Tarea 1 Resolucion Matematica Financiera

MATEMÁTICA FINANCIERA PLANIF PLANIFICA ICACI CI N ENTREGA ENTREGA DE TRABAJ TRABAJOS OS CA 4-1 Primera tarea

Lunes 7 de mayo de 2018

Primera Evaluación (Unidad I)

Lunes 7 de mayo de 2018

Examen Primer Hemisemestre

Lunes 28 de mayo de 2018

Segunda Tarea

Jueves 31 de mayo de 2018

Segunda Evaluación (Unidad II)

Jueves 31 de mayo de 2018

TAREA 1.- INTERÉS SIMPLE  – CUENTAS DE AHORRO 1. Hallar el interés simple al 6%: a) Sobre un documento de 20 .000 usd, fechado el 10 de febrero de 2017, con vencimiento el 15 de octubre de 2017; b) Sobre un documento de 12.500 usd a seis meses.  AGUAL SIERRA GISELLA ABIGAIL Datos

Datos

I=? M=? i=0.06 C= 20.000

I=? M=? i=0.06 C= 12.500

Solución

Solución

10/02/17 = 41 dias

10/02/17 = 41 dias

15/10/17 = 288 dias

10/08/17 = 222 dias

247 dias

181 dias

I=C.i.t

I=C.i.t

I=20.000*0.06*247/360

I=12.500*0.06*181/360

I=823,33 I=823,33 usd

I= 377,08 usd

2. Determine: a) Que capital produce en 10 meses 8.500 usd a una tasa del 8% anual? b) Que capital produce 3.500 usd desde el 13 de marzo al 15 de noviembre del mismo año a una tasa del7,5% anual?  ANALUISA VILCACUNDO VILCACUNDO GRACE ALEJANDRA ALEJANDRA

Datos:

solución

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c=8500 t=10 meses i=8% m=monto c=3500 i=7,5% F/I=13-03=72 F/F=15-11=319

 =  1    = 85001 0,08∗    = 9066,67  = 1    = 35001 35001 0,075 075 ∗   = 3680,10

T=319-72=247 días

3. Determine: a) el tiempo expresado en días, para que un capital de 12.500 usd a interés simple, produzca una ganancia de 850 usd, b) en que tiempo, expresado en meses, un capital crece el 25% si la tasa de interés es del 10%?  ARELLANO CEPEDA CEPEDA DANNA MYLENA MYLENA

a) DATOS

SOLUCIÓN

T= en días C= 12.500 I= 850 B) DATOS

SOLUCIÓN

T= en meses

I= C i t

C

¼ = C * 0.1 * t

 ∗

i= 10%

 = ∗.

I= ¼ C

t= 2.5 t= 30 meses

4. Determine: a) ¿A qué tasa de interés simple anual un capital de 7500 usd produce 900 usd de interés en 10 meses b) determine la tasa de interés a la que fue pactada una deuda de 3500 usd, si en 95 días el interés es de 175 usd?

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BENALCAZAR ALMEIDA RONNIE PAUL

DATOS: i=interés

C=7500 USD I=900 USD T= 10 meses

a) I= cit 900= 7500*i*10/12

900 ∗ 12  = 7500 7500 ∗10 ∗ 10  = 0.14  = 14% DATOS: i= interés C=3500 USD I=175 USD T= 95 dias

b) I= cit 175= 3500*i*95/360

∗ 360  = 175 3500 3500 ∗ 95  = 0.21  = 21%

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i nversión de 10.000 usd a interés simple durante 8 5. Hallar el monto de: a) una inversión meses con una tasa del 6% anual, b) una deuda de 3.200 usd a interés simple desde el 10 de marzo al 15 de octubre del mismo año, considerando el 7,5% de interés simple. BENAVIDES CHASIGUANO ALVARO ALEXANDER

Datos:

Solución:

M=?

15/10 10/03

a) C= 10.000 usd t= 8 meses i= 6% anual

288 69 219 días

M= C (1+it) M= 10.000 (1+0.06 x 8/12) M= 10.400 usd

b) C= 3200 t= 10/03 – 15/10 i= 7.5%

M= C (1+it) M= 3.200 (1+0.075 x 219/360) M= 3.346 usd

6. Determinar el monto que se obtiene al invertir 8.250 usd a interés simple durante 9 meses, si la tasa de interés es del 6,5%. BEDOYA NASIMBA JESSICA LIZBETH

Datos: C: 8.250 usd

Solución M= C (1+i * t)

t: 9 meses

M= 8.250 (1+0,065 * 9/12)

i: 6.5 %

M= 8.652,19 usd

M: Monto Respuesta: El monto que se obtiene al invertir 8.250 usd durante 9 meses es de 8.652,19 usd. 7. Determinar la fecha de vencimiento y el valor al vencimiento o monto de los siguientes pagares. N° 1

V/nominal (usd) 2.500

F/ colisión

Plazo (días)

10-04-17

120

Taza Interés 7%

de

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BUÑAY QUISHPI DIANA MARISOL

Datos

solución

F/venc.=?

I pagaré

M=C (1+i t)

M=?

F/emisión: 10-04-17 = 100

M= 2 500 (1+0,07 *

100 + 120 = 220

M=2 558.33 usd//

) 

F/venc= 8-agosto-2017

II pagaré M=C (1+i t)

) 

F/emisión: 21-03-17 = 80

M= 1750 (1+0,06 *

80 + 150 = 230

M=1793.75 usd//

F/venc= 18-agosto-2017

III pagaré M=C (1+i t)

) 

F/emisión: 10-10-17 = 100

M= 5 500 (1+0,08 *

283 + 210 = 493

M= 5 756.67 usd//

F/venc= 8-Mayo-2017

8. Juan debe a Luis 10.500 usd pagaderos en 10 meses al 6.5% de interés simple. ¿Cuánto recibirá Luis, Si Juan saldara su deuda: a) El día de hoy b) Dentro de 6 mese c) Al final del año CABASCANGO ULCUANGO ANA GABRIELA DATOS

MONTO= 10500 USD T= 10 meses

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−   1 0  = 10500 10500(1(1  0.065 065 ∗ 12)  = 9960.47   b) Dentro de 6 meses  = 1   ∗ − 5 −  = 10500 10500(1(1  0.065 065 ∗ 12)  = 10223.12  c) Al final del año  = 1 1   ∗     = 10500 105001 1  0. 065 0 6 5 ∗2/ ∗ 2/12 12  = 10613.75  9. Una persona debe 5.000 usd para pagar en 9 meses con interés del 8,25%; Conviene en pagar 1.500 usd al final f inal de 3 meses. ¿Qué cantidad tendrá t endrá que pagar al final de los 9 meses para liquidar la deuda, suponiendo un rendimiento del 9,5%. CANTOS TAPIA EVELYN DAYSE

1500 (1 0.095∗ 123 )    = 5000 500011 0.0825 0825∗∗ 129  1535, 1535,63 63   = 5309, 5309,38  = 3773,75  10. Se obtiene un préstamo de 3.250 usd a un año con interés al 12,5% ¿Qué cantidad tendrá que pagar como liquidación del préstamo 6 meses después, suponiendo un rendimiento del 9,5%. CELI ORTIZ KAREN DAYAN

=  = 3250 325012.5% % (1212)  = $406.25  =  = (1  )   406.25 = 19.50%∗ 6

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11. Una persona desea comprar una casa dentro de 2 años. Proyecta que la cuota inicial que deberá pagar en ese tiempo será de 60.000 usd. Si desea tener esa cantidad dentro de 2 años. ¿Qué cantidad debe invertir en su depósito de renta fija que le rinde el 12% anual simple. CHICAIZA TIPANLUISA PAMELA LILIANA

Datos: V = 120,000.00 USD CI= 60,000.00 USD M = 60,000.00 USD valor a financiar t = 2 años i = 0,12 anual Fórmula: C = M/(1 + i t) C = 60000/(1 + 0.12 * 2) C = 60000/(1+0.24) C = 60000/( 1.24) C = 48,387.10 Gráfico: i = 0.12 anual

M = 60,000.00 = 60,000.00

C = 48,387.10 = 48,387.10 C I = I = 60,000.00

0 Años

Valor total Inversión = CI + M

1

2

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F/V= 15-12 F/A= 11-07 i= 0.16% GRÁFICAS



Tiempo aproximado

i= 16%

M

154 días VA



Tiempo exacto

i= 16%

M

158 días VA

SOLUCIÓN 

Tiempo aproximado

Fecha Vencimiento Fecha Actual

15-12 11-07

346 192

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oct nov dic Total

31 30 16 158 días

 =  11  −  = 5000 10.16∗   = 4676.13 

-1

13. Un mes después de haber obtenido un préstamo, una persona debe pagar exactamente 850 usd. ¿Cuánto obtuvo su préstamo si el pago que debe hacer incluye interés al 15% anual? CHINGAY TACO KAREN ALICIA

=  = 850 850 (1  0.15∗ 15 ∗ 121 )  = $860,62 14. Una persona que cobra 5000 usd mensual es despedida por problemas financieros. Al despedir al trabajador la empresa le paga una indemnización de 4.5000 usd ¿Que ingreso fijo mensual le representaría al ahora desempleado depositar el valor de su liquidación en una inversión que le paga el 18% de interés simple anual? CORTÉS JIMENEZ FRANKLIN JAVIER

simple anual?

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M=810,00 M. mensual= 810,00/12 M. mensual= 67,50 Cada mes le representaría un ingreso fijo de 67,50 dólares

15. ¿Cuánto debe pagar por concepto de interés una persona que tiene una deuda de 22.000 usd, si la liquida 6 meses después y le cobran interés a razón del 12% anual? CUEVA ROJAS LEIDY GISSELA

Datos I= Interés C= 22.000 usd t= 6 meses i= 12% anual

Solución

 == 22. 00000 ∗ 0,0606 ∗6/12 ∗ 6/12  = 1.320 

16. Encuéntrese el interés simple: a) exacto y b) ordinario de un préstamo de 1.500 usd a 60 días con el 14% anual. ESQUIVEL SEMANATE SARA MARCELINA

17. De acuerdo con el tiempo ordinario, ¿Cuánto tiempo transcurre del 15 de marzo al 18 de diciembre del mismo año? FUENTES CUSANGUA DIANA LISBETH

DATOS Fecha Inicial: 15/03 Fecha Final: 18/12

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Octubre

31

Noviembre

30

Diciembre

18

TOTAL

278 días

RESPUESTA:  del 15 de Marzo al 18 de Diciembre ha trascurrido 278 días 18. ¿Cuál es la fecha de vencimiento de un pagaré contratado el 15 de junio a un plazo de 18 días? Calcule con el tiempo ordinario y con tiempo exacto. GARCIA COTACACHI ANDREINA ESTEFANIA

Fecha de emisión: 15-06-2017 emisión: 15-06-2017 Plazo: 18 Plazo: 18 días a) Tiempo ordinario Mes completo: 30 completo: 30 días Fecha de suscripción: 15 suscripción: 15 días Tiempo de vencimiento: 18 vencimiento: 18 días 30 días  – 15 días+ 18 días= 3 de julio 2017 b) Tiempo exacto Fecha de emisión: emisión: 15-06=166 166+18=184 Fecha de vencimiento: 3 vencimiento: 3 de julio 2017

19. Una señora reembolsa 205,08 usd por un pagare de 185 usd firmado el 10 de mayo con el 12% anual. Determinar la fecha en que cancelo el pagaré. GUADIR QUENAN JEFFERSON RICARDO

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i= 12%

M

t C

SOLUCIÒN

 = 1  205.08 = 18510.12∗  205.08 1 = 0.12 185  = 0.9045045045  = 0.904504 045045045 5045∗∗ 365  = 330.14 = 330 í FECHA DE PAGO (AÑO CALENDARIO) Mayo  junio  julio agosto sep oct

21 30 31 31 30 31

FECHA DE CANCELACIÓN 5 DE ABRIL DEL SIGUIENTE AÑO

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21. ¿En qué tiempo se incrementará en $ 2.050,00 un capital de $ 50.000,00 colocado al 10 % anual?

 

GUAMAN BAÑO SANDY PAOLA

Datos I= 2.050 USD C= 50.000 USD

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22. ¿En qué tiempo se convertirá en $ 54.500,00 un capital de $ 50.000,00, colocado a una tasa de interés del 1,5% mensual? HERNANDEZ SANCHEZ MIRIAM JANETH

DATOS

SOLUCION

t: ?

M = C (1+i*t)

M: 54500

54500=50000(1+0.015*t)

C: 50000

t= (545 -1 ) / 0.015

i : 1.5% annual

500 t= 6 meses, 180 dias

23. ¿A qué tasa de interés anual se colocó un capital de $ 4.000,00 para que se convierta en $ 4.315,00 en 210 días? días? JAMI FLORES DARIO ALEJANDRO

DATOS C = 4000 usd t = 210 dias I = 315

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24. ¿A qué tasa de interés mensual un capital de $ 1.850,00 se incrementará una cuarta parte más en 300 días? LOOR TENESACA DIANA MARITZA

Datos

Capital= $ 1.850,00 t= cuarta parte más en 300 días

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1.125,00 =  ∗ 180 360 ∗ 0,0909  = 1.125, 25,00/0, 0/0,5 ∗ 0.09  = . . ,,   26. Calcule el valor actual de un pagaré de $ 540,00 con vencimiento en 270 días y con una tasa de interés del 12% anual: a) el día de hoy, b) dentro de 30 días, c) dentro de 90 días, d) dentro de 180 días, y e) antes de 60 días del vencimiento. LOZANO SALTOS VALERIA ABIGAIL

Datos Monto= 540 F/Vencimiento= 270 días Tasa de interés= 12% anual a) el día de hoy b) dentro de 30 días c) dentro de 90 días

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90 −  = 540 54011  0,0,12 ∗ 360  = 524.27 1   ∗ ∗ − 60 e)  = 1  = 540 54011  0,0,12 ∗ 360−  = 529,41 27. Un documento de $ 900,00 suscrito el 19 de abril, con vencimiento en 180 días a una tasa de interés del 1% mensual desde su suscripción, es negociado el 15 de julio del mismo año a una tasa de interés del 18% anual, se desea conocer: a) la fecha de vencimiento, b) el monto o valor al vencimiento, c) el número de días comprendidos ente la fecha de negociación y la de vencimiento, d) el valor actual al 15 de junio. MENDOZA VALDIVIEZO XIMENA LISSETTE

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 = 911,61 28. María otorga a Pedro un préstamo por $ 1.500,00, con vencimiento en 300 días, a una tasa de interés del 18% anual desde su suscripción. Si Pedro paga su deuda 90 días antes de la fecha de vencimiento, a la misma tasa de interés, calcule cuál sería el valor del pago. MONTOYA MACAS ALEJANDRO ESTEFANO

Datos

C= 1500 usd. I= 18% F/vencimiento= 300 días F/negociación= 90 días antes del vencimiento

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30. Una empresa pagó $ 780,00 en intereses por un pagaré de ¿$....? PASQUEL YARANGA JHONNY ALEXANDER

31. Una persona invierte $ 1.500,00 durante 9 meses, por lo que obtiene un interés de $ 135. Calcule la tasa de interés que se le reconoció. SANTILLÁN LÓPEZ ODALIS PAMELA

DATOS

SOLUCIÓN

C=1500 USD t= 9 m I= 135 USD i= tasa de interés

I= Cit i=

I C*t

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= 249.92 / (1 + 0.018*133/30) = 231.45 USD.

33. Calcule el valor actual de un documento $ 95.000,00, treinta días antes de su vencimiento, si se considera una tasa de interés del 12% anual. SOLDADO CHACHA DANIELA LISSETTE

Datos: C= 95.000 USD i = 12% t = (30 Dias) M =?

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i = 18% = 0,18 anual cfm = ? a) Método Lagarto b) Método de Saldos Deudores c) Tasa de interés real

SOLUCIÓN a) Método Lagarto M = C (1 + it) M = 3600 (1 + 0,18 * 36/12) = 5544 usd Cfm = M/# cuotas = 5544 / 36 = 154 usd Interés = M – M  – C  C = 5544 – 5544  – 3600  3600 = 1944 usd 

 

b) Método de Saldos Anteriores 

Cfm = C/# cuotas = 3600/36 = 100usd.

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8 9 10 11 12 13 14 15 16

2900 2800 2700 2600 2500 2400 2300 2200 2100

42,28 40,82 39,36 37,9 36,44 34,98 33,52 32,06 30,6

100 100 100 100 100 100 100 100 100

2942,28 2840,82 2739,36 2637,9 2536,44 2434,98 2333,52 2232,06 2130,6

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 = 1   = 14500 14500 10.018(9030) = 15283  = 15283 15283 10.02(6030) = 15894.32 Se deberá para un préstamo de $ 15894.32

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E

31

28

F

28

28

M

31

A M

13

123.00 × 0.24 × 181/360 = 14.84

31

31

155.00 × 0.24 × 178/360 = 18.39

30

30

30

23

31

31

31

31

-30.00 × 0.24 × 135/360 = -2.70 1

120.00 × 0.24 × 84/360 = 6.72

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J J  A S O N D

31 31 30 31 30 31

31 31 30 31 30 31

31 30 31 30 31

31 30 31

31 30 31

30 31

27

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3600×0,24× 129 360 = 309,600 82  = 153,07 2800×0,24× 360 59  = 184,87 4700×0,24× 360 1100×0,24× 3606  = 4,4