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CHAPTER 4 Discounted Cash Flow Valuation Valuation Multiple Choice Questions: I.

DEFINITIONS

ANNUIT a 1. An annu annuiity strea tream m of of ca cash flow flow paym ayment ents is is a set set of: a. level level cash cash flows flows occu occurri rring ng each each time time perio period d for a fixed fixed leng length th of time time.. b. level cash flows occurring occurring each time period forever. forever. c. increasing increasing cash flows flows occurri occurring ng each each time time period period for a fixed length length of of time. time. d. increa increasin sing g cash cash flows flows occu occurri rring ng each each time time perio period d foreve forever. r. e. arbitrary arbitrary cash flows flows occurri occurring ng each each time time perio period d for no more more than than 10 10 years. years.

Difficulty level: Easy ANNUITIES DUE e . Annu Annuit itie iess wher wheree the the pay payment mentss occu occurr at the the end end of of each each tim timee peri period od are are cal calle led d !!!! !!!!! ! " whe where reas as !!!!! refer to annuity streams streams with payments payments occurring at the beginning of each time period. a. ordi ordina nary ry ann annui uiti ties es## ear early ly annu annuit itie iess b. late annuities# straight straight annuities c. stra straig ight ht annu annuit itie ies# s# late late annu annuit itie iess d. annu annuit itie iess due due## ord ordin inary ary annu annuit itie iess e. ordi ordina nary ry annu annuit itie ies# s# annu annuit itie iess due due

Difficulty level: Easy PERPETUIT c $. An annu annuit ity y str strea eam m whe where re the the pay payme ment ntss occu occurr fore foreve verr is is cal calle led d a%n a%n&: &: a. annuity due. b. indemnity. indemnity. c. perpetuity. d. amor amorti ti'e 'ed d cas cash h flo flow w str strea eam. m. e. amo amorti'ation tab table.

Difficulty level: Easy STATED INTEREST RATES a (. )he )he inte intere rest st rat ratee expr expres esse sed d in term termss of the the int inter eres estt paym paymen entt made made eac each h peri period od is is call called ed the the !!!!! rate. a. sta stated ted ann annual ual in intere teresst b. compound annual interest interest c. effe effect ctiv ivee annu annual al inte intere rest st d. periodic in interest e. daily in interest

Difficulty level: Easy EFFECTIVE ANNUA! RATE c *. )he )he inte intere rest st rat ratee expr expres esse sed d as if if it wer weree comp compou ound nded ed onc oncee per per year year is is call called ed the the !!! !!!!! !! rat rate. e.

a. b. c. d. e.

stated interest compound interest effective an annual periodic in interest daily in interest

Difficulty level: Easy ANNUA! PERCENTA PERCEN TA"E "E RATE RATE b +. )he interest rate charged charged per period multiplied multiplied by the number of periods periods per year is called the !!!!! rate. a. effective an annual b. annual percentage c. periodic interest d. com omp pound in interest e. daily in interest

Difficulty level: Easy

II.

CONCEPTS

ORDINAR ANNUIT VERSUS ANNUIT DUE c ,. -ou are are com compa pari ring ng two two annu annuit itie iess whi which ch off offer er mon month thly ly pay payme ment ntss for for ten ten year years. s. ot oth h annuities are identical with the exception of the payment dates. Annuity A pays on the first of each month while annuity pays on the last day of each month. /hich one of the following statements is correct concerning these two annuities a. oth oth annu annuit itie iess are are of of eua euall valu valuee toda today y. b. Annuity is an annuity annuity due. c. Annui Annuity ty A has a highe higherr futur futuree value value than than annu annuity ity . d. Annui Annuity ty has has a higher higher presen presentt value value than than annu annuity ity A. e. oth oth annui annuitie tiess have have the same same futu future re value value as as of ten ten years years from from today today..

Difficulty level: Medium

UNEVEN CASH CAS H F!O#S AND PRESENT VA!UE VA!UE b 2. -ou -ou are comparing two investment investment options. )he )he cost to invest in either either option is the same today. oth options will provide you with 30"000 of income. 4ption A pays five annual payments starting with 32"000 the first year followed by four annual payments of 3$"000 each. 4ption pays five annual payments of 3("000 each. /hich one of the following statements is correct given these two investment options a. oth options options are of of eual eual value value given that they both provide provide 30"000 30"000 of of income. income. b. 4ption A is the better choice choice of the two given any positive positive rate of return. c. 4ption 4ption has has a higher higher present present value value than option option A given given a posit positive ive rate rate of return. return. d. 4ption 4ption has has a lower lower future future value value at at year year * than optio option n A given given a 'ero rate of of return. return. e. 4ption 4ption A is prefer preferabl ablee becau because se it it is an annu annuity ity due. due.

Difficulty level: Medium UNEVEN CASH F!O#S AND FUTURE VA!UE

a. b. c. d. e.

stated interest compound interest effective an annual periodic in interest daily in interest

Difficulty level: Easy ANNUA! PERCENTA PERCEN TA"E "E RATE RATE b +. )he interest rate charged charged per period multiplied multiplied by the number of periods periods per year is called the !!!!! rate. a. effective an annual b. annual percentage c. periodic interest d. com omp pound in interest e. daily in interest

Difficulty level: Easy

II.

CONCEPTS

ORDINAR ANNUIT VERSUS ANNUIT DUE c ,. -ou are are com compa pari ring ng two two annu annuit itie iess whi which ch off offer er mon month thly ly pay payme ment ntss for for ten ten year years. s. ot oth h annuities are identical with the exception of the payment dates. Annuity A pays on the first of each month while annuity pays on the last day of each month. /hich one of the following statements is correct concerning these two annuities a. oth oth annu annuit itie iess are are of of eua euall valu valuee toda today y. b. Annuity is an annuity annuity due. c. Annui Annuity ty A has a highe higherr futur futuree value value than than annu annuity ity . d. Annui Annuity ty has has a higher higher presen presentt value value than than annu annuity ity A. e. oth oth annui annuitie tiess have have the same same futu future re value value as as of ten ten years years from from today today..

Difficulty level: Medium

UNEVEN CASH CAS H F!O#S AND PRESENT VA!UE VA!UE b 2. -ou -ou are comparing two investment investment options. )he )he cost to invest in either either option is the same today. oth options will provide you with 30"000 of income. 4ption A pays five annual payments starting with 32"000 the first year followed by four annual payments of 3$"000 each. 4ption pays five annual payments of 3("000 each. /hich one of the following statements is correct given these two investment options a. oth options options are of of eual eual value value given that they both provide provide 30"000 30"000 of of income. income. b. 4ption A is the better choice choice of the two given any positive positive rate of return. c. 4ption 4ption has has a higher higher present present value value than option option A given given a posit positive ive rate rate of return. return. d. 4ption 4ption has has a lower lower future future value value at at year year * than optio option n A given given a 'ero rate of of return. return. e. 4ption 4ption A is prefer preferabl ablee becau because se it it is an annu annuity ity due. due.

Difficulty level: Medium UNEVEN CASH F!O#S AND FUTURE VA!UE

a

5.

-ou are are con consi side deri ring ng two two pro pro6e 6ect ctss wit with h the the foll follow owin ing g cas cash h flo flows ws:: 7ro6ect A 7ro6ect -ear 1 3"*00 3("000 -ear $"000 $"*00 -ear $ $"*00 $"000 -ear ( ("000 "*00 /hich of the following statements are true concerning these two pro6ects 8. oth pro6ects pro6ects have the same same future future value value at the end end of of year year (" given a positi positive ve rate rate of return. 88. oth pro6ects pro6ects have have the the same same future future value value given given a 'ero rate of return. return. 888. oth pro6ects pro6ects have have the same same future future value at any any point point in time" time" given a positiv positivee rate of return. 89. 89. 7ro6ect 7ro6ect A has a higher higher future value value than pro6ect pro6ect " given a positive positive rate rate of return. a. 88 only b. 89 only c. 8 and 888 only d. 88 and 89 only e. 8" 88" and 888 only Difficulty level: Medium

PERPETUIT VERSUS ANNUIT d 10. 10. A perp perpet etui uity ty diff differ erss from from an annu annuit ity y beca becaus use: e: a. perpet perpetui uity ty paym payment entss vary vary with with the rate rate of infla inflatio tion. n. b. perpetuity payments payments vary with the maret rate of interest. interest. c. perpet perpetui uity ty paymen payments ts are varia variable ble whil whilee annuity annuity pay paymen ments ts are cons constan tant. t. d. perp perpet etui uity ty paym paymen ents ts neve neverr cea cease se.. e. annu annuit ity y pay payme ment ntss n nev ever er ceas cease. e.

Difficulty level: Easy ANNUA! PERCENTA PERCEN TA"E "E RATE RATE e 11. 11. /hich /hich one one of of the the follow following ing statem statement entss conc concern erning ing the the annu annual al percen percentag tagee rate rate is correct a. )he annual annual percen percentag tagee rate rate consid considers ers int interes erestt on int intere erest. st. b. )he rate of interest you you actually pay on a loan is called the annual percentage rate. rate. c. )he effec effective tive annual annual rate rate is lower lower than than the the annual annual percentage percentage rate when when an an interest interest rate is compounded uarterly. d. /hen firms firms advertis advertisee the annual annual percentag percentagee rate rate they are viola violating ting ;.or any any positi positive ve rate rate of inter interest" est" the the effect effective ive annual annual rate will will always always exceed exceed the annual annual percentage rate.

Difficulty level: Easy EFFECTIVE ANNUA! RATE c 1$. /hich /hich of the follow following ing state statemen ments ts concer concernin ning g the the effect effective ive annual annual rate rate are are corr correct ect 8. /hen maing maing financ financial ial decisi decisions" ons" you shou should ld compar comparee effectiv effectivee annual annual rates rather rather than annual percentage rates. 88. )he more more freuent freuently ly interest interest is compou compounded nded"" the higher higher the the effectiv effectivee annual annual rate. rate. 888. A uoted uoted rate of +? compoun compounded ded continuou continuously sly has a higher higher effective effective annual annual rate than if the rate were compounded daily. 89. 89. /hen borrowing borrowing and choosing choosing which which loan to to accept" you you should select the offer with with the highest effective annual rate. a. 8 and 88 only b. 8 and 89 only c. 8" 88" and 888 only d. 88" 888" and 89 only e. 8" 88" 88 888"and 89 89

Difficulty level: Medium CONTINUOUS CO$POUNDIN" d 1(. )he highes highestt effec effectiv tivee aannu nnual al rate rate that that can can be be deri derived ved from from an annual annual percen percentag tagee rate rate of of 5? is computed as: a. .05e 1 . .05 b. e × . c. e × %1 @ .05&. d. e.05 1. e. %1 @ .05&.

Difficulty level: Easy TI$E VA!UE c 1*. 1*. )he )he tim timee val value ue of money oney con concept cept can can be be def defin ined ed as a. the relations relationship hip between between the the supply supply and deman demand d of money. money. b. the relationship between between money spent versus versus money received. c. the relatio relationship nship between between a dollar dollar to be be received received in the the future future and a dollar dollar today today.. d. the relations relationship hip of intere interest st rate rate stated stated and amount amount paid. paid. e. Bone Bone of the the abov abovee.

Difficulty level: Easy CASH F!O#S d 1+. 1+. isc isco ount unting cash ash flow flowss invo nvolves lves a. discounti discounting ng only only those those cash cash flows flows that that occur occur at least least 10 10 years years in the the future. future. b. estimating only the the cash flows that occur in the the first ( years of a pro6ect. c. multiply multiplying ing expecte expected d future future cash flows flows by the cost of capit capital. al. d. discounti discounting ng all expec expected ted future future cash cash flows flows to reflect reflect the time time value value of money money..

e.

taing taing the the cash cash discou discount nt offer offered ed on trad tradee mercha merchandi ndise. se.

Difficulty level: Easy INTEREST

a

1,. a. b. c. d. e.

Compound interest allows allows for for the the reinve reinvestm stment ent of of intere interest st paym payments ents.. does not allow for the reinvestment reinvestment of interest interest payments. is the the sam samee as simp simple le int inter eres est. t. provid provides es a value value that that is is less less than than simp simple le inter interest est.. oth A and . .

Difficulty level: Easy ANNUIT c 12. An annuity a. is a debt debt instr instrume ument nt that that pays pays no inte interes rest. t. b. is a stream of payments that varies varies with current maret maret interest. c. is a leve levell strea stream m of eua euall paymen payments ts throu through gh time time.. d. has no value. e. Bone Bone of the the abov abovee.

Difficulty level: Easy CO$POUNDIN" d 15. )he state stated d rate rate of of inter interest est is 10?. 10?. /hich /hich form form of compou compoundi nding ng will will give give the the highe highest st effe effecti ctive ve rate of interest a. ann annual ual com compoun poundi ding ng b. monthly compounding compounding c. dai daily com compoun poundi din ng d. cont contin inuo uous us comp compou ound ndin ing g e. 8t is impossibl impossiblee to tell without without nowing nowing the term of the the loan. loan.

Difficulty level: Easy PRESENT VALUE

b

0. a. b. c. d. e.

)he present value of future future cash flows minus initial initial cost is called the the futu future re val value ue of the the pro6 pro6ec ect. t. the net present value of the the pro6ect. the euiv euivale alent nt sum of the invest investmen ment. t. the init initial ial invest investme ment nt ris ris euiv euivale alent nt value value.. Bone Bone of the the abov abovee.

Difficulty level: Easy

III. III. PRO% PRO%!E !E$S $S PRESENT VALUE – SINGLE SUM

a

1. >ind >ind the the presen presentt value value of 3*"$ 3*"$* * to to be receiv received ed in one period period if the the rate rate is is + +.*? .*?.. a. 3*"000.00

b. c. d. e.

3*"0$.*2 3*"+((.*0 3*"+,1.1$ Bone of the above.

Difficulty level: Easy SIMPLE & COMPOUND INTEREST

b

. 8f you have a choice to earn simple interest on 310"000 for three years at 2? or annually compound interest at ,.*? for three years which one will pay more and by how much a. amily >un Center deposited 3$"+00 in an investment account for the purpose of buying new euipment four years from today. )oday" they are adding another 3*"000 to this account. )hey plan on maing a final deposit of 3,"*00 to the account next year. Dow much will be available when they are ready to buy the euipment" assuming they earn a ,? rate of return a. 312"1*5.+* b. 315"($0.2( c. 315"+2$.* d. 30"15(.*( e. 30",50.55

Difficulty level: Medium UNEVEN CASH F!O#S AND FUTURE VA!UE c ,(. /hat is the future value of the following cash flows at the end of year $ if the interest rate is + percent )he cash flows occur at the end of each year. -ear 1 -ear -ear $ 3*"120 35"+00 3"*0 a. 31*"51+.,2 b. 312"105.02 c. 312"(+.* d. 315"$(1.0 e. 315"+02.0,

Difficulty level: Medium UNEVEN CASH F!O#S AND FUTURE VA!UE d ,*. /hat is the future value of the following cash flows at the end of year $ if the interest rate is 5 percent )he cash flows occur at the end of each year. -ear 1 -ear -ear $ 35"20 30 3("*10 a. 31*"1$.20 b. 31*"+15.,0 c. 31*"51+.,2 d. 31+"1,,.1( e. 31,"+$$.02

Difficulty level: Medium UNEVEN CASH F!O#S AND FUTURE VA!UE c ,+. /hat is the future value of the following cash flows at the end of year $ if the interest rate is ,.* percent )he cash flows occur at the end of each year. -ear 1 -ear -ear $ 3+"200 3"100 30 a. 32",*2.0( b. 32"20+.$5 c. 310"0,$.55 d. 310"$1(.00 e. 310"20(.$+

Difficulty level: Medium UNEVEN CASH F!O#S AND FUTURE VA!UE e ,,. 9

.0(5 *×1 1 − 1 P% 1 + & 1 S 31+0 )*0 = 31+0 × .0(5 1 Lnter

,.

79 =("*2.0$

100 7M)

(.*20$ S 3("*2.0$

×

.02 100 1 − 1 P% 1 + & 1 S 31"00 )*0 = 31"00 × .02 1 Lnter

+.

*$* >9

>9

22.0+2* S 3*+"(*1.51

×

9

.0$* *×1 1 − 1 P%1 + 1 & .0$* *0 = 31"*00 × × 1 + 1 S 31"*00 .0$* 1

)due

**.$05,,+

×

×

1.00,02$$$ S 32$"125.5 Lnter

*×1 $.*P1 =1"*00FB B 8P79 7M) >9 2$"125.5

9 =50"12.,5

$$.

)*0

* [ ] = 310"000 × 1 − 1 P%1 + .02*& S 310"000 × 10.$(151 S 310"$(1.51 .02*

Lnter

* B

2.* 8P-

9

1 − [1 P%1 + .02*& * ] *0 = 310"000 × × (1 + .02* ) S 310"000 × 10.$(151 × 1.02* S .02*

)due

3111"0(0.5, Lnter

* B

9 =*(",5*.$5

1 − [1 P%1 + .0,*& 0 ] 3*(",5*.$5 = C × # C S 3*"$,* .0,* Lnter 9

ecause each payment is received one year later" then the cash flow has to eual: 3*"000 × %1 @ .0,*& S 3*"$,*

$*.

02 *×1 1 − 1 P% 1 + . & .02 1 × 1+ *0 = 3100 × S 3100 .02 1 1

)due

(5.$12(05 × 1.00+++, S

×

3("5+(., Lnter

*×1 B

9 =("5+(.,

.02 *×1 1 − 1 P%1 + 1 & )*0 = 3100 × S 3100 .02 1 Lnter

*×1 B

9

ifference S 3("5+(., = 3("5$1.2(S 3$.22 .02 = 3$.22 Bote: ifference = 3("5$1 .2( × 1 $+.

),0

%1 + .0+& * = 31"000 × .0+

Lnter

* B

+ 8P-

− 1 S 31"000 × *.+$,05 S 3*"+$,.05

79

9 =*"+$,.05

= 3$"000 ×

Lnter 9 (02"5.+

79

9 ((*",*.+*

ifference S 3((*",*.+* = 3(02"5.+ S 3$+"20$.0$ Bote: ifference S 3(02"5.+ × .05 S 3$+"20$.0$

(0.

1 1 P%1 .0*5 & (×1 − + 1 3*"+00 = C × # 3*"+00 S C .0*5 1 Lnter

(×1 B

*.5P1 8P-

*"+00 79

9

1 1 P%1 .0,* &$0×1 − + 1 31(5"000 = C × # 31(5"000 S C .0,* 1 Lnter

$0×1 B

9 =1"0(1.2$

)otal interest S %31"0(1.2$ × $0 × 1& = 31(5"000 S 3+"0*2.20 S 3+"0*5 %rounded& (.

%1 + .0+*&10 3*"000"000 = C × .0+* Lnter 9 =1"2*"+1,.*

($.

1 − 1 P%1 + .0(* & ,×1 1 3(+("500 = C × # 3(+("500 S C .0(* 1

12,.$+$525$# C S

×

3"(21., Lnter

,×1 B

9

$1.5*22*# C S 3155.5(

×

(,.

0** *×( 1 − 1 P% 1 + . & ( )*0 = 3*00 × S 3*00 .0** ( Lnter

*×( B

*.*P( 8P-

9

.0(5 +0 1 − 1P%1 + . 1 & .0(5 *0 = 355 × × 1 + 1 S 355 .0(5 1

)due

*$.115*+52 × 1.00(02$$$

×

S 31*"5(,.+1 Lnter

+0 B

9 $00"+2*.11

1 − [1 P%1 + .0(*&t ] 3100"000 = 3+"000 × # ln( S t × ln1.0(*# t S $1.(5 .0(* Lnter 9

1 − 1 P%1 + .05 & 1 3("5*(.2* = 31($.2( × # ln1.$(2$(25 S t .05 1 t

*(.

Lnter 9

ln.000*,*1,, S ln.+52+*502# t

×

105*.02 days ÷ $+* days S $ years

*2.

1 − 1 P%1 + . &$0 1 31$"500 = 3("25(.$* × # )his can not be solved directly" so itHs . 1 easiest to 6ust use the calculator method to get an answer. -ou can then use the calculator answer as the rate in the formula 6ust to verify that your answer is correct. Lnter

$0 B

9 1$.*5

1 − 1 P%1 + . & (0×1 1 3100"000 = 3$2(.(0 × # )his can not be solved directly" so itHs . 1 easiest to 6ust use the calculator method to get an answer. -ou can then use the calculator answer as the rate in the formula 6ust to verify that you answer is correct. Lnter

(0×1 B

9

−1 # )his can not be solved directly" so itHs easiest to

1 6ust use the calculator method to get an answer. -ou can then use the calculator answer as the rate in the formula 6ust to verify that you answer is correct. Lnter

1*×1 B

9

7M)

5"000 >9

1*"000 7M) >9

7resent value S 3("$2*.5+ @ 3+"5*.1 @ 310"1(.*, S 31"($*.,(

+*.

*0

1 1 1 = 31"00 × + 31"*00 × + 3"000 × 1 $ # 79 S %1 + .0(& %1 + .0(& (1 + .0( )

3("$12.+, Lnter

1 B

( 8P79 =1"1*$.2*

B

( 8P-

$ B

( 8P-

9

B

+ 8P-

**"000 7M) >9

$ B

+ 8P-

9

7resent value S 31"100.5 @ 31"*1*.0 @ 3"$5.$$ S 3("2**.,

+5.

*0

1 1 1 = 3*"+00 × + 35"000 × + 3"000 × 1 $ # 79 S %1 + .11& %1 + .11& (1 + .11)

31$"21.0$ Lnter

1 B

11 8P79 =*"0(*.0*

B

11 8P-

$ B

11 8P-

9

=*"000 7M) >9

7resent value S 3*"000.00 @ 31("1*0.5( @ 3"(5.51 S 3(1"(00.2* ,$.

,0

=

3$"+00 × %1.0, & *

Lnter

+

3*"000 × %1.0, & (

, =$"+00 8P79

7M)

>9 *"0(5.15

( B

, 8P-

=*" 000 79

7M)

>9 +"**$.52

$ B

, 8P-

=,"*00 79

7M)

>9 5"12,.2

9 *"20.*

7M) >9 10"1,+.00

>uture value S 3*"20.* @ 310"1,+.00 @ 3"*0.00 S 312"(+.*

,*.

,0

=

35"20 × %1.05&

Lnter

B

+ 0 + 3("*10 # >9 S 31+"1,,.1(

5 =5"20 8P79

7M)

9 11"++,.1(

>uture value S 311"++,.1( @ 30 @ 3("*10.00 S 31+"1,,.1( ,+.

,0 = [3+"200 × %1.0,*& ] + [3"100 × %1.0,*&1 ] + 30 # >9 S 310"0,$.55 Lnter

B

,.* 8P-

=+"200 79

7M)

>9 ,"21.,(

1 B

,.* 8P-

="100 79

7M)

>9 "*.*

9 S 3*5*"052.+, Lnter

* B

11 =10"000 8P79

( B

11 =1*"000 8P79

$ B

11 =*"000 8P79

9 ,*"+*+.+2

>uture value S 31$*"2*(.+( @ 312$"*2,.$* @ 3,*"+*+.+2 S 3*5*"052.+, ,2.

310"000

= [C × %1.0$&$ ] + [3"*00 × %1.0$& ] + [3"*00 × %1.0$&1 ] + 3"*00 # CS

3"0,5.25 Lnter 9 *2",*0.00

>9 S 310,"1.*0 @ 3*2",*0.00 @ 3*0"000 S 3+1*"2,.*0 20.

*0

= 1*0"000 # 79 S 3$"*5"(11.,,

21.

*0

=

2.

*0

= *0"000 # 79 S 31"212"121.2

2$.

.

=

3 1 "000 # S $.($ percent 3$*0 "000

2(.

.

=

3 10 "000 # S $.*1 percent 32* "000

2*.

C

=

2+.

C

= 3*0.00 × .02( # C S 3(.0

2,.

A7 S .01* × 1 S .12 S 12 percent

22.

A7 S .0 × ( S .02S 2 percent

25.

)*3 .1$2 = 1 + − 1 # A7 S 1$.00 percent 1

.0(*

3(.*0 # 79 S 3*0.00 .05

.0,*

31*0"000 × .0( # C S 3+"000

1

Lnter > 1$.00

1 CP-

(

50.

.0,+( E)3 = 1 + − 1 # LA S ,.2+ percent ( Lnter > ,.2+

( CP-

1

51.

.1(5 1 # LA S 1*.5+ percent E)3 = 1 + − 1 Lnter 1*.5+

E)3 )

$+*

− 1 # A7 S $.$+ percent

1 B4M L>> $.$+

.0,(* = 1 + $+*

Lnter > ,.,$

− 1 # A7 S ,.,$ percent $+* CP-

E)3 <

.0,* = 1 + − 1 # A7 S ,.+( percent

Lnter > ,.+(

CP-

5(.

LAA S $.,* percent 1

E)3 <

.0$, = 1 + − 1 # LA S $.,+ percent 1

Lnter

$., B4M L>> $.,+

> $.,$

uture value S 32"*00 × %1 @ .0$*&1* S 3(,",(,.(( Lnter

1* B

$.* =2"*00 8P79

uture value S 3125"500 × %1 @ .0(*&+ S 3(,"55.0 Lnter

+ B

(.* =125"500 8P79

9

310,"51 S 3"*00 × %1 @ r&(0# r S 5.2, percent Lnter 9

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DEFINITIONS

ANNUIT a 1. An annu annuiity strea tream m of of ca cash flow flow paym ayment ents is is a set set of: a. level level cash cash flows flows occu occurri rring ng each each time time perio period d for a fixed fixed leng length th of time time.. b. level cash flows occurring occurring each time period forever. forever. c. increasing increasing cash flows flows occurri occurring ng each each time time period period for a fixed length length of of time. time. d. increa increasin sing g cash cash flows flows occu occurri rring ng each each time time perio period d foreve forever. r. e. arbitrary arbitrary cash flows flows occurri occurring ng each each time time perio period d for no more more than than 10 10 years. years.

Difficulty level: Easy ANNUITIES DUE e . Annu Annuit itie iess wher wheree the the pay payment mentss occu occurr at the the end end of of each each tim timee peri period od are are cal calle led d !!!! !!!!! ! " whe where reas as !!!!! refer to annuity streams streams with payments payments occurring at the beginning of each time period. a. ordi ordina nary ry ann annui uiti ties es## ear early ly annu annuit itie iess b. late annuities# straight straight annuities c. stra straig ight ht annu annuit itie ies# s# late late annu annuit itie iess d. annu annuit itie iess due due## ord ordin inary ary annu annuit itie iess e. ordi ordina nary ry annu annuit itie ies# s# annu annuit itie iess due due

Difficulty level: Easy PERPETUIT c $. An annu annuit ity y str strea eam m whe where re the the pay payme ment ntss occu occurr fore foreve verr is is cal calle led d a%n a%n&: &: a. annuity due. b. indemnity. indemnity. c. perpetuity. d. amor amorti ti'e 'ed d cas cash h flo flow w str strea eam. m. e. amo amorti'ation tab table.

Difficulty level: Easy STATED INTEREST RATES a (. )he )he inte intere rest st rat ratee expr expres esse sed d in term termss of the the int inter eres estt paym paymen entt made made eac each h peri period od is is call called ed the the !!!!! rate. a. sta stated ted ann annual ual in intere teresst b. compound annual interest interest c. effe effect ctiv ivee annu annual al inte intere rest st d. periodic in interest e. daily in interest

Difficulty level: Easy EFFECTIVE ANNUA! RATE c *. )he )he inte intere rest st rat ratee expr expres esse sed d as if if it wer weree comp compou ound nded ed onc oncee per per year year is is call called ed the the !!! !!!!! !! rat rate. e.

a. b. c. d. e.

stated interest compound interest effective an annual periodic in interest daily in interest

Difficulty level: Easy ANNUA! PERCENTA PERCEN TA"E "E RATE RATE b +. )he interest rate charged charged per period multiplied multiplied by the number of periods periods per year is called the !!!!! rate. a. effective an annual b. annual percentage c. periodic interest d. com omp pound in interest e. daily in interest

Difficulty level: Easy

II.

CONCEPTS

ORDINAR ANNUIT VERSUS ANNUIT DUE c ,. -ou are are com compa pari ring ng two two annu annuit itie iess whi which ch off offer er mon month thly ly pay payme ment ntss for for ten ten year years. s. ot oth h annuities are identical with the exception of the payment dates. Annuity A pays on the first of each month while annuity pays on the last day of each month. /hich one of the following statements is correct concerning these two annuities a. oth oth annu annuit itie iess are are of of eua euall valu valuee toda today y. b. Annuity is an annuity annuity due. c. Annui Annuity ty A has a highe higherr futur futuree value value than than annu annuity ity . d. Annui Annuity ty has has a higher higher presen presentt value value than than annu annuity ity A. e. oth oth annui annuitie tiess have have the same same futu future re value value as as of ten ten years years from from today today..

Difficulty level: Medium

UNEVEN CASH CAS H F!O#S AND PRESENT VA!UE VA!UE b 2. -ou -ou are comparing two investment investment options. )he )he cost to invest in either either option is the same today. oth options will provide you with 30"000 of income. 4ption A pays five annual payments starting with 32"000 the first year followed by four annual payments of 3$"000 each. 4ption pays five annual payments of 3("000 each. /hich one of the following statements is correct given these two investment options a. oth options options are of of eual eual value value given that they both provide provide 30"000 30"000 of of income. income. b. 4ption A is the better choice choice of the two given any positive positive rate of return. c. 4ption 4ption has has a higher higher present present value value than option option A given given a posit positive ive rate rate of return. return. d. 4ption 4ption has has a lower lower future future value value at at year year * than optio option n A given given a 'ero rate of of return. return. e. 4ption 4ption A is prefer preferabl ablee becau because se it it is an annu annuity ity due. due.

Difficulty level: Medium UNEVEN CASH F!O#S AND FUTURE VA!UE

a. b. c. d. e.

stated interest compound interest effective an annual periodic in interest daily in interest

Difficulty level: Easy ANNUA! PERCENTA PERCEN TA"E "E RATE RATE b +. )he interest rate charged charged per period multiplied multiplied by the number of periods periods per year is called the !!!!! rate. a. effective an annual b. annual percentage c. periodic interest d. com omp pound in interest e. daily in interest

Difficulty level: Easy

II.

CONCEPTS

ORDINAR ANNUIT VERSUS ANNUIT DUE c ,. -ou are are com compa pari ring ng two two annu annuit itie iess whi which ch off offer er mon month thly ly pay payme ment ntss for for ten ten year years. s. ot oth h annuities are identical with the exception of the payment dates. Annuity A pays on the first of each month while annuity pays on the last day of each month. /hich one of the following statements is correct concerning these two annuities a. oth oth annu annuit itie iess are are of of eua euall valu valuee toda today y. b. Annuity is an annuity annuity due. c. Annui Annuity ty A has a highe higherr futur futuree value value than than annu annuity ity . d. Annui Annuity ty has has a higher higher presen presentt value value than than annu annuity ity A. e. oth oth annui annuitie tiess have have the same same futu future re value value as as of ten ten years years from from today today..

Difficulty level: Medium

UNEVEN CASH CAS H F!O#S AND PRESENT VA!UE VA!UE b 2. -ou -ou are comparing two investment investment options. )he )he cost to invest in either either option is the same today. oth options will provide you with 30"000 of income. 4ption A pays five annual payments starting with 32"000 the first year followed by four annual payments of 3$"000 each. 4ption pays five annual payments of 3("000 each. /hich one of the following statements is correct given these two investment options a. oth options options are of of eual eual value value given that they both provide provide 30"000 30"000 of of income. income. b. 4ption A is the better choice choice of the two given any positive positive rate of return. c. 4ption 4ption has has a higher higher present present value value than option option A given given a posit positive ive rate rate of return. return. d. 4ption 4ption has has a lower lower future future value value at at year year * than optio option n A given given a 'ero rate of of return. return. e. 4ption 4ption A is prefer preferabl ablee becau because se it it is an annu annuity ity due. due.

Difficulty level: Medium UNEVEN CASH F!O#S AND FUTURE VA!UE

a

5.

-ou are are con consi side deri ring ng two two pro pro6e 6ect ctss wit with h the the foll follow owin ing g cas cash h flo flows ws:: 7ro6ect A 7ro6ect -ear 1 3"*00 3("000 -ear $"000 $"*00 -ear $ $"*00 $"000 -ear ( ("000 "*00 /hich of the following statements are true concerning these two pro6ects 8. oth pro6ects pro6ects have the same same future future value value at the end end of of year year (" given a positi positive ve rate rate of return. 88. oth pro6ects pro6ects have have the the same same future future value value given given a 'ero rate of return. return. 888. oth pro6ects pro6ects have have the same same future future value at any any point point in time" time" given a positiv positivee rate of return. 89. 89. 7ro6ect 7ro6ect A has a higher higher future value value than pro6ect pro6ect " given a positive positive rate rate of return. a. 88 only b. 89 only c. 8 and 888 only d. 88 and 89 only e. 8" 88" and 888 only Difficulty level: Medium

PERPETUIT VERSUS ANNUIT d 10. 10. A perp perpet etui uity ty diff differ erss from from an annu annuit ity y beca becaus use: e: a. perpet perpetui uity ty paym payment entss vary vary with with the rate rate of infla inflatio tion. n. b. perpetuity payments payments vary with the maret rate of interest. interest. c. perpet perpetui uity ty paymen payments ts are varia variable ble whil whilee annuity annuity pay paymen ments ts are cons constan tant. t. d. perp perpet etui uity ty paym paymen ents ts neve neverr cea cease se.. e. annu annuit ity y pay payme ment ntss n nev ever er ceas cease. e.

Difficulty level: Easy ANNUA! PERCENTA PERCEN TA"E "E RATE RATE e 11. 11. /hich /hich one one of of the the follow following ing statem statement entss conc concern erning ing the the annu annual al percen percentag tagee rate rate is correct a. )he annual annual percen percentag tagee rate rate consid considers ers int interes erestt on int intere erest. st. b. )he rate of interest you you actually pay on a loan is called the annual percentage rate. rate. c. )he effec effective tive annual annual rate rate is lower lower than than the the annual annual percentage percentage rate when when an an interest interest rate is compounded uarterly. d. /hen firms firms advertis advertisee the annual annual percentag percentagee rate rate they are viola violating ting ;.or any any positi positive ve rate rate of inter interest" est" the the effect effective ive annual annual rate will will always always exceed exceed the annual annual percentage rate.

Difficulty level: Easy EFFECTIVE ANNUA! RATE c 1$. /hich /hich of the follow following ing state statemen ments ts concer concernin ning g the the effect effective ive annual annual rate rate are are corr correct ect 8. /hen maing maing financ financial ial decisi decisions" ons" you shou should ld compar comparee effectiv effectivee annual annual rates rather rather than annual percentage rates. 88. )he more more freuent freuently ly interest interest is compou compounded nded"" the higher higher the the effectiv effectivee annual annual rate. rate. 888. A uoted uoted rate of +? compoun compounded ded continuou continuously sly has a higher higher effective effective annual annual rate than if the rate were compounded daily. 89. 89. /hen borrowing borrowing and choosing choosing which which loan to to accept" you you should select the offer with with the highest effective annual rate. a. 8 and 88 only b. 8 and 89 only c. 8" 88" and 888 only d. 88" 888" and 89 only e. 8" 88" 88 888"and 89 89

Difficulty level: Medium CONTINUOUS CO$POUNDIN" d 1(. )he highes highestt effec effectiv tivee aannu nnual al rate rate that that can can be be deri derived ved from from an annual annual percen percentag tagee rate rate of of 5? is computed as: a. .05e 1 . .05 b. e × . c. e × %1 @ .05&. d. e.05 1. e. %1 @ .05&.

Difficulty level: Easy TI$E VA!UE c 1*. 1*. )he )he tim timee val value ue of money oney con concept cept can can be be def defin ined ed as a. the relations relationship hip between between the the supply supply and deman demand d of money. money. b. the relationship between between money spent versus versus money received. c. the relatio relationship nship between between a dollar dollar to be be received received in the the future future and a dollar dollar today today.. d. the relations relationship hip of intere interest st rate rate stated stated and amount amount paid. paid. e. Bone Bone of the the abov abovee.

Difficulty level: Easy CASH F!O#S d 1+. 1+. isc isco ount unting cash ash flow flowss invo nvolves lves a. discounti discounting ng only only those those cash cash flows flows that that occur occur at least least 10 10 years years in the the future. future. b. estimating only the the cash flows that occur in the the first ( years of a pro6ect. c. multiply multiplying ing expecte expected d future future cash flows flows by the cost of capit capital. al. d. discounti discounting ng all expec expected ted future future cash cash flows flows to reflect reflect the time time value value of money money..

e.

taing taing the the cash cash discou discount nt offer offered ed on trad tradee mercha merchandi ndise. se.

Difficulty level: Easy INTEREST

a

1,. a. b. c. d. e.

Compound interest allows allows for for the the reinve reinvestm stment ent of of intere interest st paym payments ents.. does not allow for the reinvestment reinvestment of interest interest payments. is the the sam samee as simp simple le int inter eres est. t. provid provides es a value value that that is is less less than than simp simple le inter interest est.. oth A and . .

Difficulty level: Easy ANNUIT c 12. An annuity a. is a debt debt instr instrume ument nt that that pays pays no inte interes rest. t. b. is a stream of payments that varies varies with current maret maret interest. c. is a leve levell strea stream m of eua euall paymen payments ts throu through gh time time.. d. has no value. e. Bone Bone of the the abov abovee.

Difficulty level: Easy CO$POUNDIN" d 15. )he state stated d rate rate of of inter interest est is 10?. 10?. /hich /hich form form of compou compoundi nding ng will will give give the the highe highest st effe effecti ctive ve rate of interest a. ann annual ual com compoun poundi ding ng b. monthly compounding compounding c. dai daily com compoun poundi din ng d. cont contin inuo uous us comp compou ound ndin ing g e. 8t is impossibl impossiblee to tell without without nowing nowing the term of the the loan. loan.

Difficulty level: Easy PRESENT VALUE

b

0. a. b. c. d. e.

)he present value of future future cash flows minus initial initial cost is called the the futu future re val value ue of the the pro6 pro6ec ect. t. the net present value of the the pro6ect. the euiv euivale alent nt sum of the invest investmen ment. t. the init initial ial invest investme ment nt ris ris euiv euivale alent nt value value.. Bone Bone of the the abov abovee.

Difficulty level: Easy

III. III. PRO% PRO%!E !E$S $S PRESENT VALUE – SINGLE SUM

a

1. >ind >ind the the presen presentt value value of 3*"$ 3*"$* * to to be receiv received ed in one period period if the the rate rate is is + +.*? .*?.. a. 3*"000.00

b. c. d. e.

3*"0$.*2 3*"+((.*0 3*"+,1.1$ Bone of the above.

Difficulty level: Easy SIMPLE & COMPOUND INTEREST

b

. 8f you have a choice to earn simple interest on 310"000 for three years at 2? or annually compound interest at ,.*? for three years which one will pay more and by how much a. amily >un Center deposited 3$"+00 in an investment account for the purpose of buying new euipment four years from today. )oday" they are adding another 3*"000 to this account. )hey plan on maing a final deposit of 3,"*00 to the account next year. Dow much will be available when they are ready to buy the euipment" assuming they earn a ,? rate of return a. 312"1*5.+* b. 315"($0.2( c. 315"+2$.* d. 30"15(.*( e. 30",50.55

Difficulty level: Medium UNEVEN CASH F!O#S AND FUTURE VA!UE c ,(. /hat is the future value of the following cash flows at the end of year $ if the interest rate is + percent )he cash flows occur at the end of each year. -ear 1 -ear -ear $ 3*"120 35"+00 3"*0 a. 31*"51+.,2 b. 312"105.02 c. 312"(+.* d. 315"$(1.0 e. 315"+02.0,

Difficulty level: Medium UNEVEN CASH F!O#S AND FUTURE VA!UE d ,*. /hat is the future value of the following cash flows at the end of year $ if the interest rate is 5 percent )he cash flows occur at the end of each year. -ear 1 -ear -ear $ 35"20 30 3("*10 a. 31*"1$.20 b. 31*"+15.,0 c. 31*"51+.,2 d. 31+"1,,.1( e. 31,"+$$.02

Difficulty level: Medium UNEVEN CASH F!O#S AND FUTURE VA!UE c ,+. /hat is the future value of the following cash flows at the end of year $ if the interest rate is ,.* percent )he cash flows occur at the end of each year. -ear 1 -ear -ear $ 3+"200 3"100 30 a. 32",*2.0( b. 32"20+.$5 c. 310"0,$.55 d. 310"$1(.00 e. 310"20(.$+

Difficulty level: Medium UNEVEN CASH F!O#S AND FUTURE VA!UE e ,,. 9

.0(5 *×1 1 − 1 P% 1 + & 1 S 31+0 )*0 = 31+0 × .0(5 1 Lnter

,.

79 =("*2.0$

100 7M)

(.*20$ S 3("*2.0$

×

.02 100 1 − 1 P% 1 + & 1 S 31"00 )*0 = 31"00 × .02 1 Lnter

+.

*$* >9

>9

22.0+2* S 3*+"(*1.51

×

9

.0$* *×1 1 − 1 P%1 + 1 & .0$* *0 = 31"*00 × × 1 + 1 S 31"*00 .0$* 1

)due

**.$05,,+

×

×

1.00,02$$$ S 32$"125.5 Lnter

*×1 $.*P1 =1"*00FB B 8P79 7M) >9 2$"125.5

9 =50"12.,5

$$.

)*0

* [ ] = 310"000 × 1 − 1 P%1 + .02*& S 310"000 × 10.$(151 S 310"$(1.51 .02*

Lnter

* B

2.* 8P-

9

1 − [1 P%1 + .02*& * ] *0 = 310"000 × × (1 + .02* ) S 310"000 × 10.$(151 × 1.02* S .02*

)due

3111"0(0.5, Lnter

* B

9 =*(",5*.$5

1 − [1 P%1 + .0,*& 0 ] 3*(",5*.$5 = C × # C S 3*"$,* .0,* Lnter 9

ecause each payment is received one year later" then the cash flow has to eual: 3*"000 × %1 @ .0,*& S 3*"$,*

$*.

02 *×1 1 − 1 P% 1 + . & .02 1 × 1+ *0 = 3100 × S 3100 .02 1 1

)due

(5.$12(05 × 1.00+++, S

×

3("5+(., Lnter

*×1 B

9 =("5+(.,

.02 *×1 1 − 1 P%1 + 1 & )*0 = 3100 × S 3100 .02 1 Lnter

*×1 B

9

ifference S 3("5+(., = 3("5$1.2(S 3$.22 .02 = 3$.22 Bote: ifference = 3("5$1 .2( × 1 $+.

),0

%1 + .0+& * = 31"000 × .0+

Lnter

* B

+ 8P-

− 1 S 31"000 × *.+$,05 S 3*"+$,.05

79

9 =*"+$,.05

= 3$"000 ×

Lnter 9 (02"5.+

79

9 ((*",*.+*

ifference S 3((*",*.+* = 3(02"5.+ S 3$+"20$.0$ Bote: ifference S 3(02"5.+ × .05 S 3$+"20$.0$

(0.

1 1 P%1 .0*5 & (×1 − + 1 3*"+00 = C × # 3*"+00 S C .0*5 1 Lnter

(×1 B

*.5P1 8P-

*"+00 79

9

1 1 P%1 .0,* &$0×1 − + 1 31(5"000 = C × # 31(5"000 S C .0,* 1 Lnter

$0×1 B

9 =1"0(1.2$

)otal interest S %31"0(1.2$ × $0 × 1& = 31(5"000 S 3+"0*2.20 S 3+"0*5 %rounded& (.

%1 + .0+*&10 3*"000"000 = C × .0+* Lnter 9 =1"2*"+1,.*

($.

1 − 1 P%1 + .0(* & ,×1 1 3(+("500 = C × # 3(+("500 S C .0(* 1

12,.$+$525$# C S

×

3"(21., Lnter

,×1 B

9

$1.5*22*# C S 3155.5(

×

(,.

0** *×( 1 − 1 P% 1 + . & ( )*0 = 3*00 × S 3*00 .0** ( Lnter

*×( B

*.*P( 8P-

9

.0(5 +0 1 − 1P%1 + . 1 & .0(5 *0 = 355 × × 1 + 1 S 355 .0(5 1

)due

*$.115*+52 × 1.00(02$$$

×

S 31*"5(,.+1 Lnter

+0 B

9 $00"+2*.11

1 − [1 P%1 + .0(*&t ] 3100"000 = 3+"000 × # ln( S t × ln1.0(*# t S $1.(5 .0(* Lnter 9

1 − 1 P%1 + .05 & 1 3("5*(.2* = 31($.2( × # ln1.$(2$(25 S t .05 1 t

*(.

Lnter 9

ln.000*,*1,, S ln.+52+*502# t

×

105*.02 days ÷ $+* days S $ years

*2.

1 − 1 P%1 + . &$0 1 31$"500 = 3("25(.$* × # )his can not be solved directly" so itHs . 1 easiest to 6ust use the calculator method to get an answer. -ou can then use the calculator answer as the rate in the formula 6ust to verify that your answer is correct. Lnter

$0 B

9 1$.*5

1 − 1 P%1 + . & (0×1 1 3100"000 = 3$2(.(0 × # )his can not be solved directly" so itHs . 1 easiest to 6ust use the calculator method to get an answer. -ou can then use the calculator answer as the rate in the formula 6ust to verify that you answer is correct. Lnter

(0×1 B

9

−1 # )his can not be solved directly" so itHs easiest to

1 6ust use the calculator method to get an answer. -ou can then use the calculator answer as the rate in the formula 6ust to verify that you answer is correct. Lnter

1*×1 B

9

7M)

5"000 >9

1*"000 7M) >9

7resent value S 3("$2*.5+ @ 3+"5*.1 @ 310"1(.*, S 31"($*.,(

+*.

*0

1 1 1 = 31"00 × + 31"*00 × + 3"000 × 1 $ # 79 S %1 + .0(& %1 + .0(& (1 + .0( )

3("$12.+, Lnter

1 B

( 8P79 =1"1*$.2*

B

( 8P-

$ B

( 8P-

9

B

+ 8P-

**"000 7M) >9

$ B

+ 8P-

9

7resent value S 31"100.5 @ 31"*1*.0 @ 3"$5.$$ S 3("2**.,

+5.

*0

1 1 1 = 3*"+00 × + 35"000 × + 3"000 × 1 $ # 79 S %1 + .11& %1 + .11& (1 + .11)

31$"21.0$ Lnter

1 B

11 8P79 =*"0(*.0*

B

11 8P-

$ B

11 8P-

9

=*"000 7M) >9

7resent value S 3*"000.00 @ 31("1*0.5( @ 3"(5.51 S 3(1"(00.2* ,$.

,0

=

3$"+00 × %1.0, & *

Lnter

+

3*"000 × %1.0, & (

, =$"+00 8P79

7M)

>9 *"0(5.15

( B

, 8P-

=*" 000 79

7M)

>9 +"**$.52

$ B

, 8P-

=,"*00 79

7M)

>9 5"12,.2

9 *"20.*

7M) >9 10"1,+.00

>uture value S 3*"20.* @ 310"1,+.00 @ 3"*0.00 S 312"(+.*

,*.

,0

=

35"20 × %1.05&

Lnter

B

+ 0 + 3("*10 # >9 S 31+"1,,.1(

5 =5"20 8P79

7M)

9 11"++,.1(

>uture value S 311"++,.1( @ 30 @ 3("*10.00 S 31+"1,,.1( ,+.

,0 = [3+"200 × %1.0,*& ] + [3"100 × %1.0,*&1 ] + 30 # >9 S 310"0,$.55 Lnter

B

,.* 8P-

=+"200 79

7M)

>9 ,"21.,(

1 B

,.* 8P-

="100 79

7M)

>9 "*.*

9 S 3*5*"052.+, Lnter

* B

11 =10"000 8P79

( B

11 =1*"000 8P79

$ B

11 =*"000 8P79

9 ,*"+*+.+2

>uture value S 31$*"2*(.+( @ 312$"*2,.$* @ 3,*"+*+.+2 S 3*5*"052.+, ,2.

310"000

= [C × %1.0$&$ ] + [3"*00 × %1.0$& ] + [3"*00 × %1.0$&1 ] + 3"*00 # CS

3"0,5.25 Lnter 9 *2",*0.00

>9 S 310,"1.*0 @ 3*2",*0.00 @ 3*0"000 S 3+1*"2,.*0 20.

*0

= 1*0"000 # 79 S 3$"*5"(11.,,

21.

*0

=

2.

*0

= *0"000 # 79 S 31"212"121.2

2$.

.

=

3 1 "000 # S $.($ percent 3$*0 "000

2(.

.

=

3 10 "000 # S $.*1 percent 32* "000

2*.

C

=

2+.

C

= 3*0.00 × .02( # C S 3(.0

2,.

A7 S .01* × 1 S .12 S 12 percent

22.

A7 S .0 × ( S .02S 2 percent

25.

)*3 .1$2 = 1 + − 1 # A7 S 1$.00 percent 1

.0(*

3(.*0 # 79 S 3*0.00 .05

.0,*

31*0"000 × .0( # C S 3+"000

1

Lnter > 1$.00

1 CP-

(

50.

.0,+( E)3 = 1 + − 1 # LA S ,.2+ percent ( Lnter > ,.2+

( CP-

1

51.

.1(5 1 # LA S 1*.5+ percent E)3 = 1 + − 1 Lnter 1*.5+

E)3 )

$+*

− 1 # A7 S $.$+ percent

1 B4M L>> $.$+

.0,(* = 1 + $+*

Lnter > ,.,$

− 1 # A7 S ,.,$ percent $+* CP-

E)3 <

.0,* = 1 + − 1 # A7 S ,.+( percent

Lnter > ,.+(

CP-

5(.

LAA S $.,* percent 1

E)3 <

.0$, = 1 + − 1 # LA S $.,+ percent 1

Lnter

$., B4M L>> $.,+

> $.,$

uture value S 32"*00 × %1 @ .0$*&1* S 3(,",(,.(( Lnter

1* B

$.* =2"*00 8P79

uture value S 3125"500 × %1 @ .0(*&+ S 3(,"55.0 Lnter

+ B

(.* =125"500 8P79

9

310,"51 S 3"*00 × %1 @ r&(0# r S 5.2, percent Lnter 9

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