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 ;.<. truth truth=in= =in= lending laws. e. )he annual annual percent percentage age rate euals euals the the effectiv effectivee annual annual rate when the rate on an account is designated as simple interest.
Difficulty level: Easy INTEREST RATES RATES b 1. /hich one of the following following statements concerning concerning interest rates is is correct a. )he stated stated rate rate is the same same as the the effe effecti ctive ve annu annual al rate rate.. b. An effective annual annual rate is the rate that applies applies if interest were charged charged annually. annually. c. )he annual annual percentag percentagee rate increases increases as the the number number of of compound compounding ing period periodss per year increases.
d. e.
ans ans prefe preferr more more freuen freuentt compou compoundi nding ng on their their savi savings ngs acco account unts. s. >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.
FUTURE VA!UE & SIN"!E SU$ d $. radley
Difficulty level: Easy ORDINAR ANNUIT AND PRESENT VA!UE d (. -our parents are giving you 3100 a month for four years while you are in college. At a +? discount rate" what are these payments worth to you when you first start college a. 3$",5,.(0 b. 3("1+,.05 c. 3("152.,5 d. 3("*2.0$ e. 3(",5.$
Difficulty level: Easy ORDINAR ANNUIT AND PRESENT VA!UE b *. -ou 6ust won the lotteryE As your pri'e you will receive 31"00 a month for 100 months. 8f you can earn 2? on your money" what is this pri'e worth to you today a. 32,"00$.+5 b. 32,"$20.$ c. 32,"5+.,, d. 322"10(.+ e. 350",$.,+
Difficulty level: Easy ORDINAR ANNUIT AND PRESENT VA!UE b +. )odd is able to pay 31+0 a month for five years for a car. 8f the interest rate is (.5 percent" how much can )odd afford to borrow to buy a car a. 3+"5+1.$+ b. 32"(55.1$ c. 32"*$$.2( d. 32"+2+.2 e. 35"*22.0*
Difficulty level: Easy ORDINAR ANNUIT AND PRESENT VA!UE a ,. -ou are the beneficiary of a life insurance policy. )he insurance company informs you that you have two options for receiving the insurance proceeds. -ou can receive a lump sum of 3*0"000 today or receive payments of 3+(1 a month for ten years. -ou can earn +.*? on your money. /hich option should you tae and why a. -ou should accept the payments because they are worth 3*+"(*1.51 today. b. -ou should accept the payments because they are worth 3*+"*$.,( today. c. -ou should accept the payments because they are worth 3*+",$,.02 today. d. -ou should accept the 3*0"000 because the payments are only worth 3(,",*,.+5 today. e. -ou should accept the 3*0"000 because the payments are only worth 3(,"202.1, today.
Difficulty level: Medium ORDINAR ANNUIT AND PRESENT VA!UE c 2. -our employer contributes 3* a wee to your retirement plan. Assume that you wor for your employer for another twenty years and that the applicable discount rate is * percent. Fiven these assumptions" what is this employee benefit worth to you today a. 31$"1((.($ b. 31*"50.** c. 31+"($0.*( d. 31+"((+.$( e. 31+"*15.0
Difficulty level: Medium ORDINAR ANNUIT AND PRESENT VA!UE a 5. -ou have a sub=contracting 6ob with a local manufacturing firm. -our agreement calls for annual payments of 3*0"000 for the next five years. At a discount rate of 1 percent" what is this 6ob worth to you today a. 3120"$2.21 b. 301"2+,.(, c. 310"+12.15 d. 3$"1+.*2 e. 3("+,.10
Difficulty level: Medium ANNUIT DUE AND PRESENT VA!UE
b
$0. )he A6ax Co. 6ust decided to save 31"*00 a month for the next five years as a safety net for recessionary periods. )he money will be set aside in a separate savings account which pays $.*? interest compounded monthly. )hey deposit the first 31"*00 today. 8f the company had wanted to deposit an euivalent lump sum today" how much would they have had to deposit a. 32"5+(.*5 b. 32$"125.5 c. 32$"(2.2, d. 32$"+2,.$ e. 32("552.01 Difficulty level: Medium
ANNUIT DUE AND PRESENT VA!UE b $1. -ou need some money today and the only friend you have that has any is your GmiserlyH friend. De agrees to loan you the money you need" if you mae payments of 30 a month for the next six month. 8n eeping with his reputation" he reuires that the first payment be paid today. De also charges you 1.*? interest per month. Dow much money are you borrowing a. 311$.5( b. 311*.+* c. 3115.$( d. 3115.+$ e. 3115.5+
Difficulty level: Medium ANNUIT DUE AND PRESENT VA!UE c $. -ou buy an annuity which will pay you 31"000 a year for ten years. )he payments are paid on the first day of each year. /hat is the value of this annuity today at a ,? discount rate a. 32("2.52 b. 32,"1$2.0( c. 350"12.,5 d. 35+"151.51 e. 311+"51+.1
Difficulty level: Medium ORDINAR ANNUIT VERSUS ANNUIT DUE a $$. -ou are scheduled to receive annual payments of 310"000 for each of the next * years. -our discount rate is 2.* percent. /hat is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year a. 32"+55 b. 35"1, c. 35",0+ d. 310"000 e. 310"2*0
Difficulty level: Medium ORDINAR ANNUIT VERSUS ANNUIT DUE
d
$(. -ou are comparing two annuities with eual present values. )he applicable discount rate is ,.* percent. 4ne annuity pays 3*"000 on the first day of each year for twenty years. Dow much does the second annuity pay each year for twenty years if it pays at the end of each year a. 3("+*1 b. 3*"0,* c. 3*"000 d. 3*"$,* e. 3*"(0* Difficulty level: Medium
ORDINAR ANNUIT VERSUS ANNUIT DUE a $*. Martha receives 3100 on the first of each month.
Difficulty level: Medium ORDINAR ANNUIT AND FUTURE VA!UE c $+. /hat is the future value of 31"000 a year for five years at a +? rate of interest a. 3("1.$+ b. 3*"0,*.+5 c. 3*"+$,.05 d. 3+"001.$2 e. 3+"201.51
Difficulty level: Easy ORDINAR ANNUIT AND FUTURE VA!UE d $,. /hat is the future value of 3"(00 a year for three years at an 2? rate of interest a. 3+"12*.0$ b. 3+"2(,.+ c. 3,"1$(.1+ d. 3,",51.$+ e. 32"(1(.+,
Difficulty level: Easy ORDINAR ANNUIT AND FUTURE VA!UE c $2. Ianet plans on saving 3$"000 a year and expects to earn 2.* percent. Dow much will Ianet have at the end of twenty=five years if she earns what she expects a. 315"$1,.2 b. 3$0",0.*, c. 3$+"00$.$2 d. 3(("2+2.5 e. 3*+"0+$.++
Difficulty level: Easy ANNUIT DUE VERSUS ORDINAR ANNUIT b $5. )oni adds 3$"000 to her savings on the first day of each year. )im adds 3$"000 to his savings on the last day of each year. )hey both earn a 5? rate of return. /hat is the difference in their savings account balances at the end of thirty years a. 3$*"2.,$ b. 3$+"20$.0$ c. 3$2"511.1 d. 3$5"20$.0( e. 3(0"11*.$1
Difficulty level: Medium ORDINAR ANNUIT PA$ENTS d (0. -ou borrow 3*"+00 to buy a car. )he terms of the loan call for monthly payments for four years at a *.5? rate of interest. /hat is the amount of each payment a. 310$. b. 310$.,$ c. 31$0.+ d. 31$1.+ e. 31$$.0(
Difficulty level: Easy ORDINAR ANNUIT PA$ENTS AND COST OF INTEREST c (1. -ou borrow 31(5"000 to buy a house. )he mortgage rate is ,.*? and the loan period is $0 years. 7ayments are made monthly. 8f you pay for the house according to the loan agreement" how much total interest will you pay a. 31$2"02+ b. 312"1+1 c. 3+"0*5 d. 32,"02+ e. 3$,*"0*5
Difficulty level: Medium ORDINAR ANNUIT PA$ENTS AND FUTURE VA!UE d (. )he Freat Fiant Corp. has a management contract with their newly hired president. )he contract reuires a lump sum payment of 3* million be paid to the president upon the completion of her first ten years of service. )he company wants to set aside an eual amount of funds each year to cover this anticipated cash outflow. )he company can earn +.*? on these funds. Dow much must the company set aside each year for this purpose a. 31",,*"0(.5$ b. 31",52"$(+.1, c. 31"201"0$$.+, d. 31"2*"+1,.* e. 31"5$2"012.
Difficulty level: Easy ORDINAR ANNUIT PA$ENTS AND PRESENT VA!UE e ($. -ou retire at age +0 and expect to live another , years. 4n the day you retire" you have 3(+("500 in your retirement savings account. -ou are conservative and expect to earn (.*? on your money during your retirement. Dow much can you withdraw from your retirement savings each month if you plan to die on the day you spend your last penny a. 3"001.5+ b. 3"05.0* c. 3"$52.1, d. 3"(,.00 e. 3"(21.,
Difficulty level: Medium ORDINAR ANNUIT PA$ENTS AND PRESENT VA!UE c ((. )he Mconald Froup purchased a piece of property for 31. million. )hey paid a down payment of 0? in cash and financed the balance. )he loan terms reuire monthly payments for 1* years at an annual percentage rate of ,.,*? compounded monthly. /hat is the amount of each mortgage payment a. 3,"((0.01 b. 32"5,2.+ c. 35"0$+.* d. 35"$55.12 e. 35"(1$.+,
Difficulty level: Medium ORDINAR ANNUIT PA$ENTS AND PRESENT VA!UE d (*. -ou estimate that you will have 3("*00 in student loans by the time you graduate. )he interest rate is +.* percent. 8f you want to have this debt paid in full within five years" how much must you pay each month a. 3(,1.$0 b. 3(,$.+* c. 3(,+.,5 d. 3(,5.$, e. 3(20.(0
Difficulty level: Medium ORDINAR ANNUIT PA$ENTS AND PRESENT VA!UE b (+. -ou are buying a previously owned car today at a price of 3+"250. -ou are paying 3*00 down in cash and financing the balance for $+ months at ,.5 percent. /hat is the amount of each loan payment a. 3152.+( b. 3155.5( c. 30.0 d. 31(.,2 e. 31*.05
Difficulty level: Medium
ORDINAR ANNUIT PA$ENTS AND PRESENT VA!UE b (,. )he Food Jife 8nsurance Co. wants to sell you an annuity which will pay you 3*00 per uarter for * years. -ou want to earn a minimum rate of return of *.* percent. /hat is the most you are willing to pay as a lump sum today to buy this annuity a. 3+"522.1+ b. 3,"02.5( c. 3,"(**.$$ d. 32"(*0.+, e. 32"20+.$0
Difficulty level: Medium ANNUIT DUE PA$ENTS AND PRESENT VA!UE c (2. -our car dealer is willing to lease you a new car for 355 a month for +0 months. 7ayments are due on the first day of each month starting with the day you sign the lease contract. 8f your cost of money is (.5 percent" what is the current value of the lease a. 31*"22.,* b. 31*"50+.1( c. 31*"5(,.+1 d. 31+"$*.( e. 31+"25.*(
Difficulty level: Medium ANNUIT DUE PA$ENTS AND PRESENT VA!UE d (5. -our great=aunt left you an inheritance in the form of a trust. )he trust agreement states that you are to receive 3"*00 on the first day of each year" starting immediately and continuing for fifty years. /hat is the value of this inheritance today if the applicable discount rate is +.$* percent a. 3$+"211.$0 b. 3$,"**,.* c. 3$5"0(.0( d. 3$5"5(.( e. 3(0"00+.05
Difficulty level: Medium SI$P!E VERSUS CO$POUND INTEREST c *0. eatrice invests 31"000 in an account that pays (? simple interest. Dow much more could she have earned over a five=year period if the interest had compounded annually a. 31*.(* b. 31*.5, c. 31+.+* d. 31,.05 e. 31.+,
Difficulty level: Easy ANNUIT DUE PA$ENTS AND FUTURE VA!UE
a
*1. -our firm wants to save 3*0"000 to buy some new euipment three years from now. )he plan is to set aside an eual amount of money on the first day of each year starting today. )he firm can earn a (.,? rate of return. Dow much does the firm have to save each year to achieve their goal a. 3,*"5++.1( b. 3,+"25+.1+ c. 3,2"00(.+, d. 321.(1(.1( e. 32$"$$$.$$ Difficulty level: Medium
ANNUIT DUE PA$ENTS AND FUTURE VA!UE e *. )oday is Ianuary 1.
Difficulty level: Medium ORDINAR ANNUIT TI$E PERIODS AND PRESENT VA!UE c *$. -ou are considering an annuity which costs 3100"000 today. )he annuity pays 3+"000 a year. )he rate of return is (.* percent. /hat is the length of the annuity time period a. (.5+ years b. 5.(2 years c. $1.(5 years d. $$.02 years e. $2.00 years
Difficulty level: Medium ORDINAR ANNUIT TI$E PERIODS AND PRESENT VA!UE d *(. )oday" you signed loan papers agreeing to borrow 3("5*(.2* at 5? compounded monthly. )he loan payment is 31($.2( a month. Dow many loan payments must you mae before the loan is paid in full a. 5.25 b. $+.00 c. $2.22 d. (0.00 e. (1.0$
Difficulty level: Medium ORDINAR ANNUIT TI$E PERIODS AND FUTURE VA!UE
a
**. /inston Lnterprises would lie to buy some additional land and build a new factory. )he anticipated total cost is 31$+ million. )he owner of the firm is uite conservative and will only do this when the company has sufficient funds to pay cash for the entire expansion pro6ect. Management has decided to save 3(*0"000 a month for this purpose. )he firm earns +? compounded monthly on the funds it saves. Dow long does the company have to wait before expanding its operations a. 12(.+1 months b. 155.5, months c. $(.$( months d. 2(.+1 months e. 55.5, months Difficulty level: Medium
ANNUIT DUE TI$E PERIODS AND PRESENT VA!UE b *+. )oday" you are retiring. -ou have a total of 3(1$"5+ in your retirement savings and have the funds invested such that you expect to earn an average of $ percent" compounded monthly" on this money throughout your retirement years. -ou want to withdraw 3"*00 at the beginning of every month" starting today. Dow long will it be until you run out of money a. 12*.00 months b. 1$.5 months c. ,.02 months d. $+.2( months e. (5.+5 months
Difficulty level: Medium ANNUIT DUE TI$E PERIODS c *,. )he ad Fuys Co. is notoriously nown as a slow=payer. )hey currently need to borrow 3*"000 and only one company will even deal with them. )he terms of the loan call for daily payments of 3$0.,+. )he first payment is due today. )he interest rate is 1? compounded daily. /hat is the time period of this loan a. .22 years b. .5( years c. $.00 years d. $.1$ years e. $.* years
Difficulty level: Medium ORDINAR ANNUIT INTEREST RATE c *2. )he obertson >irm is considering a pro6ect which costs 31$"500 to undertae. )he pro6ect will yield cash flows of 3("25(.$* monthly for $0 months. /hat is the rate of return on this pro6ect a. 1.*$? b. 1$.((? c. 1$.*5? d. 1(.0? e. 1(.*5?
Difficulty level: Medium
ORDINAR ANNUIT INTEREST RATE a *5. -our insurance agent is trying to sell you an annuity that costs 3100"000 today. y buying this annuity" your agent promises that you will receive payments of 3$2(.(0 a month for the next (0 years. /hat is the rate of return on this investment a. $.(*? b. $.(,? c. $.*0? d. $.*? e. $.**?
Difficulty level: Medium ORDINAR ANNUIT INTEREST RATE e +0. -ou have been investing 310 a month for the last 1* years. )oday" your investment account is worth 3(,"$(1.15. /hat is your average rate of return on your investments a. 5.$(? b. 5.$,? c. 5.(0? d. 5.(? e. 5.(+?
Difficulty level: Medium ORDINAR ANNUIT INTEREST RATE c +1. riner" 8nc. has been investing 31$+"000 a year for the past ( years into a business venture. )oday" riner sold that venture for 3+2*"000. /hat is their rate of return on this venture a. 5.($? b. 11.0+? c. 1*.*5? d. 1+.+,? e. 12.,1?
Difficulty level: Easy ANNUIT DUE INTEREST RATE b +. -our mother helped you start saving 3* a month beginning on your 10 th birthday.
Difficulty level: Easy ANNUIT DUE INTEREST RATE a +$. )oday" you turn 1. -our birthday wish is that you will be a millionaire by your (0 th birthday. 8n an attempt to reach this goal" you decide to save 3* a day" every day until you turn (0. -ou
a. b. c. d. e.
open an investment account and deposit your first 3* today. /hat rate of return must you earn to achieve your goal 1*.0,? 1*.1$? 1*.1,? 1*.0? 1*.(?
Difficulty level: Easy UNEVEN CASH F!O#S AND PRESENT VA!UE b +(. Maro" 8nc. is considering the purchase of AC Co. Maro believes that AC Co. can generate cash flows of 3*"000" 35"000" and 31*"000 over the next three years" respectively. After that time" they feel the business will be worthless. Maro has determined that a 1(? rate of return is applicable to this potential purchase. /hat is Maro willing to pay today to buy AC Co. a. 315"01.,+ b. 31"($*.,( c. 3$"(*,.5+ d. 3,"202.1, e. 3$1",*2.00
Difficulty level: Easy UNEVEN CASH F!O#S AND PRESENT VA!UE a +*. -ou are considering two savings options. oth options offer a (? rate of return. )he first option is to save 31"00" 31"*00" and 3"000 a year over the next three years" respectively. )he other option is to save one lump sum amount today. 8f you want to have the same balance in your savings at the end of the three years" regardless of the savings method you select" how much do you need to save today if you select the lump sum option a. 3("$12.+, b. 3("(51.( c. 3("**1.,2 d. 3("+0,.$ e. 3("2*,.5
Difficulty level: Easy UNEVEN CASH F!O#S AND PRESENT VA!UE b ++. -ou are considering two insurance settlement offers. )he first offer includes annual payments of 3*"000" 3,"*00" and 310"000 over the next three years" respectively. )he other offer is the payment of one lump sum amount today. -ou are trying to decide which offer to accept given the fact that your discount rate is * percent. /hat is the minimum amount that you will accept today if you are to select the lump sum offer a. 315"2,,.+, b. 30"0$.00 c. 31"1$.1* d. 3$"$2,.*0 e. 3("**+.22
Difficulty level: Easy
UNEVEN CASH F!O#S AND PRESENT VA!UE d +,. -ou are considering a 6ob offer. )he 6ob offers an annual salary of 3*"000" 3**"000" and 3+0"000 a year for the next three years" respectively. )he offer also includes a starting bonus of 3"000 payable immediately. /hat is this offer worth to you today at a discount rate of + percent a. 31(2"2$.*+ b. 31(2"$2$.*+ c. 31*0"2$.*+ d. 31*0"$2$.*+ e. 31*"52$.*+
Difficulty level: Easy UNEVEN CASH F!O#S AND PRESENT VA!UE b +2. -ou are considering a pro6ect with the following cash flows: -ear 1 -ear -ear $ 31"00 31"200 3"500 /hat is the present value of these cash flows" given a 5? discount rate a. 3(",1$.+ b. 3("2**., c. 3*"10$.12 d. 3*"5.* e. 3+"2*$.+1
Difficulty level: Easy UNEVEN CASH F!O#S AND PRESENT VA!UE d +5. -ou are considering a pro6ect with the following cash flows: -ear 1 -ear -ear $ 3*"+00 35"000 3"000 /hat is the present value of these cash flows" given an 11? discount rate a. 32"+5*.+1 b. 32",00.25 c. 31$",$.(1 d. 31$"21.0$ e. 315"52.1+
Difficulty level: Easy UNEVEN CASH F!O#S AND PRESENT VA!UE a ,0. -ou are considering a pro6ect with the following cash flows: -ear 1 -ear -ear $ 3("00 3*"000 3*"(00 /hat is the present value of these cash flows" given a $? discount rate a. 31$",$.(1 b. 31$"21.0$ c. 31("$02.02 d. 31("5(1.,+ e. 31("52,.+5
Difficulty level: Easy
UNEVEN CASH F!O#S AND PRESENT VA!UE a ,1. -ou have some property for sale and have received two offers. )he first offer is for 3125"000 today in cash. )he second offer is the payment of 3100"000 today and an additional 3100"000 two years from today. 8f the applicable discount rate is 2.,* percent" which offer should you accept and why a. -ou should accept the 3125"000 today because it has the higher net present value. b. -ou should accept the 3125"000 today because it has the lower future value. c. -ou should accept the second offer because you will receive 300"000 total. d. -ou should accept the second offer because you will receive an extra 311"000. e. -ou should accept the second offer because it has a present value of 315("***.(.
Difficulty level: Medium UNEVEN CASH F!O#S AND PRESENT VA!UE b ,. -our local travel agent is advertising an extravagant global vacation. )he pacage deal reuires that you pay 3*"000 today" 31*"000 one year from today" and a final payment of 3*"000 on the day you leave two years from today. /hat is the cost of this vacation in todayHs dollars if the discount rate is + percent a. 3$5"0*,.(1 b. 3(1"(00.2* c. 3($"02.$5 d. 3(("(1(.1( e. 3(+"*12.00
Difficulty level: Medium UNEVEN CASH F!O#S AND FUTURE VA!UE e ,$. 4ne year ago" the Ienins >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 ,,.
Difficulty level: Medium PRESENT VA!UE' PA$ENTS AND FUTURE VA!UE b ,2. )he luebird Company has a 310"000 liability they must pay three years from today. )he company is opening a savings account so that the entire amount will be available when this debt needs to be paid. )he plan is to mae an initial deposit today and then deposit an additional 3"*00 a year for the next three years" starting one year from today. )he account pays a $? rate of return. Dow much does the luebird Company need to deposit today a. 31"2+,.,( b. 3"0,5.25
c. d. e.
3$"102.05 3(",+.$( 3("+(.2
Difficulty level: Medium UNEVEN CASH F!O#S AND FUTURE VA!UE c ,5. )he government has imposed a fine on the Bot=
Difficulty level: Medium PERPETUIT PRESENT VA!UE b 20. Feorge Iefferson established a trust fund that provides 31*0"000 in scholarships each year for worthy students. )he trust fund earns a (.*? rate of return. Dow much money did Mr. Iefferson contribute to the fund assuming that only the interest income is distributed a. 3$"51"+1$.1$ b. 3$"*5"(11.,, c. 3$",*0"000.00 d. 3("$2"5,0.(( e. 3+"$,*"000.00
Difficulty level: Easy PERPETUIT PRESENT VA!UE e 21. A 5? preferred stoc pays an annual dividend of 3(.*0. /hat is one share of this stoc worth today a. 3.(1 b. 3(.*0 c. 3*.00 d. 3(*.00 e. 3*0.00
Difficulty level: Easy PERPETUIT PRESENT VA!UE e 2. -ou would lie to establish a trust fund that will provide 3*0"000 a year forever for your heirs. )he trust fund is going to be invested very conservatively so the expected rate of return is only .,* percent. Dow much money must you deposit today to fund this gift for your heirs a. 31"$$$"$$$.$$ b. 31"$,*"000.00 c. 31"(*"000.00
d. e.
31"+++"+++.+, 31"212"121.2
Difficulty level: Easy PERPETUIT DISCOUNT RATE c 2$. -ou 6ust paid 3$*0"000 for a policy that will pay you and your heirs 31"000 a year forever. /hat rate of return are you earning on this policy a. $.*? b. $.$$? c. $.($? d. $.*0? e. $.+,?
Difficulty level: Medium PERPETUIT DISCOUNT RATE d 2(. )he Lternal Fift 8nsurance Company is offering you a policy that will pay you and your heirs 310"000 a year forever. )he cost of the policy is 32*"000. /hat is the rate of return on this policy a. .2*? b. $.*? c. $.(+? d. $.*1? e. $.+0?
Difficulty level: Easy PERPETUIT PA$ENT e 2*. -our rich uncle establishes a trust in your name and deposits 31*0"000 in it. )he trust pays a guaranteed (? rate of return. Dow much will you receive each year if the trust is reuired to pay you all of the interest earnings on an annual basis a. 3$",*0 b. 3("000 c. 3("*00 d. 3*"(00 e. 3+"000
Difficulty level: Easy PERPETUIT PA$ENT b 2+. )he preferred stoc of AC Co. offers an 2.(? rate of return. )he stoc is currently priced at 3*0.00 per share. /hat is the amount of the annual dividend a. 3.10 b. 3(.0 c. 3*.00 d. 3+.(0 e. 32.+0
Difficulty level: Easy
ANNUA! PERCENTA"E RATE d 2,. -our credit card company charges you 1.*? per month. /hat is the annual percentage rate on your account a. 1.00? b. 1*.00? c. 1*.$5? d. 12.00? e. 15.*+?
Difficulty level: Medium ANNUA! PERCENTA"E RATE d 22. /hat is the annual percentage rate on a loan with a stated rate of ? per uarter a. .00? b. .,1? c. (.0(? d. 2.00? e. 2.(?
Difficulty level: Medium ANNUA! PERCENTA"E RATE c 25. -ou are paying an effective annual rate of 1$.2? on your credit card. )he interest is compounded monthly. /hat is the annual percentage rate on your account a. 11.*0? b. 1.00? c. 1$.00? d. 1$.20? e. 1(.,1?
Difficulty level: Medium EFFECTIVE ANNUA! RATE b 50. /hat is the effective annual rate if a ban charges you ,.+(? compounded uarterly a. ,.,5? b. ,.2+? c. ,.5*? d. ,.52? e. 2.01?
Difficulty level: Medium EFFECTIVE ANNUA! RATE d 51. -our credit card company uotes you a rate of 1(.5 percent. 8nterest is billed monthly. /hat is the actual rate of interest you are paying a. 1$.5,? b. 1(.50? c. 1*.(2? d. 1*.5+? e. 1+.10?
Difficulty level: Medium EFFECTIVE ANNUA! RATE d 5. Mr. Miser loans money at an annual rate of 1 percent. 8nterest is compounded daily. /hat is the actual rate Mr. Miser is charging on his loans a. .5,? b. $.02? c. $.1? d. $.$+? e. $.($?
Difficulty level: Medium EFFECTIVE ANNUA! RATE e 5$. -ou are considering two loans. )he terms of the two loans are euivalent with the exception of the interest rates. Joan A offers a rate of ,.(*? compounded daily. Joan offers a rate of ,.*? compounded semi=annually. Joan !!!!! is the better offer because!!!!!!: a. A# you will pay less interest. b. A# the annual percentage rate is ,.(*?. c. # the annual percentage rate is ,.+(?. d. # the interest is compounded less freuently. e. # the effective annual rate is ,.+(?.
Difficulty level: Medium EFFECTIVE ANNUA! RATE b 5(. -ou have 3"*00 that you want to use to open a savings account. -ou have found five different accounts that are acceptable to you. All you have to do now is determine which account you want to use such that you can earn the highest rate of interest possible. /hich account should you use based upon the annual percentage rates uoted by each ban Account A: $.,*?" compounded annually Account : $.,0?" compounded monthly Account C: $.,0?" compounded semi=annually Account : $.+*?" compounded continuously Account L: $.++?" compounded uarterly a. Account A b. Account c. Account C d. Account e. Account L
Difficulty level: Medium CONTINUOUS CO$POUNDIN" d 5*. /hat is the effective annual rate of 1(.5? compounded continuously a. 1*.5+? b. 1+.01? c. 1+.0*? d. 1+.0,? e. 1+.1,?
Difficulty level: Medium CONTINUOUS CO$POUNDIN" c 5+. /hat is the effective annual rate of 5.,*? compounded continuously a. 5.55? b. 10.11? c. 10.(? d. 10.2? e. 10.$0?
Difficulty level: Medium CONTINUOUS CO$POUNDIN" d 5,. )he
Difficulty level: Medium CONTINUOUS CO$POUNDIN" VERSUS ANNUA! CO$POUNDIN" c 52. -ou are going to loan your friend 31"000 for one year at a *? rate of interest. Dow much additional interest can you earn if you compound the rate continuously rather than annually a. 3.5, b. 31.05 c. 31., d. 31.$+ e. 31.(5
Difficulty level: Medium FUTURE VA!UE c 55. )oday you earn a salary of 32"*00. /hat will be your annual salary fifteen years from now if you earn annual raises of $.* percent a. 3(,"0$*.$* b. 3(,"*.25 c. 3(,",(,.(( d. 3(2"051.51 e. 3(2"01.+0
Difficulty level: Medium FUTURE VA!UE e 100. -ou hope to buy your dream house six years from now. )oday your dream house costs 3125"500. -ou expect housing prices to rise by an average of (.*? per year over the next six years. Dow much will your dream house cost by the time you are ready to
a. b. c. d. e.
buy it 3(0"2(.02 3(+"015.+, 3(+"$5+.+, 3(+"2$1.5( 3(,"55.0
Difficulty level: Medium PRESENT VA!UE b 101. -our grandmother invested one lump sum 1, years ago at (.*? interest. )oday" she gave you the proceeds of that investment which totaled 3*"*$5.5. Dow much did your grandmother originally invest a. 3",00.00 b. 3",$0.$0 c. 3",*0.00 d. 3",+2.(0 e. 3",,(.50
Difficulty level: Medium PRESENT VA!UE c 10. -ou would lie to give your daughter 3(0"000 towards her college education thirteen years from now. Dow much money must you set aside today for this purpose if you can earn +.$? on your funds a. 31,",*0.00 b. 31,"525.2 c. 312"0,,.0* d. 312"1$.+5 e. 312"$5*.00
Difficulty level: Medium INTEREST RATE FOR A SIN"!E PERIOD e 10$. 4ne year ago" you invested 3$"000. )oday it is worth 3$"1(.*0. /hat rate of interest did you earn a. (.+$? b. (.+2? c. (.,0? d. (.,$? e. (.,*?
Difficulty level: Easy INTEREST RATE FOR $U!TIP!E PERIODS d 10(. >orty years ago" your father invested 3"*00. )oday that investment is worth 310,"51. /hat is the average rate of return your father earned on his investment a. 2.*0? b. 5.$$? c. 5.*0? d. 5.2,?
e.
5.55?
Difficulty level: Easy PRESENT VA!UE AND RATE CHAN"ES a 10*. -ou want to have 310"000 saved ten years from now. Dow much less do you have to deposit today to reach this goal if you can earn +? rather than *? on your savings a. 3***.12 b. 3+05.21 c. 3+1*.(2 d. 352.,$ e. 31"0(+.
Difficulty level: Medium FUTURE VA!UE & SIN"!E SU$ c 10+.-ou have deposited 31"*00 in an account that promises to pay 2? compounded uarterly for the next five years. Dow much will you have in the account at the end a. 31"*52.$$ b. 3"0$.55 c. 3"2.5 d. 3+"551.(( e. Bone of the above.
Difficulty level: Easy FUTURE VA!UE & SIN"!E SU$ d 10,./hat is the future value of investing 35"000 for , years at a continuously compounded rate of 11? a. 31*"5$0.00 b. 312"+2*.(( c. 315"$+5.2$ d. 315"($,.50 e. Bone of the above.
Difficulty level: Easy FUTURE VA!UE & CONTINUOUS CO$POUNDIN" b 102./hat is the future value of investing 3$"000 for $P( year at a continuously compounded rate of 1? a. 3$"1+$ b. 3$"+$ c. 3$"2$ d. 3$"2, e. 3$"$1,
Difficulty level: Challenge EAR ( FUTURE VA!UE d 105./hich of the following amounts is closest to the end value of investing 3*"000 for 1( months at
a. b. c. d. e.
a stated annual interest rate of +? compounded monthly 3*"5$ 3*"$(* 3*"$* 3*"$+ 3+"12$
Difficulty level: Medium EAR ( FUTURE VA!UE c 110. /hich of the following amounts is closest to the end value of investing 310"000 for 12 months at a stated annual interest rate of 1? compounded uarterly a. 311"200 b. 311"2* c. 311"5(0 d. 311"5+1 e. Bone of the above is within 3100 of the correct answer.
Difficulty level: Medium FUTURE VA!UE e 111. /hich of the following amounts is closest to the end value of investing 3,"*00 for .* years at an effective annual interest rate of 1.$+?. 8nterest is compounded semiannually. a. 3 ,"*$1 b. 3 2"(, c. 3 5"(+5 d. 3 5"212 e. 310"0$,
Difficulty level: Medium EAR d 11. 8f the stated rate of interest is 1? and it is compounded monthly" what is the effective annual interest rate a. 1.00? b. 1.*? c. 1.(+? d. 1.+2? e. 1.5?
Difficulty level: Medium PRESENT VA!UE & SIN"!E SU$ d 11$. /hat is the present value of a payment of 31"000 three years from now if the effective annual interest rate is (? a. 31,"5*1 b. 312"(20 c. 312"+*2 d. 312"++5 e. 315"12
Difficulty level: Easy PRESENT VA!UE & FUTURE SU$ a 11(. )horton will receive an inheritance of 3*00"000 three years from now. )hortons discount rate is 10? interest rate compounded semiannually. /hich of the following values is closest to the amount that )horton should accept today for the right to his inheritance a. 3 $,$"102. b. 3 $,*"+*,. c. 3 ++*"*00. d. 3 +,0"0(2. e. Bone of the above is within 310 of the correct answer.
Difficulty level: Medium PRESENT VA!UE & FUTURE SU$ d 11*. A mortgage instrument pays 31.* million at the end of each of the next two years. An investor has an alternative investment with the same amount of ris that will pay interest at 2? compounded semiannually. /hich of the following amounts is closest to what the investor should pay for the mortgage instrument a. 31"$2+"2$( b. 31"$22"225 c. 3"+,("25, d. 3"++5"0(1 e. 3$"2*("*1
Difficulty level: Easy PERPETUIT d 11+. -ou are to receive 3,* per year indefinitely. )he maret rate of interest for these types of payments is 2?. )he price you would pay for this stream is: a. 3 5.$,* b. 3 21.00 c. 3 5$.,*. d. 35$,.*0. e. Bone of the above.
Difficulty level: Easy "RO#IN" PERPETUIT c 11,. Aunt Clarisse has promised to leave you an annuity that will pay 3+0 next year and grow at an annual rate of (?. )he payments are expected to go on indefinitely and the interest rate is 5?. /hat is the value of the growing perpetuity a. 3 ++, b. 3 +5$ c. 31"00 d. 31"(2 e. Bone of the above.
Difficulty level: Medium PRESENT VA!UE ) ANNUIT
c
112. A court settlement awarded an accident victim four payments of 3*0"000 to be paid at the end of each of the next four years. ;sing a discount rate of (?" calculate the present value of the annuity. a. 31,$"** b. 31,2"(5* c. 3121"(5* d. 312("05* e. 300"000 Difficulty level: Medium
PRESENT VA!UE ) ANNUIT d 115./hat is the present value of 10 annual payments of 3*00 at a discount rate of 1? a. 31"$$ b. 31",+1 c. 31"2(0 d. 3"2* e. 3$"0(0
Difficulty level: Medium PRESENT VA!UE ) ANNUIT b 10.An
Difficulty level: Medium FUTURE VA!UE & SIN"!E SU$ e 11.)he great" great grandparents of one of your classmates sold their factory to the government 10( years ago for 31*0"000. 8f these proceeds had been invested at +?" how much would this legacy be worth today Assume annual compounding. a. 3 5$+"000.00 b. 3 1"02+"000.00 c. 3+0"(+,"1$1.*( d. 3+0"+1,"1$1.*( e. 3+("*("1*5.((
Difficulty level: Medium IV. ESSAS FUTURE VA!UE 1. Mr. Miser" who is $* years old" has 6ust inherited 311"000 and decides to use the windfall towards his retirement. De places the money in a ban which promises a return of +? per year until his planned
retirement in $0 years. 8f his funds earn +? interest compounded annually" how much will he have at retirement epeat the analysis for both semi=annual and continuous compounding. $11,000(1.06) 30 $63,1!".#0 $11,000(1.03) 60 $6#,"6!.63 $11,000 . e(.06)(30) $66,#6.1% PRESENT VA!UE OF A PERPETUIT 1$. -our aunt" in her will" left you the sum of 3*"000 a year forever with payments starting immediately. Dowever" the news is better.
3,000 & $,000(1.0)'(.1%.0) $"0,000 PRESENT VA!UE OF AN ANNUIT 1(. 8f you invest 3100"000 today at 1? per year over the next 1* years" what is the most you can spend in eual amounts out of the fund each year over that time.
$100,000 nnuity *ayment + nn.act-(.1%,1)6."10/ $1#,6"%.#% - *$100,000 '21% 41 *M5$1#,6"%.#% EFFECTIVE ANNUA! RATE VERSUS ANNUA! PERCENTA"E RATE 1*. ;sing the example of a savings account" explain the difference between the effective annual rate and the annual percentage rate.
5he effective annual ate is 7hat y-u actually ean, the annual 8ecentage ate is a 9u-ted ate. f inteest is c-m8-unded duing the yea, the ending alance -f a savings acc-unt cann-t e calculated diectly using the annual 8ecentage ate. ls-, in the case -f the savings acc-unt, the effective annual ate 7ill al7ays e highe than the annual 8ecentage ate as l-ng as the acc-unt is c-m8-unded m-e than -nce a yea and the inteest ate is geate than ;e-. PRESENT VA!UE OF AN ANNUIT 1+. )here are three factors that affect the present value of an annuity. Lxplain what these three factors are and discuss how an increase in each will impact the present value of the annuity.
5he fact-s ae the inteest ate, 8ayment am-unt, and nume -f 8ayments. n incease in the 8ayment and nume -f 8ayments 7ill incease the 8esent value, 7hile an incease in the inteest ate 7ill decease the 8esent value. FUTURE VA!UE OF AN ANNUIT 1,. )here are three factors that affect the future value of an annuity. Lxplain what these three factors are and discuss how an increase in each will impact the future value of the annuity.
5he fact-s ae the inteest ate, 8ayment am-unt, and nume -f 8ayments. n incease in any -f these thee 7ill incease the futue value -f the annuity. PERPETUIT PA$ENTS 12. A friend who owns a perpetuity that promises to pay 31"000 at the end of each year" forever" comes to you and offers to sell you all of the payments to be received after the *th year for a price of 31"000. At an interest rate of 10 percent" should you pay the 31"000 today to receive payment numbers + and onwards /hat does this suggest to you about the value of perpetual payments
5he 8esent value -f the 8e8etuity is $10,000, and the 8esent value -f the fist % 8ayments is $/,0!!.0#, thus y-u sh-uld e 7illing t- 8ay -nly $/%%./6 f- 8ayments %6 and -n7ads. 5his suggests that the value -f a 8e8etuity is deived 8imaily f-m the 8ayments eceived ealy in its life, and the 8ayments t- e eceived late have little 7-th t-day.
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100 B
>9
2P1 8P-
1"00 79 7M) =2,"$20.$
*×1 B
(.5P1 8P79 2"(55.1$
=1+0 7M)
10×1 B
+.*P1 8P-
79
+(1 7M)
*$.115*, S 32"(55.1$
×
>9
.0+* 10×1 1 − 1P%1 + 1 & )*0 = 3+(1 × S 3+(1 .0+* 1 Lnter
,.21+2*2 S 32,"$20.$
×
>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
×
2.
=*+"(*1.51
.0* *× 0 1 − 1 P%1 + * & )*0 = 3* × S 3* .0* * Lnter
0×* B
*P* 8P-
79 =1+"($0.*(
5.
>9
1 − [1 P%1 + .1&* ] )*0 = 3*0"000 × S 3*0"000 × $.+0(,,+ S 3120"$2.21 .1 Lnter
* B
1 8P-
$0.
* 7M)
+*,.1* S 31+"($0.*(
×
*0"000 79 7M) =120"$2.21
>9
.0$* *×1 1 − 1 P%1 + 1 & .0$* *0 = 31"*00 × × 1 + 1 S 31"*00 .0$* 1
)due
**.$05,,+
×
×
1.00,02$$$ S 32$"125.5 Lnter
*×1 $.*P1 =1"*00FB B 8P79 7M) >9 2$"125.5
$1.
)due *0
+ [ ] = 30 × 1 − 1 P%1 + .01*& × (1 + .01* ) S 30 × *.+5,12,1+* × 1.01* S 311*.+* .01*
Lnter
+ B
1.* 8P-
$.
79 11*.+*
=0FB 7M)
>9
1 − [1 P%1 + .0, &10 ] *0 = 3 1"000 × × (1 + .0, ) S 31"000 × ,.0$*2 × 1.0, S .0,
) due
350"12.,5 Lnter
10 B
, 8P-
1"000FB 79 7M) >9 =50"12.,5
$$.
)*0
* [ ] = 310"000 × 1 − 1 P%1 + .02*& S 310"000 × 10.$(151 S 310"$(1.51 .02*
Lnter
* B
2.* 8P-
10"000 79 7M) =10"$(1.51
>9
1 − [1 P%1 + .02*& * ] *0 = 310"000 × × (1 + .02* ) S 310"000 × 10.$(151 × 1.02* S .02*
)due
3111"0(0.5, Lnter
* B
2.* 8P-
10"000FB 79 7M) >9 =111"0(0.5,
ifference S 3111"0(0.5, = 310"$(1.51 S 32"+55.0+ S 32"+55 %rounded& Bote: )he difference S .02* × 310"$(1.51 S 32"+55.0+
$(.
1 − [1 P%1 + .0,*& 0 ] *0 = 3*"000 × × (1 + .0,* ) S 3*"000 × 10.15((51 . 0,*
)due
1.0,* S 3*(",5*.$5
×
Lnter
0 B
,.* *"000FB 8P79 7M) >9 =*(",5*.$5
1 − [1 P%1 + .0,*& 0 ] 3*(",5*.$5 = C × # C S 3*"$,* .0,* Lnter
0 B
,.* *(",5*.$5 8P79 7M) =*"$,*
>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
2P1 100FB 8P79 7M) >9 =("5+(.,
.02 *×1 1 − 1 P%1 + 1 & )*0 = 3100 × S 3100 .02 1 Lnter
*×1 B
2P1 8P79 =("5$1.2(
100 7M)
(5.$12(05 S 3("5$1.2(
×
>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
),0
$ = 3"(00 × %1 + .02& − 1 S 3"(00 × $.(+( S 3,",51.$+
.02
Lnter
$ B
2 8P-
79
),0
1"000 7M) >9 =*"+$,.05
= 3$"000 ×
Lnter
* B
%1 + .02*& * .02* 2.* 8P-
"(00 7M) >9 =,",51.$+
− 1 S 3$"000 × ,2.++,,5 S 3$+"00$.$2
79
=$"000 7M) >9 $+"00$.$2
$5.
),0
= 3$"000 ×
Lnter
$0 B
%1 + .05& $0 .05 5 8P-
− 1 S 3$"000 × 1$+.$0,*$2* S 3(02"5.+ =$"000 7M) >9 (02"5.+
79
%1 + .05& $0 )due ,0 = 3$"000 × .05 3((*",*.+* Lnter
$0 B
5 8P-
−1 ( × 1 + .05) S 3$"000 × 1$+.$0,*$2* × 1.05 S
79
=$"000FB 7M) >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
(1.
7M) =1$1.+
×
(.++$*+# C S 31$1.+
>9
1 1 P%1 .0,* &$0×1 − + 1 31(5"000 = C × # 31(5"000 S C .0,* 1 Lnter
$0×1 B
×
1($.01,+# C S 31"0(1.2$
,.*P1 1(5"000 8P79 7M) >9 =1"0(1.2$
)otal interest S %31"0(1.2$ × $0 × 1& = 31(5"000 S 3+"0*2.20 S 3+"0*5 %rounded& (.
%1 + .0+*&10 3*"000"000 = C × .0+* Lnter
10 B
+.* 8P-
− 1 # 3*"000"000 S C × 1$.(5((*(# C S 31"2*"+1,.*
*"000"000 79 7M) >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
(.*P1 =(+("500 8P79 7M) >9 "(21.,
Amount financed S 31"00"000 × %1 = .& S 35+0"000
1 1 P%1 .0,,* &1*×1 − + 1 35+0"000 = C × # 35+0"000 S C .0,,* 1
10+.$2,5$$#
×
C S 35"0$+.*
Lnter
(*.
1*×1 ,.,*P1 5+0"000 B 8P79 7M) =5"0$+.*
.0+* *×1 − + 1 1 P% 1 & 1 # 3("*00 S C 3("*00 = C × .0+* 1 Lnter
*×1 B
+.*P1 8P-
("*00 79
>9
7M) =(,5.$,
*1.102+(21$# C S 3(,5.$,
×
>9
Amount financed S 3+"250 = 3*00 S 3+"$50
.0,5 $+ 1 − 1 P% 1 + & 1 # 3+"$50 S C 3+"$50 = C × .0,5 1 Lnter
$+ B
,.5P1 8P-
+"$50 79
7M) =155.5(
>9
$1.5*22*# C S 3155.5(
×
(,.
0** *×( 1 − 1 P% 1 + . & ( )*0 = 3*00 × S 3*00 .0** ( Lnter
*×( B
*.*P( 8P-
(2.
79 =,"02.5(
*00 7M)
*(.1+*22 S 3,"02.5(
×
>9
.0(5 +0 1 − 1P%1 + . 1 & .0(5 *0 = 355 × × 1 + 1 S 355 .0(5 1
)due
*$.115*+52 × 1.00(02$$$
×
S 31*"5(,.+1 Lnter
+0 B
(5.
(.5P1 8P-
79 1*"5(,.+1
=55FB 7M) >9
1 − [1 P%1 + .0+$*&*0 ] *0 = 3"*00 × × (1 + .0+$*) S 3"*00 × 1*.0$0025 × 1.0+$* S .0+$*
)due
3$5"5(.( Lnter
*0 B
+.$* "*00FB 8P79 7M) >9 =$5"5(.(
*0.
Lnding value at (? simple interest S 31"000 @ %31"000 × .0( × *& S 31"00.00# Lnding value at (? compounded annually S 31"000 × %1 @.0(&* S 31"1+.+*# ifference S 31"1+.+* = 31"00.00 S 31+.+* Lnter
* B
( 8P-
=1"000 79
7M)
*1.
%1 + .0(, & $ 3*0 "000 = C × .0(,
>9 1"1+.+*
− 1 × (1 + .0(, ) # 3*0"000 S C × $.1($05 × 1.0(, S
3,*"5++.1( Lnter
$ B
(., 8P-
%1 + .00*&$*×1 )due ,0 = %31(0 × 1.*0& × .00* S 3$00"+2*.11 Lnter
$*×1 B
*$.
*0"000 79 7M) >9 =,*"5++.1(
.* 8P-
− 1 × (1 + .00*) S 310 × 1"((.,1055 × 1.00*
=%1(0×1.*&FB 79 7M) >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
B $1.(5
(.* =100"000 +"000 8P79 7M)
>9
1 − 1 P%1 + .05 & 1 3("5*(.2* = 31($.2( × # ln1.$(2$(25 S t .05 1 t
*(.
Lnter
**.
5P1 ("5*(.2* =1($.2( 8P79 7M) >9
B (0
31$+"000"000
ln1.00,*# t S (0
×
= 3(*0"000 ×
%1 +
.0+ t & −1 1 # ln .*111111 S t × ln1.00*# t S 12(.+1 .0+ 1
Bote: t is stated in the number of months. Lnter
B 12(.+1
+P1 8P-
=(*0"000 1$+"000"000 79 7M) >9
.0$ . 1 − 1P%1 + .1& .0$ 3(1$"5+ = 3"*00 × × 1 + .0$ 1 .1 t
*+.
# t × ln.00(5+22 S ln.*$*(5(52# t S 1$.5
Bote: t is expressed in months Lnter B
$P1 =(1$"5+ "*00FB 8P79 7M) >9
.1 1 − 1P%1 + $+* & .1 3*"000 = 3$0.,+ × × 1 + $+* # t .1 $+* t
*,.
S 1"05*.02 days S $ years Lnter B
1P$+* *"000 =$0.,+FB 8P79 7M) >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
$0 B
*5.
P1 =1$"500 ("25(.$* 8P79 7M) >9 1$.*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
+0.
P1 =100"000 $2(.(0 8P79 7M) $.(*
3(,"$(1.15 = 310 ×
%1 +
.
1
&1*×1 .
>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
P1 8P5.(+
3+2*"000 = 31$+"000 ×
79
%1 + . & ( .
=10 (,"$(1.15 7M) >9
− 1 # )his can not be solved directly" so itHs 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
( B
8P1*.*5
=1$+"000 +2*"000 79 7M) >9
+.
3(" (2 .++ = 3* ×
%1 +
. ( 1−10 ) ×1
1
&
.
− 1 . × 1 + # )his can not be solved directly" so itHs 1
1 easiest to 6ust use the calculator method to get an answer. -ou can then use the calculator answer as the rate in the formula 6ust to verify that you answer is correct. Lnter
%1=10& ×1 P1 =*FB ("(2.++ B 8P79 7M) >9
+$.
31"000"000 = 3* ×
%1 +
.
$+*
& ( (0 − 1) ×$+* .
− 1 × 1 + . # )his can not be solved directly" $+*
$+* so itHs easiest to 6ust use the calculator method to get an answer. -ou can then use the calculator answer as the rate in the formula 6ust to verify that you answer is correct. Lnter
%(0=1& ×$+* P$+* =*FB 1"000"000 B 8P79 7M) >9
*0
1 1 1 = 3*"000 × + 35"000 × + 31*"000 × 1 $ # 79 S %1 + .1(& %1 + .1(& (1 + .1( )
31"($*.,( Lnter
1 B
1( 8P79 =("$2*.5+
B
1( 8P-
$ B
1( 8P-
79 =+"5*.1
79 =10"1(.*,
7M)
*"000 >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-
7M)
1"00 >9
79 =1"$2+.2$
7M)
1"*00 >9
79 =1",,,.55
7M)
"000 >9
7resent value S 31"1*$.2* @ 31"$2+.2$ @ 31",,,.55 S 3("$12.+, ++.
*0
1 1 1 = 3*"000 × + × + × 3 , " *00 3 10 " 000 # 79 S %1 + .0*& %1 + .0*& $ (1 + .0* ) 1
30"0$.00 Lnter
1 B
* 8P79 =(",+1.50
B
* 8P-
$ B
* 8P-
79 =+"20.,
79 =2"+$2.$2
7M)
*"000 >9
7M)
,"*00 >9
10"000 7M) >9
7resent value S 3(",+1.50 @ 3+"20., @ 32"+$2.$2 S 30"0$.00
+,.
*0
1 1 = 3"000 + 3*"000 × 1 1 + 3**"000 × + 3+0"000 × $ %1 + .0+& %1 + .0+& (1 + .0+ )
79 S 31*0"$2$.*+ Lnter
1 B
+ 8P79 =(5"0*+.+0
*"000 7M) >9
B
+ 8P-
**"000 7M) >9
$ B
+ 8P-
79 =(2"5(5.20
79 7M) =*0"$,,.1+
+0"000 >9
7resent value S 3"000 @ 3(5"0*+.+0 @ 3(2"5(5.20 @ 3*0"$,,.1+ S 31*0"$2$.*+ +2.
*0
1 1 1 = 31"00 × + × + × 3 1 " 200 3 " 500 # 79 S %1 + .05& %1 + .05& $ (1 + .05 ) 1
3("2**., Lnter
1 B
5 8P79 =1"100.5
B
5 8P-
$ B
5 8P-
79 =1"*1*.0
79 ="$5.$$
7M)
1"00 >9
7M)
1"200 >9
7M)
"500 >9
7resent value S 31"100.5 @ 31"*1*.0 @ 3"$5.$$ 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-
7M)
*"+00 >9
79 =,"$0(.+0
7M)
5"000 >9
79 =1"(+.$2
7M)
"000 >9
7resent value S 3*"0(*.0* @ 3,"$0(.+0 @ 31"(+.$2 S 31$"21.0$ ,0.
*0
1 1 = 3("00 × 1 1 + 3*"000 × + × 3 * " (00 # 79 S %1 + .0$& %1 + .0$& $ (1 + .0$)
31$",$.(1 Lnter
1 B
$ 8P79 =("0,,.+,
B
$ 8P-
$ B
$ 8P-
79 =(",1.52
79 =("5(1.,+
7M)
("00 >9
7M)
*"000 >9
7M)
*"(00 >9
7resent value S 3("0,,.+, @ 3(",1.52 @ 3("5(1.,+ S 31$",$.(1 ,1.
*0
1 = 3100"000 + 3100"000 × # 79 S 312("***.( %1 + .02,*&
Lnter
B
2.,* 8P79 =2(.***.(
7M)
100"000 >9
7resent value S 3100"000 @ 32("***.( S 312("***.( -ou should accept the 3125"000 today since it is the higher net present value.
,.
*0
1 1 = 3*"000 + 31*"000 × + 3*"000 × 1 %1 + .0+& %1 + .0+&
79 S 3(1"(00.2* Lnter
1 B
+ 8P-
B
+ 8P-
79 1("1*0.5(
79 "(5.51
=1*"000 7M) >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
3,"*00 × %1.0, &$ # >9 S 30",50.55
* B
+
>uture value S 3*"0(5.15 @ 3+"**$.52 @ 35"12,.2 S 30",50.55 ,(.
,0
= [3*"120 × %1.0+& ] + [35"+00 × %1.0+&1 ] + 3"*0 # >9 S 312"(+.*
Lnter
B
+ =*"120 8P79
1 B
+ 8P-
=5"+00 79
7M)
>9 *"20.*
7M) >9 10"1,+.00
>uture value S 3*"20.* @ 310"1,+.00 @ 3"*0.00 S 312"(+.*
,*.
,0
=
35"20 × %1.05&
Lnter
B
+ 0 + 3("*10 # >9 S 31+"1,,.1(
5 =5"20 8P79
7M)
>9 11"++,.1(
>uture value S 311"++,.1( @ 30 @ 3("*10.00 S 31+"1,,.1( ,+.
,0 = [3+"200 × %1.0,*& ] + [3"100 × %1.0,*&1 ] + 30 # >9 S 310"0,$.55 Lnter
B
,.* 8P-
=+"200 79
7M)
>9 ,"21.,(
1 B
,.* 8P-
="100 79
7M)
>9 "*.*
>uture value S 3,"21.,( @ 3"*.* @ 30 S 310"0,$.55 ,,.
,0
= [310"000 × %1.11& * ] + [31*"000 × %1.11& ( ] + [3*"000 × %1.11& $ ]
>9 S 3*5*"052.+, Lnter
* B
11 =10"000 8P79
( B
11 =1*"000 8P79
$ B
11 =*"000 8P79
7M) >9 1$*"2*(.+(
7M) >9 12$"*2,.$*
7M) >9 ,*"+*+.+2
>uture value S 31$*"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
$ B
$ 8P-
79 "0,5.25
="*00 10"000 7M) >9
,5.
,0
=
3100"000 × %1.0$*&
Lnter
+
3*0"000 × %1.0$*&1
B
$.* =100"000 8P79
1 B
$.* =*0"000 8P79
+ 3*0"000 # CS 3+1*"2,.*0
7M) >9 10,"1.*0
7M) >9 *2",*0.00
>9 S 310,"1.*0 @ 3*2",*0.00 @ 3*0"000 S 3+1*"2,.*0 20.
*0
= 1*0"000 # 79 S 3$"*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$.2 B4M L>> 1$.00
1 CP-
(
50.
.0,+( E)3 = 1 + − 1 # LA S ,.2+ percent ( Lnter
,.+( B4M L>> ,.2+
( CP-
1
51.
.1(5 1 # LA S 1*.5+ percent E)3 = 1 + − 1 Lnter
5.
.1 E)3 = 1 + $+* Lnter
5$.
1(.5 B4M L>> 1*.5+
E)3 )
$+*
− 1 # A7 S $.$+ percent
1 B4M L>> $.$+
.0,(* = 1 + $+*
Lnter
1 CP-
$+* CP-
$+*
,.(* B4M L>> ,.,$
− 1 # A7 S ,.,$ percent $+* CP-
E)3 <
.0,* = 1 + − 1 # A7 S ,.+( percent
Lnter
,.* B4M L>> ,.+(
CP-
5(.
LAA S $.,* percent 1
E)3 <
.0$, = 1 + − 1 # LA S $.,+ percent 1
Lnter
$., B4M L>> $.,+
1 CP-
E)3C
.0$, = 1 + − 1 # LA S $.,$ percent
Lnter
$., B4M L>> $.,$
CP-
= e.0$+* − 1 = .,122.0$+* − 1 # LA S $., percent
;sing ex on a financial calculator: LA S $., percent 4n the )exas 8nstruments A 88 7lus" the input is: .0$+*" nd" ex" =1" S .0$, S $., percent (
E)3 E
.0$++ = 1 + − 1 # LA S $.,1 percent (
Lnter
$.++ B4M L>> $.,1
( CP-
Account offers the highest effective annual rate at $.,+ percent. 5*.
E)3
=
e
.1(5
−
1 = .,122.1(5
−
1#
LA S 1+.0, percent
;sing ex on a financial calculator: LA S 1+.0, percent 4n the )exas 8nstruments A 88 7lus" the input is: .1(5" nd" ex" =1" S .1+0, S 1+.0, percent 5+.
E)3
=
.05,*
e
−
1 = .,122.05,*
−
1#
LA S 10.( percent
;sing ex on a financial calculator: LA S 10.( percent 4n the )exas 8nstruments A 88 7lus" the input is: .05,*" nd" ex" =1" S .10( S 10.( percent
5,.
E)3
=
e
.0,5
−
1 = .,122.0,5
−
1#
LA S 2. percent
;sing ex on a financial calculator: LA S 2. percent 4n the )exas 8nstruments A 88 7lus" the input is: .0,5" nd" ex" =1" S .02 S 2. percent 52.
E)3
=
.0*
e
−
1 = .,122.0*
−
1#
LA S *.1, percent
;sing ex on a financial calculator: LA S *.1, percent 4n the )exas 8nstruments A 88 7lus" the input is: .0*" nd" ex" =1" S .0*1, S *.1, percent
55.
Additional interest S 31"000 × %.0*1, = .0*& S 31., >uture value S 32"*00 × %1 @ .0$*&1* S 3(,",(,.(( Lnter
1* B
$.* =2"*00 8P79
>uture value S 3125"500 × %1 @ .0(*&+ S 3(,"55.0 Lnter
+ B
(.* =125"500 8P79
1, B
(.* 8P-
1$ B
+.$ 8P-
79 =12"0,,.0*
(0"000 7M) >9
3$"1(.*0 S 3$"000 × %1 @ r&1# r S (.,* percent Lnter
1 B
79 =",$0.$0
*"*$5.5 7M) >9
7resent value S 3(0"000 × T1 ÷ %1 @ .0+$&1$U S 312"0,,.0* Lnter
10$.
7M) >9 (,"55.0
7resent value S 3*"*$5.5 × T1 ÷ %1 @ .0(*&1,U S 3",$0.$0 Lnter
10.
7M) >9 (,",(,.((
=$"000 8P79 (.,*
$"1(.*0 7M) >9
310,"51 S 3"*00 × %1 @ r&(0# r S 5.2, percent Lnter
(0 B
="*00 8P79 5.2,
10,"51 7M) >9
