Exercise-for-TVM貨幣時(shí)間價(jià)值練習(xí)

ExerciseforTVM

1.Simpleinterestversuscompoundinterest.1stSimpletonBankpays5%simpleinterestonitssavingsaccountbalances,while1stComplexityBankpays5%interestcompoundedannually.Ifyoumadea￡10000depositineachbank,howmuchadditionalmoneywouldyouearnfromyour1stComplexityBankaccountattheendof12years?

￡10000*(S/P,5%,12)=￡10000*1.7959=￡17959

￡10000*(1+5%*12)=￡16000

￡17959-￡16000=￡1959

2.Calculatingfuturevalue:foreachofthefollowing,computethefuturevalue:

Presentvalue

Years

Interestrate

Futurevalue

￡570

15

9%

￡2076.22

￡8922

9

18%

￡39573.12

￡61133

3

12%

￡85887.46

￡219850

10

4%

￡325431.71

3.Calculatingpresentvalue:foreachofthefollowing,computethepresentvalue.

Futurevalue

Years

Interestrate

Presentvalue

￡349

5

6%

￡260.81

￡5227

20

2%

￡3517.77

￡48950

12

25%

￡3363.82

￡612511

7

33%

￡83205.57

4.What’sthevaluetodayof￡1250tobereceived3yearsfromnow,assuminga12%discountrate.

￡1250*(P/S,12%,3)=￡1250*0.7118=￡889.75

5.Whatwouldbethepresentvaluetodayof￡1250tobereceived3yearsfromnow,assuminga12%discountrateandquarterlycompounding.

￡1250*(P/S,12%/4,3*4)=￡1250*0.7014=￡876.75

6.Howmuchwillbeinanaccountearning10%attheendof5yearsif￡100isdepositedtoday?

￡100*(S/P,10%,5)=￡100*1.6105=161.05

7.Howmuchwillbeinanaccountearning8%attheendof5yearsif￡100isdepositedtoday,assumingquarterlycompounding?

￡100*(S/P,8%/4,5*4)=￡100*1.4859=￡148.59

8.Whatisthepresentvalueofalumpsumof￡300thatwillbepaidattheendofthefifthyear,assumingthattheinterestrateis10%?

￡300*(P/S,10%,5)=￡300*1.6105=￡483.15

9.Whatisthefuturevalueafter5yearsof￡1000thatisplacedinasavingsaccounttodaythatpaysinterestquarterly,assuminganannualinterestrateof8%?

￡1000*(S/P,8%,5)=￡1000*1.4693=￡1469.3

10.Whatistheeffectiveannualinterestrateforanaccountthatpaysinterestquarterlyattheannualrateof8%?

(1+8%/4)2-1=8.24%

11.What'sthefuturevalueofa5-yearordinaryannuitywithannualpaymentof￡200,evaluatedata15%interestrate?

￡200*(S/A,15%,5)=￡200*6.7424=￡1348.48

12.What'sthepresentvalueofa5-yearordinaryannuitywithannualpaymentof￡200,evaluatedata15%interestrate?

￡200*(P/A,15%,5)=￡200*3.3522=￡670.44

13.Whichamountisworthmoreat14%,compoundedannually:￡1000inhandtodayor￡2000duein6years?

￡2000*(P/S,14%,6)=￡911.17

￡911.17<￡1000

14.Washington-Atlanticinvests￡4milliontoclearatractoflandandtosetoutsomeyoungpinetree.Thetreeswillmaturein10years,atwhichtimeWashington-Atlanticplanstoselltheforestatanexpectedpriceof￡8million.WhatisWashington-Atlanticexpectedrateofreturn?

￡4million*(S/P,i,10)=￡8million

i=1.07%

15.Yourbrokerofferstosellyouanotefor￡13250thatwillpay￡2345.05peryearfor10yearsattheend.Ifyoubuythenote,whatinterestratewillyoubeearning?

￡13250=￡2345.05*(P/A,i,10)

i=12%

16.Amortgagecompanyofferstolendyou￡85000,theloanscallsforpaymentsof￡8273.59peryearfor30years.Whatinterestrateisthemortgagecompanychargingyou?

￡85000=￡8273.59*(P/A,i,30)

i=9%

17.Tocompleteyourlastyearinbusinessschoolandthengothroughlawschool,youwillneed.￡10000peryearfor4years,startingnextyear(ie,youwillneedtowithdrawthefirst￡10000oneyearfromtoday).Yourrichuncleofferstoputyouthroughschool,andhewilldepositinabankpaying70hinterest,compoundingannually,asumofmoneythatissufficienttoprovidethe4paymentsof￡10000each.Hisdepositwillbemadetoday.

a.Howlargemustthedepositbe?

b.Howmuchwillbeintheaccountimmediatelyafteryoumakethefirstwithdrawal?Afterthelastwithdrawal?

a.￡40000*(P/A,7%,4)=￡33872

b.first=￡33872*(1+7%)-￡10000=￡26243.04

last=0

18.Whileyouwereastudentincollege,youborrowed￡12000instudentloansataninterestrateof9%,compoundingannually.Ifyourepay￡1500peryear,how

long,tothenearestyear,willittakeyouLurepaytheloan?

(P/A,9%,n)=￡12000/￡1500=8

n=15

19.Youneedtoaccumulate￡10000.Todoso,youplantomakedepositsof￡1250peryear,withthefirstpaymentbeingmadeayearfromtoday,inabankaccountwhichpays12%interest,compoundedannually.Youlastdepositwillbelessthan￡1250iflessisneededtoroundoutto￡10000.Howmanyyearswillittakeyoutoreachyour￡10000goal,andhowlargewillthelastdepositbe?

￡1250*(S/A,12%,n)=￡10000

￡1250*(1+12%)n-1=￡

12%

n=6

S=￡1250[(S/A,12%,5+1)-1]=￡1250*7.1152=￡8894

￡10000-￡8894=￡1106

20.Whatisthepresentvalueofaperpetuityof￡100peryeariftheappropriatediscountrateis7%?Ifinterestratesingeneralweretodoubleandtheappropriatediscountrateroset014%,whatwouldhappentothepresentvalueoftheperpetuity?

￡100=￡1428.57￡100=￡714.29

7%14%

21.TheprizeinlastweekFloridalotterywasestimatedtobeworth$35million.Ifyouwere

luckyenoughtowin,thestatewillpayyou$1.75millionperyearoverthenext20years.Assumethatthefirstinstallmentisreceivedimmediately.

a.Ifinterestrateare8%,whatisthepresentvalueoftheprize?

b.Ifinterestrateare8%,whatisthefuturevalueafter20years?

c.Howwouldyouranswerschangeifthepaymentswerereceivedattheendofeachyear?

a.$1.75million*[(P/A,8%,20-1)+1]=$1.75million*10.6036=$18.5563million

b.$1.75million*[(S/A,8%,20+1)-1]=$1.75million*50.423=$88.24025million

c.a.$1.75million*(P/A,8%,20)=$1.75million*9.8181=$17.181675million

b.$1.75million*(S/A,8%,20)=$1.75million*45.762=$80.0835million

22.Yourclientis40yearsoldandwantstobeginsavingforretirement.Youadvisetheclienttoput￡5000ayearintothestockmarket.Youestimatethatthemarket'sreturnwillbe,onaverage,12%ayear.Assumetheinvestmentwillbemadeattheendoftheyear.

a.Iftheclientfollowsyouradvice,howmuchmoneywillshehavebyage65?

b.Howmuchwillshehavebyage70?

a.￡5000*(S/A,12%,65-40)=￡5000*133.33=￡666650

b.￡5000*(P/A,12%,70-40)=￡5000*241.33=￡1206650

23.Youjuststartedyourfirstjob,andyouwanttobuyahousewithin3years.Youarecurrentlysavingforthedownpayment.Youplantosave￡5000thefirstyear.Youalsoanticipatethattheamountyousaveeachyearwillriseby10%ayearasyoursalaryincreasesovertime.Interestrateareassumedtobe7%,andallsavingoccuratyearend.Howmuchmoneywillyouhaveforadownpaymentin3years?

￡5000*(S/P,7%,2)+￡5000*10%*(1+7%)+￡5000*(1+10%)*10%

=￡5000*1.1449+￡5000*0.1*1.07+￡5000*1.1*0.1

=￡5724.5+￡535+￡550

=￡6809.5變額年金

24.A15-yearsecurityhasapriceof￡340.4689.thesecuritypays￡50attheendofeachofthenext5years,andthenitpaysadifferentfixedcashflowamountattheendofeachofthefollowing10years.Interestrateis9%.Whatistheannualcashflowamountbetweenyear6and15?

￡340.4869=￡50*(P/A,9%,5)+A*(P/A,9%,10)*(P/S,9%,5)

￡340.4869=￡50*3.8897+A*6.4177*0.6499

146.0019=4.1709*A

A=35

25.Findthefuturevalueofthefollowingannuities.Thefirstpaymentintheseannuitiesismadeattheendofyearl,ie,theyareordinaryannuities.Assumethatcompoundingoccursonceayear.

a.￡400peryearfor10yearsat10%.

b.￡200peryearfor5yearsat5%.

c.￡400peryearfor5yearsat0%.

d.Nowreworkpartsa,bandcassumingthatpaymentsaremadeatthebeginningofeach

year,thatis,theyareannuitiesdue.

a.￡400*(S/A,10%,10)=￡400*15.937=￡6374.8

b.￡200*(S/A,5%,5)=￡200*5.5256=￡1105.12

c.￡400*5=￡2000

d.￡400*[(S/A,5%,5+1)-1]=￡400*6.8019=￡2720.76

￡200*[(S/A,10%,5+1)-1]=￡1160.38

￡400

26.Findthepresentvalueofthefollowingordinaryannuities.Assumethatdiscountingoccursonceayear,

a.￡400peryearfor10yearsat10%.

b.￡200peryearfor5yearsat5%.

c.￡400peryearfor5yearsat0%.

d.Nowreworkpartsa,bandcassumingthatpaymentsaremadeatthebeginningofeachyear,thatis,theyareannuitiesdue.

a.￡400*(P/A,10%,10)=￡400*6.1446=￡2457.84

b.￡200*(P/A,5%,5)=￡200*4.3295=￡865.9

c.￡400

d.￡400*[(P/A,5%,5-1)+1]=￡400*(4.3101+1)=￡2124.04

￡200*[(P/A,10%,5-1)+1]=￡200*(3.1699+1)=￡833.98

￡400

Usingthepresentvaluetablesoracalculatoranswerthefollowingquestions.

Thereisonlyonecorrectanswerforeachquestion.

(1)Youareconsideringdepositing￡300inanaccountforeightyearswithaninterestrateof10%.Thepresentvalueinthiscaseis￡

A.300

B.567.31

C.578.99

D.612.13

E.643.08

(2)Thevalueof￡300ineightyearsifitearns10%compounded.annuallywillbe￡

A.300

B.567.31

C.578.99

D.612.13

E.643,08

(3)Youborrow￡2,000fromaloansharkforsixyearsataninterestrateof75%peryearwithannualcompounding.Thefuturevalueoftheloanaftersixyearswillbe￡

A.46,786.87

B.57,445.80

C.59,786.97

D.61,777.34

E.63,796.46

(4)Supposeyouconvincethesharktochargesimpleinterestinsteadofcompoundinterest.Inthiscasethefuturevalueoftheloanwillbe￡

A.11,000

B.9,000

C.24,500

D.6,000

E.2,600

(5)Thepresentvalueof￡200,000tobepaidinyear10ifthediscountrateis8%willbe￡

A.92,639

B.92,889

C.93,882

D.94,234

E.95,124

(6)Findthepresentvaluefactorforaninterestrateof15%and10periods.

A.0.2472

B.0.2657

C.0.3561

D.0.4479

E.0.5960

(7)Ifonespeaksofanannuitywithoutanyqualification,a/anisbeingdiscussed.

A.Ordinaryannuity

B.Firstannuity

C.Timeannuity

D.Annuitydue

E.Realannuity

(8)Youplantosave￡1,700peryearfor20yearsasaretirementfundThefirstpaymentismadeattheendofthisyear,yearl,andthelastpaymentismadeattheendofyear20.Youwillhaveaccumulated￡attheendof20yearsinpresentvalueterms,usingadiscountfactorof5%toaccountforthetimevalueofmoney.

A.34,567

B.38,990

C.56,212

D.214,509

E.21,185

(9)Youplantosave￡1,700peryearfortheforeseeablefutureasaretirementfundandexpecttoearn7%peryearThefirstpaymentismadeattheendofthisyear,yearl,andthelastpaymentismadeattheendofyear20.Youwillhaveaccumulated￡attheendof20yearsinpresentvalueterms,usingadiscountfactorof10%toaccountforthetimevalueofmoney.

A.8,679

B.38,990

C.12,453

D.60,633

E.211,100

(10)Assumearetiree