0284737966 13.0210364382 15.1929297177 17.5602933923 20.1407197976 22.9533845794 26.0191891915 29.3609162188 33.0033986784 36.9737045595 41.3013379699 46.0184583871 51.1601196420 56.7645304098 62.8733381466 69.5319385798 76.7898130520 84.7008962267 93.3239768871 102.7231348069 112.9682169396 124.1353564641 136.3075385459 149.5752170150 164.0369865464 179.8003153356 196.9823437158 215.7107546502 236.1247225687 258.3759475999 282.6297828839 309.0664633434

295.6825362387 321.8155518190 350.1698737236 380.9343129901 414.3137295943 450.5303966098 489.8254803217 532.4606461490 578.7198010717 628.9109841627 683.3684178166 742.4547333310 806.5633856641 876.1212734456 951.5915816884 1033.4768661320 1122.3223997532 1218.7198037322 1323.3109870494 1436.7924209486 1559.9197767293

305.6783291154 333.0430850017 362.7680510830 395.0567954890 430.1304440999 468.2291949035 509.6139629639 554.5681672696 603.3996716966 656.4428933804 714.0610929345 776.6488622000 844.6348265648 918.4845803560 998.7038754117 1085.8420846660 1180.4959644684 1283.3137414038 1394.9995515999 1516.3182629254 1648.1007131027

316.0346817833 344.6877164393 375.8478916277 409.7345821452 446.5863580829 486.6626644151 530.2456475514 577.6421417122 629.1858291120 685.2395891593 746.1980532107 812.4903828667 884.5832913675 962.9843293622 1048.2454581814 1140.9669357722 1241.8015426523 1351.4591776344 1470.7118556774 1600.3991430492 1741.4340680660

326.7648177352 356.7651953092 389.4281063929 424.9898508353 463.7077000969 505.8617584805 551.7569895457 601.7254223679 656.1285536030 715.3599627353 779.8481594280 850.0596835773 926.5024804948 1009.7295756387 1100.3430754766 1198.9985234252 1306.4096423791 1423.3534981403 1550.6761211002 1689.2986268479 1840.2238799806

337.8824450443 369.2918650983 403.5281329572 440.8456649233 481.5217747664 525.8587344954 574.1860206000 626.8627624540 684.2804110748 746.8656480716 815.0835563980 889.4410764738 970.4907733565 1058.8349429585 1155.1300878248 1260.0917957290 1374.5000573447 1499.2050625057 1635.1335181312 1783.2955347630 1944.7921328917

0.09125000 9.1250% 1.0000000000 2.0912500000 3.2820765625 4.5815660488 5.9996339508 7.5471005488 9.2357734739 11.0785378034 13.0894543779 15.2838670899 17.6785199619 20.2916849084 23.1433011563 26.2551273868 29.6509077608 33.3565530940 37.4003385638 41.8131194578 46.6285666083 51.8834233113 57.6177856884 63.8754086325 70.7040396702 78.1557832901 86.2874985154 95.1612327549 104.8446952438 115.4117736848 126.9430980335 139.5266557291 153.2584630644 168.2432978190 184.5954987450 202.4398380054 221.9124732234 243.1619864051 266.3505176645 291.6550024014 319.2685213706

0.09250000 9.2500% 1.0000000000 2.0925000000 3.2860562500 4.5900164531 6.0145929750 7.5709428252 9.2712550366 11.1288461274 13.1582643942 15.3754038507 17.7976287069 20.4439093623 23.3349709783 26.4934557938 29.9441004547 33.7139297468 37.8324682483 42.3319715613 47.2476789307 52.6180892318 58.4852624858 64.8951492657 71.8979505728 79.5485110008 87.9067482683 97.0381224832 107.0141488129 117.9129575780 129.8199061540 142.8282474733 157.0398603645 172.5660474483 189.5284068372 208.0597844697 228.3053145331 250.4235561274 274.5877350692 300.9871005631 329.8284073652

0.09375000 9.3750% 1.0000000000 2.0937500000 3.2900390625 4.5984802246 6.0295877457 7.5948615968 9.3068798715 11.1793998595 13.2274685963 15.4675437772 17.9176260063 20.5974034444 23.5284100173 26.7341984565 30.2405295617 34.0755792082 38.2701647589 42.8579927051 47.8759295212 53.3642979138 59.3672008432 65.9328759223 73.1140830400 80.9685283250 89.5593278554 98.9555148419 109.2325943583 120.4731500794 132.7675078993 146.2144617649 160.9220675554 177.0085113887 194.6030593314 213.8470961437 234.8952614071 257.9166921641 283.0963820544 310.6366678721 340.7588554851

0.09500000 9.5000% 1.0000000000 2.0950000000 3.2940250000 4.6069573750 6.0446183256 7.6188570666 9.3426484879 11.2302000942 13.2970691032 15.5602906680 18.0385182814 20.7521775182 23.7236343824 26.9773796487 30.5402307154 34.4415526333 38.7135001335 43.3912826462 48.5134544976 54.1222326748 60.2638447789 66.9889100329 74.3528564861 82.4163778522 91.2459337482 100.9142974543 111.5011557124 123.0937655051 135.7876732281 149.6875021848 164.9078148923 181.5740573071 199.8235927513 219.8068340627 241.6884832986 265.6488892120 291.8855336871 320.6146593874 352.0730520292

0.09625000 9.6250% 1.0000000000 2.0962500000 3.2980140625 4.6154479160 6.0596847779 7.6429294378 9.3785613962 11.2812479306 13.3670680439 15.6536483431 18.1603119962 20.9082420258 23.9206603208 27.2230238766 30.8432399248 34.8119017675 39.1625473126 43.9319424915 49.1603919563 54.8920796821 61.1754423515 68.0635786778 75.6146981256 83.8926128201 92.9672768041 102.9153771965 113.8209822516 125.7762517933 138.8822160285 153.2496293212 168.9999061434 186.2661471097 205.1942637690 225.9442116567 248.6913420287 273.6278836989 300.9645675050 330.9324071273 363.7846513133

349.4017739456 382.2846858181 418.1681633991 457.3260083092 500.0570065674 546.6872084167 597.5724161847 653.1008991616 713.6963562101 779.8211487143 851.9798285344 930.7229878882 1016.6514605330 1110.4209063066 1212.7468140071 1324.4099607853 1446.2623697069 1579.2338109427 1724.3388961912 1882.6848204687 2055.4798103364

361.3375350465 395.7612570383 433.3691733143 474.4558218459 519.3429853666 568.3822115130 621.9575660780 680.4886409402 744.4338402272 814.2939704482 890.6161627146 973.9981577657 1065.0929873591 1164.6140886898 1273.3408918936 1392.1249243938 1521.8964799002 1663.6719042909 1818.5615554379 1987.7784993159 2172.6480105026

373.7049981868 409.7398417668 449.1529519324 492.2610411761 539.4105137864 590.9802494538 647.3846478401 709.0769585751 776.5529234416 850.3547600142 931.0755187655 1019.3638486498 1115.9292094607 1221.5475728477 1337.0676578021 1463.4177507211 1601.6131648512 1752.7643990560 1918.0860614675 2098.9066297300 2296.6791262672

386.5199919720 424.2393912093 465.5421333742 510.7686360447 560.2916564690 614.5193638335 673.8987033977 738.9190802205 810.1163928415 888.0774501614 973.4448079267 1066.9220646798 1169.2796608244 1281.3612286027 1404.0905453199 1538.4791471253 1685.6346661022 1846.7699593819 2023.2131055232 2216.4183505479 2427.9780938500

399.7989240022 439.2795704375 482.5602290921 530.0066511422 582.0197913146 639.0391962286 701.5467188656 770.0705905565 845.1898848975 927.5394113189 1017.8150796584 1116.7797810755 1225.2698350040 1344.2020566231 1474.5815045731 1617.5099743882 1774.1953094231 1945.9616079551 2134.2604127208 2340.6829774451 2566.9737140242

0.09750000 9.7500% 1.0000000000 2.0975000000 3.3020062500 4.6239518594 6.0747871657 7.6670789143 9.4146191085 11.3325444715 13.4374675575 15.7476206444 18.2830136572 21.0656074888 24.1195042189 27.4711558803 31.1495935786 35.1866789525 39.6173801504 44.4800747150 49.8168819998 55.6740279947 62.1022457242 69.1572146823 76.9000431139 85.3977973175 94.7240825559 104.9596806051 116.1932494641 128.5220912869 142.0529951873 156.9031622181 173.2012205344 191.0883395365 210.7194526413 232.2645992738 255.9103977030 281.8616614791 310.3431734733 341.6016328869 375.9077920934

0.09875000 9.8750% 1.0000000000 2.0987500000 3.3060015625 4.6324692168 6.0899255520 7.6913057002 9.4508221381 11.3840908242 13.5082697931 15.8422114352 18.4066298144 21.2242845086 24.3201826038 27.7218006360 31.4593284488 35.5659371331 40.0780734250 45.0357831757 50.4830667643 56.4682696073 63.0445112310 70.2701567150 78.2093346907 86.9325064914 96.5170915074 107.0481542937 118.6191595302 131.3328015339 145.3019156853 160.6504798593 177.5147147454 196.0442928265 216.4036667431 238.7735288340 263.3524148063 290.3584657684 320.0313642631 352.6344614840 388.4571145556

0.10000000 10.0000% 1.0000000000 2.1000000000 3.3100000000 4.6410000000 6.1051000000 7.7156100000 9.4871710000 11.4358881000 13.5794769100 15.9374246010 18.5311670611 21.3842837672 24.5227121439 27.9749833583 31.7724816942 35.9497298636 40.5447028499 45.5991731349 51.1590904484 57.2749994933 64.0024994426 71.4027493868 79.5430243255 88.4973267581 98.3470594339 109.1817653773 121.0999419150 134.2099361065 148.6309297171 164.4940226889 181.9434249578 201.1377674535 222.2515441989 245.4766986188 271.0243684806 299.1268053287 330.0394858616 364.0434344477 401.4477778925

413.5588018225 454.8807850002 500.2316615377 550.0042485376 604.6296627700 664.5810548901 730.3777077419 802.5895342467 881.8420138358 968.8216101848 1064.2817171778 1169.0491846026 1284.0314801014 1410.2245494113 1548.7214429789 1700.7217836693 1867.5421575770 2050.6275179408 2251.5637009400 2472.0911617817 2714.1200500554

427.8172546179 471.0642085115 518.5817991020 570.7917517633 628.1574372499 691.1879841784 760.4427976160 836.5365238805 920.1445056137 1012.0087755431 1112.9446421280 1223.8479255381 1345.7029081850 1479.5910703683 1626.7006885671 1788.3373815632 1965.9356979925 2161.0718481693 2375.4776931760 2611.0561153771 2869.8979067706

442.5925556818 487.8518112499 537.6369923749 592.4006916124 652.6407607737 718.9048368510 791.7953205361 871.9748525898 960.1723378487 1057.1895716336 1163.9085287970 1281.2993816767 1410.4293198443 1552.4722518288 1708.7194770116 1880.5914247128 2069.6505671841 2277.6156239025 2506.3771862927 2758.0149049220 3034.8163954142

Tabla para Calcular Valor Presente de una Anualidad Ordinaria. C=

0.99502488 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

1-(1+i/p)-np i/p

0.00666667 0.6667% 0.9933774834 1.9801763081 2.9604400411 3.9342119614 4.9015350610 5.8624520473 6.8170053450 7.7652370977 8.7071891699 9.6429031489 10.5724203466 11.4957818013 12.4130282794 13.3242002775 14.2293380240 15.1284814808 16.0216703452 16.9089440515 17.7903417730 18.6659024236 19.5356646592 20.3996668800 21.2579472317 22.1105436077 22.9574936500 23.7988347517 24.6346040580 25.4648384682 26.2895746373 27.1088489774 27.9226976597 28.7311566156 29.5342615387 30.3320478861 31.1245508802 31.9118055101 32.6938465333 33.4707084767 34.2424256392

I/P

0.00750000 0.7500% 0.9925558313 1.9777229094 2.9555562377 3.9261104096 4.8894396125 5.8455976303 6.7946378464 7.7366132471 8.6715764239 9.5995795771 10.5206745182 11.4349126731 12.3423450850 13.2430224169 14.1369949547 15.0243126101 15.9050249232 16.7791810652 17.6468298414 18.5080196937 19.3627987034 20.2112145940 21.0533147335 21.8891461374 22.7187554714 23.5421890535 24.3594928571 25.1707125132 25.9758933134 26.7750802118 27.5683178281 28.3556504497 29.1371220344 29.9127762128 30.6826562907 31.4468052513 32.2052657581 32.9580801569 33.7052904783

0.005 np=

0.00875000 0.8750% 0.9913258984 1.9740529352 2.9482556978 3.9140081267 4.8713835209 5.8204545437 6.7612932279 7.6939709818 8.6185585941 9.5351262395 10.4437434841 11.3444792903 12.2374020226 13.1225794524 14.0000787632 14.8699665558 15.7323088534 16.5871711062 17.4346181970 18.2747144456 19.1075236139 19.9331089110 20.7515329972 21.5628579898 22.3671454670 23.1644564729 23.9548515220 24.7383906042 25.5151331888 26.2851382293 27.0484641679 27.8051689396 28.5553099773 29.2989442155 30.0361280946 30.7669175659 31.4913680951 32.2095346668 32.9214717886

0.01000000 1.0000% 0.9900990099 1.9703950593 2.9409852072 3.9019655517 4.8534312393 5.7954764746 6.7281945293 7.6516777518 8.5660175760 9.4713045307 10.3676282482 11.2550774735 12.1337400728 13.0037030423 13.8650525172 14.7178737794 15.5622512667 16.3982685809 17.2260084959 18.0455529663 18.8569831349 19.6603793415 20.4558211302 21.2433872576 22.0231557006 22.7952036640 23.5596075881 24.3164431565 25.0657853035 25.8077082213 26.5422853676 27.2695894729 27.9896925474 28.7026658885 29.4085800876 30.1075050373 30.7995099379 31.4846633048 32.1630329751

1

0.01125000 1.1250% 0.9888751545 1.9667492257 2.9337445990 3.8899822981 4.8355820006 5.7706620525 6.6953394833 7.6097300206 8.5139481044 9.4081069018 10.2923183207 11.1666930242 12.0313404442 12.8863687952 13.7318850880 14.5679951426 15.3948036021 16.2124139452 17.0209284996 17.8204484545 18.6110738734 19.3929037067 20.1660358039 20.9305669260 21.6865927575 22.4342079184 23.1735059762 23.9045794573 24.6275198589 25.3424176602 26.0493623339 26.7484423574 27.4397452236 28.1233574523 28.7993646005 29.4678512737 30.1289011359 30.7825969206 31.4290204406

40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

35.0090320919 35.7705616807 36.5270480272 37.2785245303 38.0250243678 38.7665804978 39.5032256601 40.2349923776 40.9619129579 41.6840194946 42.4013438688 43.1139177504 43.8217725998 44.5249396687 45.2234500020 45.9173344391 46.6066236150 47.2913479619 47.9715377105 48.6472228912 49.3184333356

34.4469384400 35.1830654492 35.9137126046 36.6389206994 37.3587302227 38.0731813625 38.7823140074 39.4861677493 40.1847818852 40.8781954195 41.5664470665 42.2495752521 42.9276181163 43.6006135149 44.2685990222 44.9316119327 45.5896892633 46.2428677551 46.8911838760 47.5346738224 48.1733735210

33.6272334955 34.3268733537 35.0204444646 35.7079994693 36.3895905519 37.0652694443 37.7350874293 38.3990953450 39.0573435886 39.7098821201 40.3567604660 40.9980277234 41.6337325635 42.2639232352 42.8886475689 43.5079529804 44.1218864737 44.7304946456 45.3338236883 45.9319193936 46.5248271560

32.8346861140 33.4996892217 34.1581081403 34.8100080597 35.4554535245 36.0945084401 36.7272360793 37.3536990884 37.9739594935 38.5880787064 39.1961175311 39.7981361694 40.3941942271 40.9843507199 41.5686640791 42.1471921576 42.7199922352 43.2871210250 43.8486346782 44.4045887903 44.9550384062

32.0682525989 32.7003733982 33.3254619512 33.9435964907 34.5548543789 35.1593121176 35.7570453573 36.3481289071 36.9326367438 37.5106420210 38.0822170789 38.6474334525 39.2063618814 39.7590723178 40.3056339360 40.8461151407 41.3805835755 41.9091061315 42.4317489557 42.9485774593 43.4596563256

m=

0.01250000 1.2500% 0.9876543210 1.9631153788 2.9265337074 3.8780579826 4.8178350446 5.7460099206 6.6627258475 7.5681242938 8.4623449815 9.3455259077 10.2178033656 11.0793119660 11.9301846578 12.7705527485 13.6005459244 14.4202922710 15.2299182924 16.0295489307 16.8193075859 17.5993161342 18.3696949474 19.1305629110 19.8820374430 20.6242345116 21.3572686534 22.0812529910 22.7962992504 23.5025177782 24.2000175587 24.8889062308 25.5692901045 26.2412741773 26.9049621504 27.5604564448 28.2078582171 28.8472673749 29.4787825925 30.1025013259 30.7185198281

0.9950249

0.01375000 1.3750% 0.9864364982 1.9594934630 2.9193523680 3.8661922249 4.8001896176 5.7215187350 6.6303514032 7.5268571179 8.4112030756 9.2835542053 10.1440731988 10.9929205413 11.8302545414 12.6562313602 13.4710050409 14.2747275372 15.0675487420 15.8496165150 16.6210767102 17.3820732036 18.1327479197 18.8732408579 19.6036901188 20.3242319298 21.0350006706 21.7361288982 22.4277473718 23.1099850770 23.7829692498 24.4468254006 25.1016773372 25.7476471884 26.3848554263 27.0134208890 27.6334608030 28.2450908044 28.8484249612 29.4435757940 30.0306542975

0.01500000 1.5000% 0.9852216749 1.9558834235 2.9122004173 3.8543846476 4.7826449730 5.6971871655 6.5982139561 7.4859250799 8.3605173201 9.2221845519 10.0711177851 10.9075052070 11.7315322236 12.5433815011 13.3432330060 14.1312640453 14.9076493057 15.6725608924 16.4261683669 17.1686387851 17.9001367341 18.6208243685 19.3308614468 20.0304053663 20.7196111984 21.3986317225 22.0676174606 22.7267167100 23.3760755763 24.0158380062 24.6461458189 25.2671387379 25.8789544216 26.4817284941 27.0755945755 27.6606843109 28.2371273999 28.8050516255 29.3645828822

0.01625000 1.6250% 0.9840098401 1.9522852055 2.9050776930 3.8426348763 4.7652003702 5.6730138945 6.5663113353 7.4453248071 8.3102827131 9.1614098037 9.9989272362 10.8230526309 11.6340001288 12.4319804466 13.2172009314 13.9898656152 14.7501752671 15.4983274461 16.2345165521 16.9589338766 17.6717676523 18.3732031019 19.0634224865 19.7426051527 20.4109275796 21.0685634239 21.7156835660 22.3524561535 22.9790466455 23.5956178553 24.2023299930 24.7993407065 25.3868051232 25.9648758900 26.5337032128 27.0934348957 27.6442163796 28.1861907794 28.7194989219

0.01750000 1.7500% 0.9828009828 1.9486987546 2.8979840340 3.8309425396 4.7478550757 5.6489976174 6.5346413930 7.4050529661 8.2604943156 9.1012229146 9.9274918080 10.7395496884 11.5376409714 12.3220058687 13.0928804607 13.8504967672 14.5950828179 15.3268627203 16.0460567276 16.7528813048 17.4475491939 18.1302694780 18.8012476442 19.4606856454 20.1087819611 20.7457316571 21.3717264443 21.9869547364 22.5916017066 23.1858493431 23.7698765042 24.3438589722 24.9079695059 25.4623778928 26.0072510003 26.5427528258 27.0690445462 27.5862845663 28.0946285664

0.01875000 1.8750% 0.9815950920 1.9451240167 2.8909192802 3.8193072689 4.7306083621 5.6251370426 6.5032020050 7.3651062626 8.2111472516 9.0416169341 9.8568018985 10.6569834586 11.4424377508 12.2134358290 12.9702437585 13.7131227078 14.4423290383 15.1581143934 15.8607257850 16.5504056785 17.2273920770 17.8919186032 18.5442145799 19.1845051091 19.8130111500 20.4299495951 21.0355333449 21.6299713815 22.2134688407 22.7862270829 23.3484437624 23.9003128956 24.4420249282 24.9737668007 25.4957220129 26.0080706875 26.5109896319 27.0046523994 27.4892293491

31.3269331635 31.9278352233 32.5213187390 33.1074752978 33.6863953558 34.2581682527 34.8228822249 35.3806244196 35.9314809083 36.4755366995 37.0128757526 37.5435809902 38.0677343114 38.5854166038 39.0967077568 39.6016866734 40.1004312824 40.5930185505 41.0795244943 41.5600241919 42.0345917945

30.6097699605 31.1810307872 31.7445433166 32.3004126427 32.8487424343 33.3896349536 33.9231910763 34.4495103096 34.9686908109 35.4808294066 35.9860216095 36.4843616370 36.9759424286 37.4608556632 37.9391917763 38.4110399766 38.8764882630 39.3356234407 39.7885311375 40.2352958200 40.6760008089

29.9158452042 30.4589607923 30.9940500417 31.5212315681 32.0406222346 32.5523371770 33.0564898295 33.5531919503 34.0425536456 34.5246833947 34.9996880736 35.4676729789 35.9287418511 36.3829968977 36.8305388154 37.2714668132 37.7058786337 38.1338705751 38.5555375124 38.9709729186 39.3802688853

29.2442793820 29.7606685185 30.2688005103 30.7688073902 31.2608190801 31.7449634245 32.2213662233 32.6901512653 33.1514403594 33.6053533672 34.0520082334 34.4915210169 34.9240059207 35.3495753217 35.7683398000 36.1804081672 36.5858874954 36.9848831443 37.3774987890 37.7638364468 38.1439965036

28.5942295493 29.0852378863 29.5678013625 30.0420652211 30.5081722075 30.9662626117 31.4164743113 31.8589428121 32.2938012895 32.7211806285 33.1412094629 33.5540142142 33.9597191294 34.3584463188 34.7503157925 35.1354454963 35.5139513477 35.8859472705 36.2515452290 36.6108552619 36.9639855154

27.9648877047 28.4317916119 28.8901021958 29.3399776155 29.7815731195 30.2150410989 30.6405311400 31.0581900761 31.4681620379 31.8705885034 32.2656083469 32.6533578866 33.0339709316 33.4075788286 33.7743105066 34.1342925218 34.4876491011 34.8345021852 35.1749714701 35.5091744492 35.8372264532

0.02000000 2.0000% 0.9803921569 1.9415609381 2.8838832726 3.8077286987 4.7134595085 5.6014308907 6.4719910693 7.3254814405 8.1622367064 8.9825850062 9.7868480453 10.5753412209 11.3483737460 12.1062487706 12.8492635006 13.5777093143 14.2918718768 14.9920312517 15.6784620115 16.3514333446 17.0112091614 17.6580481974 18.2922041151 18.9139256031 19.5234564736 20.1210357584 20.7068978024 21.2812723553 21.8443846620 22.3964555510 22.9377015206 23.4683348241 23.9885635530 24.4985917187 24.9986193320 25.4888424824 25.9694534141 26.4406406021 26.9025888256

0.02125000 2.1250% 0.9791921665 1.9380094653 2.8768758534 3.7962064660 4.6964078003 5.5778778950 6.4410065067 7.2861752820 8.1137579261 8.9241203682 9.7176209236 10.4946104515 11.2554325107 12.0004235111 12.7299128627 13.4442231214 14.1436701311 14.8285631639 15.4992050564 16.1558923441 16.7989153920 17.4285585234 18.0451001453 18.6488128718 19.2399636444 19.8188138500 20.3856194370 20.9406310277 21.4840940295 22.0162487437 22.5373304712 23.0475696169 23.5471917913 24.0364179107 24.5154642944 24.9845427608 25.4438607205 25.8936212685 26.3340232739

0.02250000 2.2500% 0.9779951100 1.9344695453 2.8698968658 3.7847402110 4.6794525291 5.5544768011 6.4102462602 7.2471846066 8.0657062167 8.8662163489 9.6491113436 10.4147788202 11.1635978681 11.8959392354 12.6121655113 13.3126313069 13.9976834298 14.6676610560 15.3228958983 15.9637123700 16.5904277457 17.2033523185 17.8027895536 18.3890362382 18.9623826291 19.5231125957 20.0715037610 20.6078276392 21.1323497693 21.6453298478 22.1470218560 22.6376741868 23.1175297670 23.5868261780 24.0457957731 24.4946657928 24.9336584771 25.3629911756 25.7828764554

0.02375000 2.3750% 0.9768009768 1.9309411251 2.8629461539 3.7733295765 4.6625929929 5.5312263667 6.3797082947 7.2085062708 8.0180769434 8.8088663671 9.5813102487 10.3358341868 11.0728539065 11.7927754887 12.4959955933 13.1829016785 13.8538722134 14.5092768873 15.1494768130 15.7748247258 16.3856651778 16.9823347280 17.5651621275 18.1344685006 18.6905675219 19.2337655892 19.7643619919 20.2826490763 20.7889124067 21.2834309223 21.7664770913 22.2383170611 22.6992108045 23.1494122633 23.5891694879 24.0187247745 24.4383147981 24.8481707429 25.2485184302

0.02500000 2.5000% 0.9756097561 1.9274241523 2.8560235632 3.7619742080 4.6458284956 5.5081253616 6.3493905967 7.1701371675 7.9708655292 8.7520639310 9.5142087131 10.2577645982 10.9831849738 11.6909121696 12.3813777264 13.0550026599 13.7121977170 14.3533636264 14.9788913428 15.5891622856 16.1845485714 16.7654132404 17.3321104784 17.8849858326 18.4243764220 18.9506111434 19.4640108717 19.9648886553 20.4535499076 20.9302925928 21.3954074076 21.8491779586 22.2918809352 22.7237862783 23.1451573447 23.5562510680 23.9573181151 24.3486030391 24.7303444284

0.02625000 2.6250% 0.9744214373 1.9239185747 2.8491289400 3.7506737540 4.6291583474 5.4851725675 6.3192911741 7.1320742257 7.9240674550 8.6958026358 9.4477979399 10.1805582849 10.8945756735 11.5903295235 12.2682869900 12.9289032789 13.5726219527 14.1998752280 14.8110842660 15.4066594553 15.9870006872 16.5524976246 17.1035299631 17.6404676863 18.1636713143 18.6734921455 19.1702724925 19.6543459123 20.1260374298 20.5856637562 21.0335335018 21.4699473830 21.8951984243 22.3095721553 22.7133468017 23.1067934731 23.4901763440 23.8637528322 24.2277737707

27.3554792407 27.7994894517 28.2347935801 28.6615623334 29.0799630720 29.4901598745 29.8923136025 30.2865819632 30.6731195718 31.0520780115 31.4236058937 31.7878489153 32.1449499170 32.4950489382 32.8382832728 33.1747875223 33.5046936494 33.8281310288 34.1452264988 34.4561044106 34.7608866770

26.7652614677 27.1875265290 27.6010051692 28.0058802146 28.4023306875 28.7905318849 29.1706554565 29.5428694800 29.9073385361 30.2642237808 30.6136830167 30.9558707630 31.2909383236 31.6190338542 31.9403024276 32.2548860980 32.5629239638 32.8645522289 33.1599042633 33.4491106618 33.7322993016

26.1935222057 26.5951317416 26.9879039037 27.3720331577 27.7477096897 28.1151195009 28.4744444997 28.8258625913 29.1695477666 29.5056701874 29.8343962713 30.1558887739 30.4703068693 30.7778062291 31.0785390994 31.3726543760 31.6602976782 31.9416114212 32.2167348863 32.4858042898 32.7489528506

25.6395784422 26.0215662439 26.3946923018 26.7591621995 27.1151767517 27.4629321140 27.8026198915 28.1344272445 28.4585369910 28.7751277079 29.0843738294 29.3864457430 29.6815098833 29.9697288238 30.2512613663 30.5262626289 30.7948841308 31.0572738762 31.3135764359 31.5639330265 31.8084815887

25.1027750521 25.4661220020 25.8206068313 26.1664456890 26.5038494527 26.8330238563 27.1541696159 27.4674825521 27.7731537094 28.0713694726 28.3623116805 28.6461577371 28.9230807191 29.1932494821 29.4568287630 29.7139792810 29.9648578351 30.2096174001 30.4484072196 30.6813728972 30.9086564851

24.5824835768 24.9281204159 25.2649163614 25.5930975507 25.9128843369 26.2244914366 26.5281280747 26.8239981239 27.1123002426 27.3932280074 27.6669700437 27.9337101522 28.1936274321 28.4468964016 28.6936871148 28.9341652763 29.1684923521 29.3968256780 29.6193185657 29.8361204051 30.0473767650

0.02750000 2.7500% 0.9732360097 1.9204243404 2.8422621317 3.7394278654 4.6125818642 5.4623667778 6.2894080562 7.0943144100 7.8776782579 8.6400761634 9.3820692588 10.1042036582 10.8070108595 11.4910081358 12.1566989156 12.8045731539 13.4351076923 14.0487666106 14.6460015675 15.2272521338 15.7929461156 16.3434998692 16.8793186075 17.4007966983 17.9083179545 18.4022559168 18.8829741283 19.3508264022 19.8061570825 20.2493012968 20.6805852037 21.1003262323 21.5088333161 21.9064071203 22.2933402631 22.6699175310 23.0364160885 23.3931056823 23.7402488392

0.02875000 2.8750% 0.9720534629 1.9169413978 2.8354229869 3.7282361962 4.5960983682 5.4397067977 6.2597392930 7.0568547199 7.8316935308 8.5848782803 9.3170141242 10.0286893066 10.7204756322 11.3929289256 12.0465894781 12.6819824818 13.2996184513 13.8999936343 14.4835904100 15.0508776768 15.6023112290 16.1383341229 16.6593770332 17.1658585985 17.6581857580 18.1367540782 18.6019480712 19.0541415030 19.4936976943 19.9209698122 20.3363011540 20.7400254231 21.1324669969 21.5139411878 21.8847544960 22.2452048564 22.5955818774 22.9361670740 23.2672340938

0.03000000 3.0000% 0.9708737864 1.9134696955 2.8286113549 3.7170984028 4.5797071872 5.4171914439 6.2302829552 7.0196921895 7.7861089219 8.5302028368 9.2526241134 9.9540039936 10.6349553336 11.2960731394 11.9379350868 12.5611020260 13.1661184718 13.7535130795 14.3237991063 14.8774748605 15.4150241364 15.9369166372 16.4436083857 16.9355421220 17.4131476913 17.8768424187 18.3270314745 18.7641082277 19.1884545900 19.6004413495 20.0004284946 20.3887655288 20.7657917755 21.1318366752 21.4872200731 21.8322524981 22.1672354351 22.4924615874 22.8082151334

0.03125000 3.1250% 0.9696969697 1.9100091827 2.8218270863 3.7060141443 4.5634076551 5.3948195443 6.2010371339 6.9828238874 7.7409201332 8.4760437656 9.1888909242 9.8801366537 10.5504355430 11.2004223447 11.8307125767 12.4419031047 13.0345727076 13.6092826255 14.1665770914 14.7069838462 15.2310146388 15.7391657103 16.2319182646 16.7097389232 17.1730801680 17.6223807689 18.0580662002 18.4805490426 18.8902293746 19.2874951512 19.6727225708 20.0462764323 20.4085104798 20.7597677380 21.1003808369 21.4306723267 21.7509549834 22.0615321051 22.3626977989

0.03250000 3.2500% 0.9685230024 1.9065598086 2.8150700326 3.6949830824 4.5471991113 5.3725899383 6.1719999402 6.9462469155 7.6961229206 8.4223950804 9.1258063733 9.8070763906 10.4669020732 11.1059584244 11.7248992004 12.3243575791 12.9049468079 13.4672608309 14.0118748967 14.5393461469 15.0502141859 15.5450016328 16.0242146565 16.4883434930 16.9378629472 17.3732328786 17.7948986718 18.2032916918 18.5988297257 18.9819174099 19.3529466440 19.7122969917 20.0603360695 20.3974199220 20.7238933869 21.0400904474 21.3463345738 21.6429390545 21.9302073167

0.03375000 3.3750% 0.9673518742 1.9031215228 2.8083400463 3.6840048815 4.5310809011 5.3505014763 6.1431695055 6.9099584092 7.6517130923 8.3692508753 9.0633623945 9.7348124735 10.3843409659 11.0126635704 11.6204726195 12.2084378423 12.7772071026 13.3274071125 13.8596441234 14.3745045933 14.8725558339 15.3543466350 15.8204078694 16.2712530780 16.7073790356 17.1292662980 17.5373797321 17.9321690274 18.3140691922 18.6835010323 19.0408716153 19.3865747186 19.7209912634 20.0444897349 20.3574265875 20.6601466385 20.9529834471 21.2362596828 21.5102874804

24.0781010600 24.4069110073 24.7269206884 25.0383656335 25.3414750691 25.6364720867 25.9235738070 26.2029915397 26.4749309389 26.7395921546 26.9971699802 27.2478539953 27.4918287059 27.7292736797 27.9603636785 28.1852687869 28.4041545371 28.6171820312 28.8245080596 29.0262852162 29.2226620109

23.5890489369 23.9018701695 24.2059491320 24.5015301404 24.7888506833 25.0681416120 25.3396273263 25.6035259551 25.8600495311 26.1094041615 26.3517901934 26.5874023751 26.8164300123 27.0390571201 27.2554625711 27.4658202393 27.6702991390 27.8690635616 28.0622732069 28.2500833117 28.4326447744

23.1147719742 23.4123999750 23.7013591990 23.9819021349 24.2542739174 24.5187125412 24.7754490691 25.0247078341 25.2667066350 25.5016569272 25.7297640070 25.9512271913 26.1662399915 26.3749902830 26.5776604690 26.7744276398 26.9654637279 27.1509356582 27.3310054934 27.5058305761 27.6755636661

22.6547372596 22.9379270396 23.2125353111 23.4788221199 23.7370396314 23.9874323698 24.2302374495 24.4656847995 24.6939973814 24.9153914001 25.1300765092 25.3382560089 25.5401270390 25.7358807650 25.9257025600 26.1097721794 26.2882639316 26.4613468427 26.6291848172 26.7919367924 26.9497568896

22.2084332365 22.4779014397 22.7388875929 22.9916586857 23.2364733033 23.4735818918 23.7032270139 23.9256435970 24.1410591738 24.3496941151 24.5517618548 24.7474691088 24.9370160860 25.1205966934 25.2983987346 25.4706041013 25.6373889601 25.7989239323 25.9553742685 26.1069000180 26.2536561917

21.7753687839 22.0317956797 22.2798507180 22.5198072242 22.7519296002 22.9764736157 23.1936866899 23.4038081643 23.6070695665 23.8036948648 23.9939007156 24.1778967019 24.3558855641 24.5280634236 24.6946199986 24.8557388137 25.0115974014 25.1623674983 25.3082152342 25.4493013148 25.5857811993

0.03500000 3.5000% 0.9661835749 1.8996942752 2.8016369809 3.6730792086 4.5150523755 5.3285530198 6.1145439805 6.8739555367 7.6076865089 8.3166053226 9.0015510363 9.6633343346 10.3027384875 10.9205202778 11.5174108964 12.0941168081 12.6513205876 13.1896817271 13.7098374175 14.2124033020 14.6979742048 15.1671248355 15.6204104691 16.0583676030 16.4815145923 16.8903522631 17.2853645054 17.6670188458 18.0357670008 18.3920454114 18.7362757598 19.0688654684 19.3902081820 19.7006842338 20.0006610955 20.2904938121 20.5705254223 20.8410873645 21.1024998691

0.03625000 3.6250% 0.9650180941 1.8962780160 2.7949606910 3.6622057331 4.4991128908 5.3067434411 6.0861215354 6.8382354986 7.5640390819 8.2644526725 8.9403644608 9.5926315665 10.2220811257 10.8295113397 11.4156924870 11.9813679006 12.5272549101 13.0540457516 13.5624084455 14.0529876434 14.5264054460 14.9832621915 15.4241372174 15.8495895946 16.2601588368 16.6563655843 17.0387122647 17.4076837295 17.7637478693 18.1073562068 18.4389444698 18.7589331433 19.0677280032 19.3657206303 19.6532889075 19.9307974981 20.1985983094 20.4570309379 20.7064231005

0.03750000 3.7500% 0.9638554217 1.8928726956 2.7883110319 3.6513841271 4.4832618093 5.2850716234 6.0579003599 6.8027955276 7.5207667736 8.2127872517 8.8797949414 9.5226939194 10.1423555850 10.7396198409 11.3152962322 11.8701650431 12.4049783548 12.9204610649 13.4173118698 13.8962042118 14.3577871921 14.8026864502 15.2315050123 15.6448241082 16.0432039597 16.4271845395 16.7972863031 17.1540108946 17.4978418261 17.8292451336 18.1486700083 18.4565494056 18.7533006319 19.0393259102 19.3150129255 19.5807353499 19.8368533493 20.0837140716 20.3216521172

0.03875000 3.8750% 0.9626955475 1.8894782648 2.7816878602 3.6406140652 4.4674984984 5.2635364605 6.0298786623 6.7676328879 7.4778655961 8.1616034619 8.8198348611 9.4535112983 10.0635487829 10.6508291532 11.2162013509 11.7604826483 12.2844598299 12.7888903296 13.2745033257 13.7420007949 14.1920585270 14.6253271018 15.0424328297 15.4439786567 15.8305450365 16.2026907692 16.5609538091 16.9058520425 17.2378840361 17.5575297580 17.8652512712 18.1614934019 18.4466843821 18.7212364689 18.9855465405 19.2399966695 19.4849546758 19.7207746578 19.9477975045

0.04000000 4.0000% 0.9615384615 1.8860946746 2.7750910332 3.6298952243 4.4518223310 5.2421368567 6.0020546699 6.7327448750 7.4353316105 8.1108957794 8.7604767109 9.3850737605 9.9856478466 10.5631229295 11.1183874322 11.6522956079 12.1656688537 12.6592969747 13.1339393988 13.5903263450 14.0291599471 14.4511153337 14.8568416671 15.2469631414 15.6220799437 15.9827691766 16.3295857467 16.6630632180 16.9837146327 17.2920333007 17.5884935583 17.8735514984 18.1476456715 18.4111977611 18.6646132318 18.9082819537 19.1425788016 19.3678642323 19.5844848388

0.04125000 4.1250% 0.9603841537 1.8827218763 2.7685204094 3.6192272839 4.4362326856 5.2208717269 5.9744266285 6.6981288149 7.3931609266 8.0606587531 8.7017130882 9.3173715133 9.9086401088 10.4764850985 11.0218344283 11.5455792829 12.0485755418 12.5316451782 12.9955776021 13.4411309504 13.8690333257 14.2799839863 14.6746544886 15.0536897850 15.4177092773 15.7673078293 16.1030567389 16.4255046712 16.7351785557 17.0325844473 17.3182083527 17.5925170254 17.8559587279 18.1089639644 18.3519461843 18.5853024579 18.8094141252 19.0246474192 19.2313540640

21.3550723373 21.5991037075 21.8348828092 22.0626887046 22.2827910189 22.4954502598 22.7009181254 22.8994378023 23.0912442535 23.2765644961 23.4556178706 23.6286163001 23.7957645412 23.9572604263 24.1132950978 24.2640532346 24.4097132702 24.5504476040 24.6864228058 24.8177998124 24.9447341182

20.9470910500 21.1793399758 21.4034643917 21.6197485082 21.8284665942 22.0298833237 22.2242541121 22.4118254399 22.5928351652 22.7675128253 22.9360799279 23.0987502320 23.2557300188 23.4072183535 23.5534073375 23.6944823522 23.8306222941 23.9619998013 24.0887814729 24.2111280800 24.3291947696

20.5509899925 20.7720385470 20.9850973947 21.1904553202 21.3883906701 21.5791717302 21.7630570893 21.9402959897 22.1111286648 22.2757866649 22.4344931709 22.5874632973 22.7349043829 22.8770162727 23.0139915882 23.1460159886 23.2732684227 23.3959213713 23.5141410808 23.6280877887 23.7379159409

20.1663513882 20.3767522390 20.5793042012 20.7743000733 20.9620217313 21.1427405355 21.3167177237 21.4842047882 21.6454438394 21.8006679561 21.9501015221 22.0939605508 22.2324529971 22.3657790586 22.4941314644 22.6176957539 22.7366505453 22.8511677933 22.9614130381 23.0675456443 23.1697190319

19.7927738834 19.9930518110 20.1856267413 20.3707949436 20.5488412919 20.7200397038 20.8846535613 21.0429361166 21.1951308814 21.3414720013 21.4821846167 21.6174852083 21.7475819311 21.8726749337 21.9929566671 22.1086121799 22.2198194037 22.3267494267 22.4295667564 22.5284295735 22.6234899745

19.4298718502 19.6205251863 19.8036256291 19.9794723929 20.1483528383 20.3105429420 20.4663077474 20.6159017982 20.7595695541 20.8975457902 21.0300559810 21.1573166685 21.2795358160 21.3969131487 21.5096404789 21.6179020206 21.7218746896 21.8217283934 21.9176263082 22.0097251459 22.0981754102

0.04250000 4.2500% 0.9592326139 1.8793598215 2.7619758480 3.6086099261 4.4207289459 5.1997399961 5.9469928020 6.6637820642 7.3513497019 8.0108870042 8.6435366947 9.2503949110 9.8325131041 10.3908998600 10.9265226475 11.4403094940 11.9331505938 12.4058998501 12.8593763551 13.2943658082 13.7116218784 14.1118675092 14.4957961719 14.8640730666 15.2173362749 15.5561978656 15.8812449550 16.1930407243 16.4921253950 16.7790171654 17.0542131083 17.3181900320 17.5714053064 17.8142976561 18.0472879195 18.2707797789 18.4851604594 18.6908013999 18.8880588968

0.04375000 4.3750% 0.9580838323 1.8760084621 2.7554572092 3.5980428352 4.4053105008 5.1787405995 5.9197514726 6.6297020097 7.3098941410 7.9615752249 8.5859403353 9.1841344529 9.7572545657 10.3063516797 10.8324327470 11.3364625121 11.8193652811 12.2820266166 12.7252949620 13.1499831971 13.5568701290 13.9467019200 14.3201934563 14.6780296587 15.0208667389 15.3493334025 15.6640320024 15.9655396430 16.2544092388 16.5311705282 16.7963310450 17.0503770491 17.2937744183 17.5269695026 17.7503899426 17.9644454540 18.1695285787 18.3660154047 18.5542662560

0.04500000 4.5000% 0.9569377990 1.8726677503 2.7489643543 3.5875256979 4.3899767444 5.1578724827 5.8927009404 6.5958860674 7.2687904951 7.9127181771 8.5289169159 9.1185807808 9.6828524218 10.2228252840 10.7395457263 11.2340150491 11.7071914346 12.1599918034 12.5932935918 13.0079364515 13.4047238770 13.7844247627 14.1477748925 14.4954783660 14.8282089627 15.1466114476 15.4513028206 15.7428735126 16.0218885288 16.2888885443 16.5443909515 16.7888908627 17.0228620695 17.2467579613 17.4610124031 17.6660405772 17.8622397868 18.0499902266 18.2296557192

0.04625000 4.6250% 0.9557945042 1.8693376384 2.7424971454 3.5770582035 4.3747270762 5.1371346009 5.8658395230 6.5623316827 7.2280350611 7.8643106916 8.4724594424 9.0537246761 9.6092947920 10.1403056554 10.6478429204 11.1329442489 11.5966014326 12.0397624207 12.4633332575 12.8681799355 13.2551301653 13.6249750684 13.9784707942 14.3163400661 14.6392736594 14.9479318130 15.2429455800 15.5249181170 15.7944259183 16.0520199936 16.2982269951 16.5335502940 16.7584710098 16.9734489938 17.1789237695 17.3753154308 17.5630255014 17.7424377552 17.9139190014

0.04750000 4.7500% 0.9546539379 1.8660180792 2.7360554455 3.5666400435 4.3595609007 5.1165259195 5.8391655556 6.5290363299 7.1876241813 7.8163476671 8.4165610187 8.9895570585 9.5365699842 10.0587780279 10.5573059932 11.0332276785 11.4875681895 11.9213061475 12.3353757971 12.7306690187 13.1080372494 13.4682933168 13.8122131903 14.1405376518 14.4539738920 14.7531970329 15.0388515827 15.3115528236 15.5718881371 15.8204182693 16.0576785387 16.2841799892 16.5004104909 16.7068357908 16.9039005163 17.0920291325 17.2716268568 17.4430805316 17.6067594573

0.04875000 4.8750% 0.9535160906 1.8627090256 2.7296391186 3.5562709116 4.3444776273 5.0960454134 5.8126773906 6.4959975119 7.1475542426 7.7688240692 8.3612148455 8.9260689826 9.4646664911 9.9782278819 10.4679169315 10.9348433196 11.3800651439 11.8045913172 12.2093838543 12.5953600518 12.9633945666 13.3143213985 13.6489357792 13.9679959754 14.2722250064 14.5623122826 14.8389151681 15.1026604702 15.3541458596 15.5939412248 15.8225899641 16.0406102161 16.2484960344 16.4467185072 16.6357268245 16.8159492963 16.9877943230 17.1516513211 17.3078916054

19.0772747211 19.2587767109 19.4328793390 19.5998842580 19.7600808230 19.9137465928 20.0611478109 20.2025398666 20.3381677377 20.4682664151 20.5930613094 20.7127686421 20.8275958198 20.9377417936 21.0433974039 21.1447457112 21.2419623129 21.3352156478 21.4246672881 21.5104722188 21.5927791068

18.7346263531 18.9074264460 19.0729834214 19.2316008827 19.3835697080 19.5291685825 19.6686645102 19.8023133032 19.9303600510 20.0530395698 20.1705768333 20.2831873852 20.3910777343 20.4944457335 20.5934809423 20.6883649746 20.7792718320 20.8663682223 20.9498138656 21.0297617874 21.1063585987

18.4015844203 18.5661094931 18.7235497542 18.8742102911 19.0183830536 19.1563474198 19.2883707366 19.4147088389 19.5356065444 19.6512981286 19.7620077785 19.8679500273 19.9693301697 20.0663446600 20.1591814928 20.2480205673 20.3330340357 20.4143866370 20.4922360163 20.5667330299 20.6380220382

18.0778198341 18.2344753492 18.3842058295 18.5273173998 18.6641026521 18.7948412446 18.9198004727 19.0392358162 19.1533914611 19.2625007992 19.3667869048 19.4664629915 19.5617328473 19.6527912519 19.7398243746 19.8230101549 19.9025186666 19.9785124651 20.0511469200 20.1205705329 20.1869252405

17.7630161884 17.9121872920 18.0545940735 18.1905432683 18.3203277024 18.4442269236 18.5625078029 18.6754251102 18.7832220622 18.8861308470 18.9843731236 19.0781604999 19.1676949880 19.2531694396 19.3347679614 19.4126663116 19.4870322784 19.5580260414 19.6258005169 19.6905016867 19.7522689134

17.4568692304 17.5989217930 17.7343711971 17.8635243834 17.9866740247 18.1040991892 18.2160659731 18.3228281030 18.4246275118 18.5216948861 18.6142501894 18.7025031603 18.7866537882 18.8668927658 18.9434019221 19.0163546337 19.0859162181 19.1522443081 19.2154892091 19.2757942399 19.3332960571

0.05000000 5.0000% 0.9523809524 1.8594104308 2.7232480294 3.5459505042 4.3294766706 5.0756920673 5.7863733974 6.4632127594 7.1078216756 7.7217349292 8.3064142183 8.8632516364 9.3935729871 9.8986409401 10.3796580382 10.8377695602 11.2740662478 11.6895869027 12.0853208597 12.4622103425 12.8211527072 13.1630025783 13.4885738841 13.7986417943 14.0939445660 14.3751853010 14.6430336200 14.8981272571 15.1410735782 15.3724510269 15.5928105018 15.8026766684 16.0025492080 16.1929040076 16.3741942929 16.5468517076 16.7112873405 16.8678927053 17.0170406717

0.05125000 5.1250% 0.9512485137 1.8561222484 2.7168820437 3.5356785196 4.3145574502 5.0554648754 5.7602519623 6.4306796312 7.0684229548 7.6750753434 8.2521525265 8.8010963391 9.3232783249 9.8200031628 10.2925119266 10.7419851858 11.1695459556 11.5762625023 11.9631510129 12.3311781336 12.6812633851 13.0142814603 13.3310644093 13.6324037187 13.9190522889 14.1917263152 14.4511070775 14.6978426421 14.9325494812 15.1558140130 15.3681940671 15.5702202779 15.7623974106 15.9452056224 16.1191016622 16.2845200116 16.4418739706 16.5915566903 16.7339421548

0.05250000 5.2500% 0.9501187648 1.8528444322 2.7105410282 3.5254546586 4.2997193906 5.0353628414 5.7343114883 6.3983957133 7.0293545970 7.6288404722 8.1984232515 8.7395945382 9.2537715328 9.7423007437 10.2064615142 10.6474693722 11.0664792135 11.4645883263 11.8428392649 12.2022225795 12.5436794105 12.8681039529 13.1763457985 13.4692121601 13.7474699859 14.0118479676 14.2630384490 14.5016992389 14.7284553339 14.9439005548 15.1485991019 15.3430870327 15.5278736653 15.7034429124 15.8702545486 16.0287454143 16.1793305599 16.3224043325 16.4583414085

0.05375000 5.3750% 0.9489916963 1.8495769360 2.7042248503 3.5152786243 4.2849619210 5.0153849784 5.7085503947 6.3663586189 6.9906131615 7.5830255388 8.1452199656 8.6787378084 9.1850418111 9.6655201054 10.1214900170 10.5542016769 10.9648414490 11.3545351829 11.7243513005 12.0753037253 12.4083546622 12.7244172358 13.0243579936 13.3089992822 13.5791215015 13.8354652446 14.0787333282 14.3095927195 14.5286763649 14.7365849252 14.9338884225 15.1211278031 15.2988164205 15.4674414429 15.6274651890 15.7793263952 15.9234414190 16.0602053798 16.1899932430

0.05500000 5.5000% 0.9478672986 1.8463197143 2.6979333785 3.5051501218 4.2702844756 4.9955303086 5.6829671172 6.3345659879 6.9521952492 7.5376258286 8.0925363304 8.6185178487 9.1170785296 9.5896478954 10.0375809435 10.4621620317 10.8646085609 11.2460744653 11.6076535216 11.9503824849 12.2752440615 12.5831697266 12.8750423949 13.1516989525 13.4139326564 13.6624954089 13.8980999136 14.1214217191 14.3331011555 14.5337451711 14.7239290722 14.9041981727 15.0750693580 15.2370325668 15.3905521960 15.5360684322 15.6739985140 15.8047379279 15.9286615431

0.05625000 5.6250% 0.9467455621 1.8430727215 2.6916664819 3.4950688586 4.2556864934 4.9757978636 5.6575601075 6.3030154864 6.9140975019 7.4926366882 8.0403660953 8.5589264808 9.0498712244 9.5146709817 9.9547180892 10.3713307353 10.7657569092 11.1391781389 11.4927130309 11.8274206210 12.1443035465 12.4443110499 12.7283418224 12.9972466958 13.2518311913 13.4928579325 13.7210489302 13.9370877446 14.1416215333 14.3352629901 14.5185921800 14.6921582769 14.8564812089 15.0120532156 15.1593403224 15.2987837372 15.4308011713 15.5557880912 15.6741189029

17.1590863540 17.2943679562 17.4232075773 17.5459119784 17.6627733128 17.7740698217 17.8800664968 17.9810157113 18.0771578203 18.1687217336 18.2559254606 18.3389766291 18.4180729801 18.4934028382 18.5651455602 18.6334719621 18.6985447258 18.7605187865 18.8195417014 18.8757540013 18.9292895251

16.8693861164 16.9982269835 17.1207866668 17.2373713834 17.3482724218 17.4537668697 17.5541183065 17.6495774616 17.7403828410 17.8267613232 17.9089287260 17.9870903457 18.0614414704 18.1321678672 18.1994462470 18.2634447059 18.3243231447 18.3822336691 18.4373209695 18.4897226820 18.5395697332

16.5874977753 16.7102116630 16.8268044304 16.9375814066 17.0428326903 17.1428339101 17.2378469454 17.3281206132 17.4138913190 17.4953836760 17.5728110936 17.6463763359 17.7162720532 17.7826812857 17.8457779436 17.9057272623 17.9626862350 18.0168040238 18.0682223504 18.1170758673 18.1634925105

16.3131608475 16.4300458813 16.5409688079 16.6462337442 16.7461292946 16.8409293424 16.9308938006 17.0162693244 17.0972899876 17.1741779242 17.2471439375 17.3163880783 17.3821001930 17.4444604441 17.5036398046 17.5598005263 17.6130965849 17.6636741019 17.7116717456 17.7572211109 17.8004470803

16.0461246854 16.1574641568 16.2629992007 16.3630324177 16.4578506329 16.5477257184 16.6329153729 16.7136638606 16.7902027114 16.8627513853 16.9315179007 16.9966994320 17.0584828739 17.1170453781 17.1725548608 17.2251704841 17.2750431129 17.3223157468 17.3671239307 17.4095961428 17.4498541638

15.7861480738 15.8922111941 15.9926259826 16.0876932379 16.1776977401 16.2629091030 16.3435825827 16.4199598416 16.4922696726 16.5607286841 16.6255419494 16.6869036208 16.7449975108 16.7999976433 16.8520687748 16.9013668873 16.9480396567 16.9922268939 17.0340609646 17.0736671854 17.1111641992

0.05750000 5.7500% 0.9456264775 1.8398359126 2.6854240308 3.4850345445 4.2411674180 4.9561866836 5.6323278332 6.2717048068 6.8763166022 7.4480535246 7.9887030965 8.4999556468 8.9834095951 9.4405764493 9.8728855312 10.2816884456 10.6682633055 11.0338187286 11.3794976157 11.7063807241 12.0154900464 12.3077920061 12.5842004786 12.8455796488 13.0927467128 13.3264744329 13.5474935535 13.7564950861 13.9541324691 14.1410236115 14.3177528241 14.4848726469 14.6429055762 14.7923456986 14.9336602351 15.0672910024 15.1936557943 15.3131496872 15.4261462763

0.05875000 5.8750% 0.9445100354 1.8366092424 2.6792058960 3.4750468912 4.2267266977 4.9366958184 5.6072687777 6.2406316672 6.8388492725 7.4038718040 7.9375412552 8.4415974075 8.9176835018 9.3673515956 9.7920676227 10.1932161726 10.5721050036 10.9299693069 11.2679757326 11.5872261937 11.8887614580 12.1735645412 12.4425639114 12.6966365161 12.9366106410 13.1632686101 13.3773493366 13.5795507311 13.7705319775 13.9509156812 14.1212898996 14.2822100586 14.4342007638 14.5777575101 14.7133482976 14.8414151571 14.9623755911 15.0766239349 15.1845326422

0.06000000 6.0000% 0.9433962264 1.8333926664 2.6730119495 3.4651056127 4.2123637856 4.9173243260 5.5823814396 6.2097938110 6.8016922745 7.3600870514 7.8868745768 8.3838439404 8.8526829626 9.2949839270 9.7122489877 10.1058952715 10.4772596901 10.8276034812 11.1581164917 11.4699212186 11.7640766213 12.0415817182 12.3033789794 12.5503575278 12.7833561583 13.0031661870 13.2105341387 13.4061642818 13.5907210206 13.7648311515 13.9290859920 14.0840433887 14.2302296119 14.3681411433 14.4982463616 14.6209871336 14.7367803147 14.8460191648 14.9490746838

0.06125000 6.1250% 0.9422850412 1.8301861401 2.6668420637 3.4552104252 4.1980781392 4.8980712737 5.5576643332 6.1791890066 6.7648424090 7.3166948495 7.8366971491 8.3266875375 8.7883981507 9.2234611550 9.6334145159 10.0197074355 10.3837054751 10.7266953829 11.0498896423 11.3544307584 11.6413952965 11.9117976881 12.1665938168 12.4066843974 12.6329181601 12.8460948505 13.0469680570 13.2362478747 13.4146034155 13.5826651736 13.7410272543 13.8902494740 14.0308593395 14.1633539123 14.2882015664 14.4058436433 14.5166960125 14.6211505418 14.7195764823

0.06250000 6.2500% 0.9411764706 1.8269896194 2.6606961124 3.4453610469 4.1838692206 4.8789357371 5.5331159878 6.1488150474 6.7282965152 7.2736908378 7.7870031415 8.2701206037 8.7248193917 9.1527711922 9.5555493574 9.9346346893 10.2914208841 10.6272196556 10.9432655582 11.2407205254 11.5206781415 11.7841676626 12.0321578001 12.2655602824 12.4852332070 12.6919841948 12.8865733598 13.0697161034 13.2420857444 13.4043159947 13.5570032891 13.7007089780 13.8359613911 13.9632577798 14.0830661457 14.1958269607 14.3019547865 14.4018397991 14.4958492227

0.06375000 6.3750% 0.9400705053 1.8238030602 2.6545739696 3.4355571982 4.1697364966 4.8599168006 5.5087349476 6.1186697510 6.6920514698 7.2310707119 7.7377868032 8.2141356552 8.6619371612 9.0829021492 9.4786389181 9.8506593825 10.2003848484 10.5291514439 10.8382152234 11.1287569667 11.4018866902 11.6586478874 11.9000215158 12.1269297446 12.3402394779 12.5407656666 12.7292744222 12.9064859433 13.0730772675 13.2296848578 13.3769070344 13.5153062603 13.6454112905 13.7677191920 13.8826972428 13.9907847171 14.0923945637 14.1879149835 14.2777109128

15.5329988429 15.6340414590 15.7295900321 15.8199432928 15.9053837284 15.9861784666 16.0625801103 16.1348275274 16.2031465980 16.2677509201 16.3288424777 16.3866122720 16.4412409192 16.4928992143 16.5417486660 16.5879420010 16.6316236416 16.6729301575 16.7119906927 16.7489273690 16.7838556681

15.2864534991 15.3827187713 15.4736422870 15.5595204599 15.6406332561 15.7172451062 15.7896057673 15.8579511380 15.9225040264 15.9834748774 16.0410624580 16.0954545058 16.1468283407 16.1953514434 16.2411820009 16.2844694223 16.3253548263 16.3639715006 16.4004453371 16.4348952416 16.4674335222

15.0462968715 15.1380159165 15.2245433175 15.3061729410 15.3831820198 15.4558320942 15.5243699002 15.5890282077 15.6500266110 15.7075722746 15.7618606364 15.8130760721 15.8613925208 15.9069740762 15.9499755436 15.9905429657 16.0288141186 16.0649189798 16.0989801696 16.1311133676 16.1614277052

14.8123217736 14.8997142743 14.9820629205 15.0596588179 15.1327762712 15.2016737538 15.2665948210 15.3277689715 15.3854124584 15.4397290539 15.4909107693 15.5391385341 15.5845828354 15.6274043208 15.6677543658 15.7057756097 15.7416024591 15.7753615634 15.8071722623 15.8371470081 15.8653917626

14.5843286801 14.6676034637 14.7459797305 14.8197456287 14.8891723564 14.9545151590 15.0160142673 15.0738957810 15.1283724997 15.1796447056 15.2279008994 15.2733184936 15.3160644645 15.3562959666 15.3941609098 15.4297985033 15.4633397678 15.4949080168 15.5246193099 15.5525828799 15.5789015340

14.3621254174 14.4414810034 14.5160808493 14.5862099641 14.6521362765 14.7141116582 14.7723728867 14.8271425492 14.8786298935 14.9270316273 14.9725326696 15.0153068574 15.0555176098 15.0933185521 15.1288541030 15.1622600263 15.1936639496 15.2231858515 15.2509385208 15.2770279867 15.3015539240

0.06500000 6.5000% 0.9389671362 1.8206264189 2.6484755107 3.4257986016 4.1556794381 4.8410135569 5.4845197718 6.0887509594 6.6561041872 7.1888302228 7.6890424627 8.1587253171 8.5997420818 9.0138423303 9.4026688547 9.7677641828 10.1105766975 10.4324663826 10.7347102184 11.0185072474 11.2849833309 11.5351956158 11.7701367285 11.9907387122 12.1978767251 12.3923725118 12.5749976637 12.7464766795 12.9074898399 13.0586759060 13.2006346535 13.3339292521 13.4590884997 13.5766089199 13.6869567323 13.7905697017 13.8878588748 13.9792102111 14.0649861137

0.06625000 6.6250% 0.9378663540 1.8174596521 2.6424006116 3.4160849815 4.1416975208 4.8222251074 5.4604690339 6.0590565383 6.6204516185 7.1469651757 7.6407645258 8.1038823220 8.5382249210 8.9455802307 9.3276250698 9.6859320702 10.0219761502 10.3371405864 10.6327227070 10.9099392329 11.1699312852 11.4137690834 11.6424563502 11.8569344434 12.0580862306 12.2467397239 12.4236714878 12.5896098362 12.7452378299 12.8911960890 13.0280854293 13.1564693358 13.2768762821 13.3898019059 13.4957110489 13.5950396707 13.6881966431 13.7755654332 13.8575056817

0.06750000 6.7500% 0.9367681499 1.8143027165 2.6363491490 3.4064160646 4.1277902245 4.8035505615 5.4365813223 6.0295843769 6.5850907512 7.1054714297 7.5929474751 8.0495995083 8.4773765885 8.8781045326 9.2534937074 9.6051463301 9.9345633069 10.2431506387 10.5322254227 10.8030214733 11.0566945885 11.2943274834 11.5169344107 11.7254654901 11.9208107636 12.1038039940 12.2752262239 12.4358091090 12.5862380412 12.7271550737 12.8591616616 12.9828212287 13.0986615725 13.2071771171 13.3088310230 13.4040571644 13.4932619807 13.5768262115 13.6551065213

0.06875000 6.8750% 0.9356725146 1.8111555692 2.6303210005 3.3967915794 4.1139570333 4.7849890370 5.4128552393 6.0003323877 6.5500186084 7.0643448967 7.5455858683 7.9958698183 8.4171881340 8.8114041020 9.1802611481 9.5253905479 9.8483186413 10.1504735825 10.4331916562 10.6977231871 10.9452380698 11.1768309425 11.3935260280 11.5962816637 11.7859945391 11.9635036623 12.1295940700 12.2850002994 12.4304096369 12.5664651573 12.6937685683 12.8128828709 12.9243348499 13.0286174035 13.1261917225 13.2174893310 13.3029139939 13.3828435031 13.4576313479

0.07000000 7.0000% 0.9345794393 1.8080181675 2.6243160444 3.3872112565 4.1001974359 4.7665396598 5.3892894016 5.9712985062 6.5152322488 7.0235815409 7.4986743373 7.9426862966 8.3576507444 8.7454679855 9.1079140051 9.4466486029 9.7632229934 10.0590869097 10.3355952427 10.5940142455 10.8355273323 11.0612404974 11.2721873808 11.4693340007 11.6535831783 11.8257786713 11.9867090386 12.1371112510 12.2776740664 12.4090411835 12.5318141902 12.6465553179 12.7537900168 12.8540093615 12.9476723004 13.0352077574 13.1170165957 13.1934734539 13.2649284616

0.07125000 7.1250% 0.9334889148 1.8048904689 2.6183341600 3.3776748285 4.0865109251 4.7482015637 5.3658824398 5.9424806906 6.4807287660 6.9831773779 7.4522075873 7.8900420885 8.2987557419 8.6802854066 9.0364391194 9.3689046622 9.6792575610 9.9689685517 10.2394105500 10.4918651575 10.7275287351 10.9475180725 11.1528756803 11.3445747307 11.5235236693 11.6905705197 11.8465069029 11.9920717880 12.1279549946 12.2548004617 12.3732092992 12.4837426363 12.5869242813 12.6832432031 12.7731558488 12.8570883070 12.9354383262 13.0085772007 13.0768515292

14.1455268673 14.2211519881 14.2921614912 14.3588370809 14.4214432685 14.4802284211 14.5354257475 14.5872542230 14.6359194582 14.6816145148 14.7245206711 14.7648081419 14.8026367530 14.8381565756 14.8715085216 14.9028249030 14.9322299558 14.9598403341 14.9857655719 15.0101085182 15.0329657448

13.9343546839 14.0064287774 14.0740246447 14.1374205343 14.1968774062 14.2526400058 14.3049378718 14.3539862807 14.3999871331 14.4431297849 14.4835918264 14.5215398137 14.5571299542 14.5905087496 14.6218135987 14.6511733633 14.6787088988 14.7045335510 14.7287536235 14.7514688145 14.7727726279

13.7284370223 13.7971307000 13.8614807494 13.9217618262 13.9782312189 14.0311299474 14.0806837915 14.1271042544 14.1705894654 14.2113250262 14.2494848020 14.2852316647 14.3187181870 14.3500872947 14.3794728756 14.4070003518 14.4327872148 14.4569435267 14.4795723904 14.5007703891 14.5206279992

13.5276082788 13.5930837696 13.6543473868 13.7116700695 13.7653053282 13.8154903655 13.8624471257 13.9063832755 13.9474931232 13.9859584779 14.0219494530 14.0556252192 14.0871347080 14.1166172706 14.1442032942 14.1700147782 14.1941658743 14.2167633912 14.2379072666 14.2576910097 14.2762021143

13.3317088426 13.3941204137 13.4524489847 13.5069616680 13.5579081009 13.6055215896 13.6500201772 13.6916076423 13.7304744320 13.7667985346 13.8007462940 13.8324731720 13.8621244598 13.8898359437 13.9157345269 13.9399388102 13.9625596357 13.9837005941 14.0034584991 14.0219238310 14.0391811504

13.1405848581 13.2000792141 13.2556165359 13.3074600102 13.3558553187 13.4010318028 13.4432035498 13.4825704083 13.5193189342 13.5536232758 13.5856459984 13.6155388550 13.6434435052 13.6694921869 13.6938083425 13.7165072042 13.7376963400 13.7574761634 13.7759404092 13.7931765780 13.8092663505

0.07250000 7.2500% 0.9324009324 1.8017724311 2.6123752272 3.3681820300 4.0728969977 4.7299738906 5.3426329982 5.9138769214 6.4465052880 6.9431284737 7.4061803951 7.8379304383 8.2404945811 8.6158457633 8.9658235555 9.2921431753 9.5964038931 9.8800968700 10.1446124662 10.3912470547 10.6212093750 10.8356264569 11.0355491440 11.2219572438 11.3957643299 11.5578222190 11.7089251459 11.8498136559 11.9811782339 12.1036626890 12.2178673091 12.3243518033 12.4236380451 12.5162126294 12.6025292582 12.6830109634 12.7580521803 12.8280206809 12.8932593761

0.07375000 7.3750% 0.9313154831 1.7986640122 2.6064391266 3.3587325976 4.0593551549 4.7118557903 5.3195397349 5.8854852013 6.4125589768 6.9034309446 7.3605876085 7.7863446878 8.1828588477 8.5521386242 8.8960545976 9.2163488686 9.5146438823 9.7924506470 10.0511763884 10.2921316772 10.5165370684 10.7255292837 10.9201669697 11.1014360603 11.2702547709 11.4274782500 11.5739029103 11.7102704636 11.8372716774 11.9555498742 12.0657041902 12.1682926102 12.2638347941 12.3528147093 12.4356830820 12.5128596806 12.5847354417 12.6516744510 12.7140157867

0.07500000 7.5000% 0.9302325581 1.7955651704 2.6005257399 3.3493262696 4.0458849020 4.6938464205 5.2966013214 5.8573035548 6.3788870277 6.8640809560 7.3154241451 7.7352782745 8.1258402554 8.4891537259 8.8271197450 9.1415067396 9.4339597577 9.7060090770 9.9590782111 10.1944913592 10.4134803341 10.6171910085 10.8066893102 10.9829668002 11.1469458607 11.2994845215 11.4413809503 11.5733776282 11.6961652355 11.8103862656 11.9166383866 12.0154775689 12.1074209943 12.1929497622 12.2725114067 12.3465222388 12.4153695244 12.4794135111 12.5389893127

0.07625000 7.6250% 0.9291521487 1.7924758640 2.5946349492 3.3399627867 4.0324857484 4.6759449462 5.2738164425 5.8293300279 6.3454866693 6.8250747218 7.2706849912 7.6847247305 8.0694306439 8.4268809699 8.7590067084 9.0676020520 9.3543340785 9.6207517570 9.8682943155 10.0982990155 10.3120083768 10.5105768890 10.6950772488 10.8665061545 11.0257896906 11.1737883304 11.3113015846 11.4390723202 11.5577907737 11.6680982798 11.7705907362 11.8658218223 11.9543059905 12.0365212455 12.1129117264 12.1838901058 12.2498398196 12.3111171378 12.3680530897

0.07750000 7.7500% 0.9280742459 1.7893960519 2.5887666375 3.3306418910 4.0191572074 4.6581505405 5.2511837963 5.8015626880 6.3123551628 6.7864085038 7.2263652007 7.6346776805 8.0136219773 8.3653104197 8.6917034058 8.9946203302 9.2757497264 9.5366586788 9.7788015580 10.0035281281 10.2120910702 10.4056529654 10.5852927753 10.7520118564 10.9067395419 11.0503383220 11.1836086515 11.3072934120 11.4220820529 11.5286144343 11.6274843938 11.7192430569 11.8044019089 11.8834356463 11.9567848226 12.0248583040 12.0880355490 12.1466687229 12.2010846617

12.9540879964 13.0108046587 13.0636873274 13.1129951771 13.1589698621 13.2018367012 13.2418057820 13.2790729902 13.3138209699 13.3462200186 13.3764289218 13.4045957312 13.4308584907 13.4553459120 13.4781780066 13.4994666728 13.5193162450 13.5378240047 13.5550806570 13.5711707758 13.5861732175

12.7720752379 12.8261469038 12.8765046834 12.9234036632 12.9670814093 13.0077591704 13.0456429993 13.0809247956 13.1137832788 13.1443848929 13.1728846500 13.1994269150 13.2241461374 13.2471675319 13.2686077131 13.2885752857 13.3071713953 13.3244902401 13.3406195484 13.3556410230 13.3696307548

12.5944086629 12.6459615469 12.6939177181 12.7385281098 12.7800261487 12.8186289755 12.8545385819 12.8879428669 12.9190166203 12.9479224375 12.9748115698 12.9998247161 13.0230927591 13.0447374504 13.0648720469 13.0836019040 13.1010250270 13.1172325833 13.1323093798 13.1463343068 13.1593807505

12.4209552518 12.4701094093 12.5157811004 12.5582170503 12.5976465044 12.6342824663 12.6683228491 12.6999515438 12.7293394136 12.7566452159 12.7820164607 12.8055902074 12.8274938048 12.8478455794 12.8667554744 12.8843256441 12.9006510050 12.9158197491 12.9299138203 12.9430093568 12.9551771027

12.2515866930 12.2984563276 12.3419548284 12.3823246667 12.4197908740 12.4545622960 12.4868327573 12.5167821414 12.5445773934 12.5703734509 12.5943141076 12.6165328145 12.6371534241 12.6562908808 12.6740518616 12.6905353704 12.7058332904 12.7200308959 12.7332073280 12.7454360353 12.7567851836

0.07875000 7.8750% 0.9269988413 1.7863256929 2.5829206887 3.3213633267 4.0058987965 4.6404623838 5.2287020939 5.7739996235 6.2794898016 6.7480786110 7.1824598943 7.5851308406 7.9584063413 8.3044322978 8.6251979586 8.9225473544 9.1981898998 9.4537102200 9.6905772607 9.9101527330 10.1136989414 10.3023860407 10.4772987631 10.6394426541 10.7897498531 10.9290844525 11.0582474646 11.1779814272 11.2889746718 11.3918652810 11.4872447564 11.5756614196 11.6576235639 11.7336023768 11.8040346482 11.8693252822 11.9298496243 11.9859556193 12.0379658116

0.08000000 8.0000% 0.9259259259 1.7832647462 2.5770969872 3.3121268400 3.9927100371 4.6228796640 5.2063700592 5.7466389437 6.2468879109 6.7100813989 7.1389642583 7.5360780169 7.9037759416 8.2442369830 8.5594786879 8.8513691555 9.1216381069 9.3718871360 9.6035992000 9.8181474074 10.0168031550 10.2007436621 10.3710589464 10.5287582837 10.6747761886 10.8099779524 10.9351647707 11.0510784914 11.1584060106 11.2577833431 11.3497993918 11.4349994368 11.5138883674 11.5869336736 11.6545682163 11.7171927928 11.7751785119 11.8288689925 11.8785824004

0.08125000 8.1250% 0.9248554913 1.7802131712 2.5712954184 3.3029321789 3.9795904545 4.6054015764 5.1841864290 5.7194787783 6.2145468470 6.6724132689 7.0958735435 7.4875131038 7.8497231018 8.1847150074 8.4945341109 8.7810720101 9.0460781596 9.2911705522 9.5178455975 9.7274872578 9.9213754985 10.1006941027 10.2665378984 10.4199194436 10.5617752080 10.6929712906 10.8143087081 10.9265282849 11.0303151768 11.1263030537 11.2150779687 11.2971819364 11.3731162418 11.4433445011 11.5082954923 11.5683657732 11.6239221024 11.6753036785 11.7228242114

0.08250000 8.2500% 0.9237875289 1.7771709274 2.5655158682 3.2937790931 3.9665395779 4.5880273237 5.1621499526 5.6925172772 6.1824639974 6.6350706674 7.0531830645 7.4394300827 7.7962402612 8.1258570542 8.4303529369 8.7116424359 8.9714941672 9.2115419558 9.4332951093 9.6381479070 9.8273883667 10.0022063434 10.1637010100 10.3128877691 10.4507046366 10.5780181400 10.6956287668 10.8042759970 10.9046429534 10.9973606959 11.0830121903 11.1621359725 11.2352295358 11.3027524580 11.3651292915 11.4227522323 11.4759835864 11.5251580475 11.5705848014

0.08375000 8.3750% 0.9227220300 1.7741379746 2.5597582234 3.2846673342 3.9535569404 4.5707561157 5.1402593917 5.6657526105 6.1506367802 6.5980500855 7.0108881989 7.3918230209 7.7433199731 8.0676539544 8.3669240641 8.6430671872 8.8978705302 9.1329831882 9.3499268173 9.5501054831 9.7348147479 9.9052500558 10.0625144690 10.2076258076 10.3415232365 10.4650733440 10.5790757499 10.6842682814 10.7813317475 10.8708943460 10.9535357287 11.0297907532 11.1001529441 11.1650776878 11.2249851790 11.2802631410 11.3312693342 11.3783338724 11.4217613586

12.0861791997 12.1308729545 12.1723040134 12.2107105571 12.2463133785 12.2793171527 12.3099116132 12.3382726426 12.3645632840 12.3889346781 12.4115269322 12.4324699255 12.4518840561 12.4698809327 12.4865640164 12.5020292156 12.5163654374 12.5296550984 12.5419745988 12.5533947613 12.5639812388

11.9246133337 11.9672345683 12.0066986743 12.0432395133 12.0770736234 12.1084015032 12.1374087992 12.1642674067 12.1891364877 12.2121634145 12.2334846431 12.2532265214 12.2715060383 12.2884315169 12.3041032564 12.3186141263 12.3320501170 12.3444908490 12.3560100454 12.3666759680 12.3765518222

11.7667738371 11.8074208898 11.8450135397 11.8797813084 11.9119364702 11.9416753481 11.9691795127 11.9946168904 12.0181427888 12.0399008451 12.0600239030 12.0786348236 12.0958472357 12.1117662295 12.1264889984 12.1401054321 12.1526986655 12.1643455866 12.1751173055 12.1850795889 12.1942932614

11.6125494701 11.6513159077 11.6871278593 11.7202104936 11.7507718186 11.7790039894 11.8050845168 11.8291773827 11.8514340718 11.8719945236 11.8909880126 11.9085339608 11.9247426890 11.9397161099 11.9535483694 11.9663264383 11.9781306589 11.9890352507 11.9991087766 12.0084145743 12.0170111541

11.4618328569 11.4988077111 11.5329252236 11.5644062040 11.5934543981 11.6202578068 11.6449899025 11.6678107520 11.6888680526 11.7082980878 11.7262266092 11.7427696510 11.7580342800 11.7721192895 11.7851158381 11.7971080397 11.8081735084 11.8183838601 11.8278051766 11.8364984328 11.8445198919

0.08500000 8.5000% 0.9216589862 1.7711142730 2.5540223714 3.2755966557 3.9406420790 4.5535871695 5.1185135203 5.6391829680 6.1190626434 6.5613480584 6.9689843856 7.3446860697 7.6909549029 8.0100966847 8.3042365758 8.5753332496 8.8251919351 9.0554764379 9.2677202192 9.4633366076 9.6436282098 9.8097955850 9.9629452397 10.1040969951 10.2341907789 10.3540928838 10.4646017362 10.5664532131 10.6603255420 10.7468438175 10.8265841636 10.9000775701 10.9678134287 11.0302427914 11.0877813746 11.1408123268 11.1896887805 11.2347362032 11.2762545652

0.08625000 8.6250% 0.9205983890 1.7680997827 2.5483082004 3.2665668128 3.9277945342 4.5365197093 5.0969111248 5.6128065591 6.0877390647 6.5249611643 6.9274671248 7.2980134636 7.6391378261 7.9531763646 8.2422797373 8.5084278364 8.7534433477 8.9790042326 9.1866552199 9.3778183842 9.5538028854 9.7158139336 9.8649610436 10.0022656328 10.1286680164 10.2450338470 10.3521600433 10.4507802470 10.5415698476 10.6251506077 10.7020949208 10.7729297315 10.8381401440 10.8981727448 10.9534386604 11.0043163732 11.0511543136 11.0942732461 11.1339684659

0.08750000 8.7500% 0.9195402299 1.7650944643 2.5426155993 3.2575775626 3.9150138507 4.5195529661 5.0754510033 5.5866216123 6.0566635515 6.4888860244 6.8863319764 7.2517995186 7.5878616263 7.8968842540 8.1810429922 8.4423383836 8.6826100080 8.9035494326 9.1067121219 9.2935283880 9.4653134602 9.6232767450 9.7685303403 9.9020968646 10.0249166571 10.1378543973 10.2417051930 10.3372001774 10.4250116574 10.5057578459 10.5800072146 10.6482824962 10.7110643643 10.7687948178 10.8218802922 10.8706945216 10.9155811692 10.9568562476 10.9948103426

0.08875000 8.8750% 0.9184845006 1.7620982784 2.5369444577 3.2486286638 3.9022995764 4.5026861781 5.0541319661 5.5606263753 6.0258336398 6.4531193018 6.8455745596 7.2060386311 7.5371192938 7.8412117509 8.1205159595 8.3770525460 8.6126774246 8.8290952235 9.0278716174 9.2104446544 9.3781351590 9.5321562884 9.6736223085 9.8035566554 9.9228993390 10.0325137442 10.1331928764 10.2256650989 10.3105994020 10.3886102429 10.4602619912 10.5260730114 10.5865194135 10.6420384969 10.6930319145 10.7398685782 10.7828873278 10.8223993826 10.8586905925

0.09000000 9.0000% 0.9174311927 1.7591111859 2.5312946660 3.2397198771 3.8896512634 4.4859185902 5.0329528351 5.5348191147 5.9952468943 6.4176577012 6.8051905515 7.1607252766 7.4869039235 7.7861503885 8.0606884299 8.3125581925 8.5436313693 8.7556251094 8.9501147793 9.1285456691 9.2922437331 9.4424254432 9.5802068286 9.7066117694 9.8225796049 9.9289721146 10.0265799217 10.1161283685 10.1982829069 10.2736540430 10.3428018743 10.4062402517 10.4644405979 10.5178354109 10.5668214779 10.6117628237 10.6529934163 10.6908196480 10.7255226128

11.3145203366 11.3497883286 11.3822933904 11.4122519728 11.4398635694 11.4653120455 11.4887668622 11.5103842048 11.5303080229 11.5486709888 11.5655953814 11.5811938999 11.5955704146 11.6088206587 11.6210328651 11.6322883550 11.6426620783 11.6522231136 11.6610351278 11.6691567998 11.6766422118

11.1705118214 11.2041535755 11.2351241201 11.2636355536 11.2898831334 11.3140466130 11.3362914734 11.3567700561 11.3756226063 11.3929782336 11.4089557962 11.4236647146 11.4372057211 11.4496715499 11.4611475719 11.4717123792 11.4814383237 11.4903920127 11.4986347642 11.5062230281 11.5132087715

11.0297106599 11.0618029056 11.0913130167 11.1184487510 11.1434011503 11.1663458853 11.1874444923 11.2068455101 11.2246855266 11.2410901394 11.2561748408 11.2700458306 11.2828007638 11.2945294380 11.3053144257 11.3152316558 11.3243509479 11.3327365038 11.3404473598 11.3475378021 11.3540577491

10.8920235063 10.9226392710 10.9507593764 10.9765872573 11.0003097656 11.0220985218 11.0421111566 11.0604924516 11.0773753861 11.0928820997 11.1071247758 11.1202064531 11.1322217710 11.1432576542 11.1533939418 11.1627039649 11.1712550769 11.1791091406 11.1863229765 11.1929487729 11.1990344642

10.7573601952 10.7865689865 10.8133660426 10.8379504978 10.8605050439 10.8811972880 10.9001809981 10.9175972460 10.9335754550 10.9482343624 10.9616829013 10.9740210104 10.9853403765 10.9957251160 11.0052524000 11.0139930276 11.0220119519 11.0293687632 11.0361181314 11.0423102123 11.0479910204

0.09125000 9.1250% 0.9163802978 1.7561331481 2.5256661151 3.2308509645 3.8770684669 4.4692494542 5.0119124437 5.5091981157 5.9649009079 6.3824979682 6.7651756868 7.1158540085 7.4372087134 7.7316918336 8.0015503630 8.2488434025 8.4754578717 8.6831229065 8.8734230529 9.0478103578 9.2076154481 9.3540576844 9.4882544645 9.6112297499 9.7239218785 9.8271907248 9.9218242610 10.0085445691 10.0880133508 10.1608369767 10.2275711127 10.2887249601 10.3447651409 10.3961192586 10.4431791602 10.4863039269 10.5258226134 10.5620367591 10.5952226888

0.09250000 9.2500% 0.9153318078 1.7531641261 2.5200586967 3.2220216903 3.8645507463 4.4526780286 4.9910096372 5.4837616816 5.9347933013 6.3476368890 6.7255257566 7.0714194568 7.3880269627 7.6778278835 7.9430918842 8.1858964615 8.4081432142 8.6115727361 8.7977782482 8.9682180761 9.1242270720 9.2670270682 9.3977364468 9.5173788987 9.6268914405 9.7271317533 9.8188849000 9.9028694737 9.9797432254 10.0501082154 10.1145155290 10.1734695918 10.2274321206 10.2768257397 10.3220372903 10.3634208607 10.4013005590 10.4359730517 10.4677098872

0.09375000 9.3750% 0.9142857143 1.7502040816 2.5144723032 3.2132318201 3.8520976641 4.4362035786 4.9702432718 5.4585081343 5.9049217227 6.3130712894 6.6862366074 7.0274163268 7.3393520702 7.6245504642 7.8853032815 8.1237058574 8.3416739268 8.5409590188 8.7231625314 8.8897486002 9.0420558630 9.1813082176 9.3086246561 9.4250282570 9.5314544064 9.6287583144 9.7177218875 9.7990600114 9.8734262961 9.9414183279 10.0035824712 10.0604182594 10.1123824086 10.1598924879 10.2033302746 10.2430448225 10.2793552663 10.3125533863 10.3429059532

0.09500000 9.5000% 0.9132420091 1.7472529764 2.5089068277 3.2044811212 3.8397087865 4.4198253758 4.9496122153 5.4334358131 5.8752838476 6.2787980343 6.6473041409 6.9838393981 7.2911775325 7.5718516279 7.8281750026 8.0622602764 8.2760367821 8.4712664676 8.6495584179 8.8123821168 8.9610795588 9.0968763094 9.2208916067 9.3341475861 9.4375777042 9.5320344330 9.6182962859 9.6970742337 9.7690175650 9.8347192374 9.8947207648 9.9495166802 9.9995586120 10.0452590064 10.0869945264 10.1251091565 10.1599170379 10.1917050575 10.2207352123

0.09625000 9.6250% 0.9122006842 1.7443107723 2.5033621640 3.1957693629 3.8273836833 4.4035426986 4.9291153465 5.4085430755 5.8458773779 6.2448140277 6.6087243126 6.9406835235 7.2434969427 7.5197235510 7.7716976520 8.0015485993 8.2112187907 8.4024800827 8.5769487642 8.7360992147 8.8812763646 9.0137070601 9.1345104311 9.2447073488 9.3452290525 9.4369250194 9.5205701431 9.5968712822 9.6664732335 9.7299641810 9.7878806669 9.8407121248 9.8889050170 9.9328666061 9.9729683978 10.0095492797 10.0429183851 10.0733577059 10.1011244752

10.6256336209 10.6535015999 10.6790392668 10.7024414816 10.7238868102 10.7435388868 10.7615476626 10.7780505499 10.7931734707 10.8070318173 10.8197313332 10.8313689193 10.8420333739 10.8518060700 10.8607615762 10.8689682256 10.8764886375 10.8833801947 10.8896954820 10.8954826868 10.9007859673

10.4967596221 10.5233497685 10.5476885753 10.5699666593 10.5903584982 10.6090237970 10.6261087387 10.6417471292 10.6560614455 10.6691637945 10.6811567913 10.6921343628 10.7021824831 10.7113798472 10.7197984872 10.7275043361 10.7345577447 10.7410139539 10.7469235276 10.7523327484 10.7572839802

10.3706568715 10.3960291397 10.4192266420 10.4404357870 10.4598270052 10.4775561191 10.4937655946 10.5085856865 10.5221354848 10.5345238718 10.5458503971 10.5562060773 10.5656741278 10.5743306312 10.5822451485 10.5894812786 10.5960971690 10.6021459831 10.6076763274 10.6127326422 10.6173555586

10.2472467692 10.2714582367 10.2935691660 10.3137617954 10.3322025529 10.3490434273 10.3644232213 10.3784686952 10.3912956121 10.4030096914 10.4137074807 10.4234771513 10.4323992250 10.4405472374 10.4479883447 10.4547838764 10.4609898415 10.4666573895 10.4718332324 10.4765600296 10.4808767393

10.1264533411 10.1495583499 10.1706347548 10.1898606657 10.2073985548 10.2233966292 10.2379900837 10.2513022428 10.2634456035 10.2745227854 10.2846273983 10.2938448331 10.3022529834 10.3099229039 10.3169194107 10.3233016289 10.3291234927 10.3344342009 10.3392786325 10.3436977263 10.3477288268

0.09750000 9.7500% 0.9111617312 1.7413774316 2.4978382065 3.1870963157 3.8151219278 4.3873548317 4.9087515550 5.3838282962 5.8167000421 6.2111162115 6.5704931312 6.8979436275 7.1963039886 7.4681585318 7.7158619879 7.9415598979 8.1472071963 8.3345851446 8.5053167605 8.6608808752 8.8026249432 8.9317767136 9.0494548644 9.1566786919 9.2543769402 9.3433958453 9.4245064650 9.4984113576 9.5657506675 9.6271076697 9.6830138221 9.7339533686 9.7803675341 9.8226583454 9.8611921142 9.8963026098 9.9282939497 9.9574432343 9.9840029470

0.09875000 9.8750% 0.9101251422 1.7384529167 2.4923348502 3.1784617522 3.8029230964 4.3712610661 4.8885197417 5.3592898673 5.7877495948 6.1777015652 6.5326066578 6.8556147056 7.1495924510 7.4171489884 7.6606589201 7.8822834312 8.0839894710 8.2675672091 8.4346459241 8.5867084633 8.7251044035 8.8510620282 8.9656992293 9.0700334283 9.1649906059 9.2514135208 9.3300691884 9.4016556891 9.4668083632 9.5261054500 9.5800732196 9.6291906436 9.6738936460 9.7145789725 9.7516077110 9.7853084969 9.8159804295 9.8438957265 9.8693021402

0.10000000 10.0000% 0.9090909091 1.7355371901 2.4868519910 3.1698654463 3.7907867694 4.3552606995 4.8684188177 5.3349261979 5.7590238163 6.1445671057 6.4950610052 6.8136918229 7.1033562026 7.3666874569 7.6060795063 7.8237086421 8.0215533110 8.2014121009 8.3649200917 8.5135637198 8.6486942907 8.7715402643 8.8832184221 8.9847440201 9.0770400182 9.1609454711 9.2372231556 9.3065665051 9.3696059137 9.4269144670 9.4790131518 9.5263755926 9.5694323569 9.6085748699 9.6441589726 9.6765081569 9.7059165063 9.7326513694 9.7569557903

10.0082031408 10.0302534312 10.0503448121 10.0686513094 10.0853314892 10.1005298307 10.1143779779 10.1269958796 10.1384928288 10.1489684089 10.1585133567 10.1672103477 10.1751347132 10.1823550918 10.1889340244 10.1949284960 10.2003904292 10.2053671336 10.2099017163 10.2140334545 10.2177981362

9.8924251560 9.9134699941 9.9326234304 9.9500554543 9.9659207775 9.9803602070 9.9935018949 10.0054624755 10.0163481005 10.0262553816 10.0352722472 10.0434787233 10.0509476435 10.0577452955 10.0639320096 10.0695626936 10.0746873207 10.0793513726 10.0835962436 10.0874596074 10.0909757519

9.7790507185 9.7991370168 9.8173972880 9.8339975345 9.8490886678 9.8628078798 9.8752798907 9.8866180825 9.8969255295 9.9062959359 9.9148144872 9.9225586247 9.9295987498 9.9359988634 9.9418171486 9.9471064987 9.9519149988 9.9562863626 9.9602603296 9.9638730269 9.9671572972

Tabla para Calcular Tasa Nominal i Compuesta en p Periodos por Año, Equivalente a la Tasa Efec i=

(1+e)1/p-1

2 3 4 6 12 24

0.00250000 0.2500% 0.00249844 0.00249792 0.00249766 0.00249740 0.00249714 0.00249701

I/P

0.005

0.00333333 0.3333% 0.00333056 0.00332964 0.00332917 0.00332871 0.00332825 0.00332802

0.00416667 0.4167% 0.00416234 0.00416089 0.00416017 0.00415945 0.00415873 0.00415837

0.00458333 0.4583% 0.00457809 0.00457635 0.00457548 0.00457460 0.00457373 0.00457330

0.00500000 0.5000% 0.00499377 0.00499169 0.00499065 0.00498962 0.00498858 0.00498806

uivalente a la Tasa Efectiva e Indicada.

0.00541667 0.5417% 0.00540935 0.00540692 0.00540570 0.00540448 0.00540327 0.00540266

0.00583333 0.5833% 0.00582485 0.00582203 0.00582062 0.00581921 0.00581780 0.00581709

0.00625000 0.6250% 0.00624026 0.00623702 0.00623540 0.00623379 0.00623217 0.00623136

0.00666667 0.6667% 0.00665559 0.00665191 0.00665006 0.00664822 0.00664638 0.00664546

0.00750000 0.7500% 0.00748599 0.00748133 0.00747900 0.00747667 0.00747434 0.00747318

0.00875000 0.8750% 0.00873094 0.00872460 0.00872143 0.00871827 0.00871510 0.00871352

0.01000000 1.0000% 0.00997512 0.00996685 0.00996272 0.00995859 0.00995446 0.00995239

0.01125000 1.1250% 0.01121854 0.01120807 0.01120285 0.01119763 0.01119241 0.01118980

0.01625000 1.6250% 0.01618452 0.01616277 0.01615190 0.01614105 0.01613021 0.01612480

0.01750000 1.7500% 0.01742410 0.01739890 0.01738631 0.01737374 0.01736119 0.01735491

0.01875000 1.8750% 0.01866292 0.01863402 0.01861959 0.01860517 0.01859077 0.01858358

0.02000000 2.0000% 0.01990099 0.01986813 0.01985173 0.01983534 0.01981898 0.01981080

0.02250000 2.2500% 0.02237484 0.02233333 0.02231261 0.02229192 0.02227125 0.02226093

0.02500000 2.5000% 0.02484567 0.02479451 0.02476899 0.02474349 0.02471804 0.02470532

0.02750000 2.7500% 0.02731349 0.02725170 0.02722087 0.02719009 0.02715936 0.02714401

0.03000000 3.0000% 0.02977831 0.02970490 0.02966829 0.02963173 0.02959524 0.02957701

0.03250000 3.2500% 0.03224014 0.03215414 0.03211125 0.03206844 0.03202571 0.03200437

0.03500000 3.5000% 0.03469899 0.03459943 0.03454978 0.03450024 0.03445078 0.03442609

0.03750000 3.7500% 0.03715488 0.03704078 0.03698390 0.03692714 0.03687050 0.03684222

0.04000000 4.0000% 0.03960781 0.03947821 0.03941363 0.03934918 0.03928488 0.03925278

0.04500000 4.5000% 0.04450483 0.04434138 0.04425996 0.04417874 0.04409771 0.04405727

0.05000000 5.0000% 0.04939015 0.04918907 0.04908894 0.04898908 0.04888949 0.04883979

0.05500000 5.500% 0.05426386 0.05402139 0.05390070 0.05378036 0.05366039 0.05360053

0.06000000 6.000% 0.05912603 0.05883847 0.05869538 0.05855277 0.05841061 0.05833970

0.06500000 6.500% 0.06397674 0.06364042 0.06347314 0.06330644 0.06314033 0.06305749

0.07000000 7.000% 0.06881609 0.06842737 0.06823410 0.06804156 0.06784974 0.06775411

0.07500000 7.500% 0.07364414 0.07319942 0.07297840 0.07275827 0.07253903 0.07242974

0.08000000 8.000% 0.07846097 0.07795670 0.07770619 0.07745674 0.07720836 0.07708457

0.08500000 8.500% 0.08326667 0.08269933 0.08241758 0.08213712 0.08185792 0.08171880

0.09000000 9.000% 0.08806130 0.08742740 0.08711272 0.08679955 0.08648788 0.08633260

0.09500000 9.500% 0.09284495 0.09214104 0.09179174 0.09144420 0.09109841 0.09092617

0.10000000 10.000% 0.09761770 0.09684035 0.09645476 0.09607121 0.09568969 0.09549968

0.10500000 10.500% 0.10237960 0.10152544 0.10110190 0.10068072 0.10026187 0.10005331

0.11000000 11.000% 0.10713075 0.10619642 0.10573331 0.10527288 0.10481513 0.10458724

0.11500000 11.500% 0.11187121 0.11085339 0.11034909 0.10984784 0.10934962 0.10910164

0.12000000 12.000% 0.11660105 0.11549646 0.11494938 0.11440574 0.11386552 0.11359668

0.12500000 12.500% 0.12132034 0.12012573 0.11953429 0.11894671 0.11836297 0.11807253

0.13000000 13.000% 0.12602916 0.12474131 0.12410394 0.12347089 0.12284213 0.12252935

0.13500000 13.500% 0.13072758 0.12934329 0.12865845 0.12797842 0.12730317 0.12696732

0.14000000 14.000% 0.13541565 0.13393178 0.13319794 0.13246943 0.13174622 0.13138659

0.14500000 14.500% 0.14009346 0.13850687 0.13772252 0.13694406 0.13617145 0.13578732

0.15000000 15.000% 0.14476106 0.14306866 0.14223231 0.14140244 0.14057900 0.14016968

0.15500000 15.500% 0.14941853 0.14761725 0.14672741 0.14584469 0.14496902 0.14453381

0.16000000 16.000% 0.15406592 0.15215272 0.15120794 0.15027094 0.14934166 0.14887988

0.16500000 16.500% 0.15870331 0.15667519 0.15567401 0.15468133 0.15369704 0.15320803

0.17000000 17.000% 0.16333077 0.16118473 0.16012573 0.15907597 0.15803533 0.15751842

0.17500000 17.500% 0.16794834 0.16568144 0.16456321 0.16345498 0.16235666 0.16181118

0.18000000 18.000% 0.17255610 0.17016542 0.16898654 0.16781850 0.16666116 0.16608648

0.18500000 18.500% 0.17715411 0.17463674 0.17339584 0.17216663 0.17094898 0.17034445

0.19000000 19.000% 0.18174242 0.17909551 0.17779121 0.17649950 0.17522024 0.17458524

0.19500000 19.500% 0.18632111 0.18354180 0.18217275 0.18081723 0.17947509 0.17880899

0.20000000 20.000% 0.19089023 0.18797571 0.18654056 0.18511993 0.18371365 0.18301584

Tabla de Mortalidad, Experiencia Mexicana 82-89. Edad x 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

Ix 10000000 9988800 9977413 9965839 9953980 9941935 9929607 9916997 9904105 9890833 9887184 9863158 9848659 9833689 9818250 9802149 9785485 9768165 9750093 9731178 9711424 9690642 9668838 9645922 9621808 9596310 9569344 9540828 9510583 9478437 9444315 9408049 9369382 9328156 9284128 9237057 9186715 9132881 9075252 9013541 8947471 8876697

dx 11200 11387 11574 11859 12045 12328 12610 12892 13272 13649 14026 14499 14970 15439 16101 16664 17320 18072 18915 19754 20782 21804 22916 24114 25498 26966 28516 30245 32146 34122 36266 38667 41226 44028 47071 50342 53834 57629 61711 66070 70774 75896

px 0.99888 0.99886 0.99884 0.99881 0.99879 0.99876 0.99873 0.9987 0.99866 0.99862 0.99858 0.99853 0.99848 0.99843 0.99836 0.9983 0.99823 0.99815 0.99806 0.99797 0.99786 0.99775 0.99763 0.9975 0.99735 0.99719 0.99702 0.99683 0.99662 0.9964 0.99616 0.99589 0.9956 0.99528 0.99493 0.99455 0.99414 0.99369 0.9932 0.99267 0.99209 0.99145

qx 0.00112 0.00114 0.00116 0.00119 0.00121 0.00124 0.00127 0.0013 0.00134 0.00138 0.00142 0.00147 0.00152 0.00157 0.00164 0.0017 0.00177 0.00185 0.00194 0.00203 0.00214 0.00225 0.00237 0.0025 0.00265 0.00281 0.00298 0.00317 0.00338 0.0036 0.00384 0.00411 0.0044 0.00472 0.00507 0.00545 0.00586 0.00631 0.0068 0.00733 0.00791 0.00855

Dx 4.0% 6245970.50 5999014.43 5761707.40 5533676.64 5314511.30 5103923.44 4901533.25 4707027.50 4520104.24 4340429.87 4167790.99 4001742.93 3842173.37 3688781.97 3541337.06 3399547.70 3263238.79 3132175.93 3006135.69 2884907.54 2768318.52 2656148.51 2548242.46 2444425.86 2344533.66 2248385.18 2155833.78 2066739.95 1980950.25 1898321.72 1818738.30 1742071.52 1668184.25 1596965.49 1528296.12 1462064.99 1398169.93 1336516.03 1277002.44 1219537.43 1164036.65 1110412.68

Nx 4.0% 143615765.33 137369794.83 131370780.40 125609073.00 120075396.37 114760885.06 109656961.62 104755428.38 100048400.88 95528296.65 91187866.77 87020135.78 83018392.85 79176219.48 75487437.51 71946100.45 68546552.75 65283313.96 62151138.03 59145002.34 58260094.81 53491776.29 50835627.76 48287385.32 45842959.46 43498425.80 41250040.62 39094206.83 37027466.88 35046516.64 33148194.92 31329456.61 29587385.09 27919200.84 26322235.35 24793939.23 23331874.24 21933704.31 20597188.28 19320185.84 18100648.40 16936611.75

Dx 6.5% 4696828.54 4405228.26 4131649.20 3874982.54 3634151.59 3408219.74 3196238.07 2997351.21 2810755.57 2635670.44 2471392.78 2317261.31 2172633.71 2036930.80 1909608.28 1790118.95 1678005.34 1572803.12 1474078.20 1381425.84 1294480.36 1212873.46 1136285.90 1064406.39 996944.10 933617.07 874172.36 818373.13 765989.52 716807.94 670636.12 627287.22 586581.29 548357.07 512459.04 478742.58 447073.65 417327.51 389384.18 363132.77 338470.40 315298.70

54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

8800801 8719482 8632287 8538886 8438810 8331722 8217077 8094478 7963429 7823750 7674551 7520523 7351387 7171792 6981453 6780108 6567619 6343926 8109074 5863245 5606728 5340128 5064097 4779596 4487801 4190081 3888060 3583663 3278945 2976232 2677984 2386780 2105236 1835976 1581473 1143983 1125465 927462 751012 596619 464182 353019 261859 189101 132569 89987

81319 87195 93401 100076 107088 114645 122599 131049 139679 149199 154028 169136 179595 190339 201345 212489 223693 234852 245829 256517 266600 276031 284501 291795 297720 302021 304397 304718 302713 298248 291204 281544 269260 254503 237490 218518 198003 176450 154393 132437 111163 91160 72758 56532 42582 89987

0.99076 0.99 0.98918 0.98828 0.98731 0.98624 0.98508 0.98381 0.98246 0.98093 0.97993 0.97751 0.97557 0.97346 0.97116 0.96866 0.96594 0.96298 0.95976 0.95625 0.95245 0.94831 0.94382 0.93895 0.93366 0.92792 0.92171 0.91497 0.90768 0.89979 0.89126 0.88204 0.8721 0.86138 0.84983 0.83741 0.82407 0.80975 0.79442 0.77802 0.76052 0.74177 0.72215 0.70105 0.67879 0

0.00924 0.01 0.01082 0.01172 0.01269 0.01376 0.01492 0.01619 0.01754 0.01907 0.02007 0.02249 0.02443 0.02654 0.02884 0.03134 0.03406 0.03702 0.04024 0.04375 0.04755 0.05169 0.05618 0.06105 0.06634 0.07208 0.07829 0.08503 0.09232 0.10021 0.10874 0.11796 0.1279 0.13862 0.15017 0.16259 0.17593 0.19025 0.20558 0.22198 0.23948 0.25823 0.27785 0.29895 0.32121 1

1058575.60 1008456.16 959972.67 913063.28 867655.91 823697.51 781118.63 739869.54 699895.30 661172.21 623618.89 587598.92 552292.18 518076.57 484929.66 452831.05 421768.56 391733.78 362722.88 334737.43 307781.41 281871.53 257020.76 233251.29 210587.76 189055.19 168660.86 149495.00 131522.58 114788.83 99313.31 85109.60 72182.78 60529.42 50133.49 40966.28 32986.14 26137.39 20350.71 15545.21 11629.32 8504.15 6065.50 4211.72 2839.06 1853.02

15826129.07 14767623.47 13759167.31 12799194.64 11886131.36 11018475.45 10194777.94 9413659.31 8673789.76 7973894.47 7312722.26 6689103.37 6101504.45 5549212.27 5031135.70 4546206.04 4093374.99 3671606.43 3279872.68 2917149.77 2582412.35 2274630.94 1992759.41 1735738.63 1502487.34 1291899.58 1102844.38 934163.52 784668.52 653145.94 538357.11 439043.80 353934.20 281751.42 221222.00 171088.51 130122.23 97138.09 70998.70 50647.98 35102.78 23473.45 14969.31 8903.80 4692.08 1853.02

293523.84 273062.62 253832.86 235761.87 218778.16 202818.66 187819.59 173725.18 160481.30 148043.61 136357.20 125465.27 115158.28 105488.22 96421.19 87925.26 79971.53 72533.05 65584.86 59103.97 53068.71 47460.37 42260.23 37451.69 33019.02 28946.99 25221.12 21827.75 18752.81 15982.67 13503.33 11300.45 9359.11 7663.92 6196.64 4946.28 3889.26 3009.41 2288.14 1706.50 1246.88 890.40 620.16 420.52 276.81 176.43

Nx 6.5% 73587378.70 68890550.15 64485321.90 60353672.69 56478690.15 52844538.56 49436318.82 46240080.75 43242729.54 40431973.96 37796303.52 35324910.74 33007649.43 30835015.72 28798084.92 26888476.66 25098357.71 23420352.37 21847549.26 20373471.05 18992045.21 17697564.85 16484691.39 15348405.48 14283999.09 13287054.99 12353437.93 11479265.56 10660892.43 9894902.91 9178094.97 8507458.85 7880171.64 7293590.35 6745233.27 6232774.23 5754031.65 5306958.00 4889630.49 4500246.31 4137113.54 ###########

Dx 8% 3971137.59 3672861.03 3396920.42 3141648.08 2905471.88 2686996.35 2484874.51 2297887.84 2124907.97 1964870.82 1816814.23 1679846.56 1553127.00 1435894.67 1327444.72 1227099.85 1134271.98 1048392.92 968938.23 895424.55 827413.76 764484.38 706263.23 652397.52 602561.65 556448.94 513782.68 474307.07 437781.01 403982.69 372711.45 343776.00 317004.70 292231.35 269307.45 248094.49 228465.18 210302.18 193495.52 177944.23 163555.45 150242.35

Nx 8% 52093974.20 48122836.61 44449975.58 41053055.16 37911407.08 35005935.20 32318938.86 29834064.35 27536176.50 25411268.53 23446397.70 21629583.47 19949736.91 18396609.92 16960715.25 15633270.53 14406170.69 13271898.71 12223505.80 11254567.56 10359143.01 9531729.25 8767244.87 8060981.63 7408584.11 6806022.48 6249573.52 5735790.84 5261483.77 4823702.76 4419720.07 4047008.82 3703230.82 3386225.92 3093994.57 2824687.12 2576592.63 2348127.47 2137825.29 1944329.77 1766385.54 1602830.09

Edad x 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

3483344.43 3189820.59 2916757.97 2662925.12 2427163.24 2208385.09 2005566.43 1817746.83 1644021.65 1483540.35 1335496.74 1199139.54 1073674.27 958515.99 853027.77 756606.58 668681.31 588709.78 516176.73 450591.86 391487.89 338419.18 290958.82 248698.59 211246.90 178227.88 149280.89 124059.78 102232.03 83479.22 67496.55 53993.22 42692.77 33333.66 25669.74 19471.10 14524.82 10635.56 7626.14 5338.00 3631.20 2384.32 1493.91 873.75 453.24 176.43

137923.86 126527.27 115983.33 106229.99 97208.31 88865.50 81150.65 74018.41 67425.98 61336.41 55709.93 50548.00 45751.09 41327.21 37250.36 33496.35 30043.12 26870.24 23958.80 21291.38 18851.75 16625.32 14598.11 12757.40 11091.25 9588.39 8238.20 7030.77 5956.43 5008.05 4170.73 3441.86 2810.98 2269.87 1810.39 1424.58 1104.57 842.82 631.92 464.82 334.85 235.80 161.95 108.29 70.29 44.18

1452587.74 1314663.88 1188136.61 1072153.29 965923.29 868714.98 779849.48 698698.83 624680.42 557254.44 495918.02 440208.09 389660.10 343909.01 302581.80 265331.44 231835.09 201791.97 174921.74 150962.94 129671.56 110819.81 94194.49 79596.38 66838.99 55747.73 46159.34 37921.14 30890.37 24933.93 19927.88 15757.15 12315.29 9504.31 7234.44 5424.06 3999.50 2894.93 2052.11 1420.19 955.37 620.51 384.72 222.76 114.47 44.18

54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99