Ch04SolutionsManualWord文档格式.docx

Ch04SolutionsManualWord文档格式.docx

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h.Annualcompoundingmeansthatinterestispaidonceayear.Insemiannual,quarterly,monthly,anddailycompounding,interestispaid2,4,12,and365timesperyearrespectively.Whencompoundingoccursmorefrequentlythanonceayear,youearninterestoninterestmoreoften,thusincreasingthefuturevalue.Themorefrequentthecompounding,thehigherthefuturevalue.

i.Theeffectiveannualrateistheratethat,underannualcompounding,wouldhaveproducedthesamefuturevalueattheendof1yearaswasproducedbymorefrequentcompounding,sayquarterly.Thenominal（quoted）interestrate,iNom,istherateofintereststatedinacontract.Ifthecompoundingoccursannually,theeffectiveannualrateandthenominalratearethesame.Ifcompoundingoccursmorefrequently,theeffectiveannualrateisgreaterthanthenominalrate.Thenominalannualinterestrateisalsocalledtheannualpercentagerate,orAPR.Theperiodicrate,iPER,istheratechargedbyalenderorpaidbyaborrowereachperiod.Itcanbearateperyear,per6-monthperiod,perquarter,permonth,perday,orperanyothertimeinterval（usuallyoneyearorless）.

j.Anamortizationscheduleisatablethatbreaksdowntheperiodicfixedpaymentofaninstallmentloanintoitsprincipalandinterestcomponents.Theprincipalcomponentofeachpaymentreducestheremainingprincipalbalance.Theinterestcomponentistheinterestpaymentonthebeginning-of-periodprincipalbalance.Anamortizedloanisonethatisrepaidinequalperiodicamounts（or"

killedoff"

overtime）.

4-2Theopportunitycostrateistherateofinterestonecouldearnonanalternativeinvestmentwithariskequaltotheriskoftheinvestmentinquestion.ThisisthevalueofiintheTVMequations,anditisshownonthetopofatimeline,betweenthefirstandsecondtickmarks.Itisnotasinglerate--theopportunitycostratevariesdependingontheriskinessandmaturityofaninvestment,anditalsovariesfromyeartoyeardependingoninflationaryexpectations.

4-3True.Thesecondseriesisanunevenpaymentstream,butitcontainsanannuityof$400for8years.Theseriescouldalsobethoughtofasa$100annuityfor10yearsplusanadditionalpaymentof$100inYear2,plusadditionalpaymentsof$300inYears3through10.

4-4True,becauseofcompoundingeffects--growthongrowth.Thefollowingexampledemonstratesthepoint.TheannualgrowthrateisIinthefollowingequation:

$1（1+I）10=$2.

Theterm（1+I）10istheFVIFforIpercent,10years.WecanfindIinoneoftwoways:

1.UsingafinancialcalculatorinputN=10,PV=-1,PMT=0,FV=2,andI/YR=?

.SolvingforI/YRyouobtain7.18%.

2.Usingafinancialcalculator,inputN=10,I/YR=10,PV=-1,PMT=0,andFV=?

.SolvingforFVyouobtain$2.59.Thisformulationrecognizesthe"

interestoninterest"

phenomenon.

4-5Forthesamestatedrate,dailycompoundingisbest.Youwouldearnmore"

interestoninterest."

SOLUTIONSTOEND-OF-CHAPTERPROBLEMS

10%

4-1012345

||||||

PV=10,000FV5=?

FV5=$10,000（1.10）5

=$10,000（1.61051）=$16,105.10.

Alternatively,withafinancialcalculatorenterthefollowing:

N=5,I/YR=10,PV=-10000,andPMT=0.SolveforFV=$16,105.10.

7%

4-205101520

|||||

PV=?

FV20=5,000

Withafinancialcalculatorenterthefollowing:

N=20,I/YR=7,PMT=0,andFV=5000.SolveforPV=$1,292.10.

I/YR=?

4-3018

||

PV=250,000FV18=1,000,000

N=18,PV=-250000,PMT=0,andFV=1000000.SolveforI/YR=8.01%≈8%.

6.5%

4-40N=?

PV=1FVN=2

$2=$1（1.065）N.

I/YR=6.5,PV=-1,PMT=0,andFV=2.SolveforN=11.01≈11years.

12%

4-5012N–2N–1N

||||||

PV=42,180.535,0005,0005,0005,000FV=250,000

Usingyourfinancialcalculator,enterthefollowingdata:

I/YR=12;

PV=42180.53;

PMT=5000;

FV=250000;

N=?

SolveforN=11.Itwilltake11yearstoaccumulate$250,000.

4-6Ordinaryannuity:

012345

300300300300300

FVA5=?

N=5,I/YR=7,PV=0,andPMT=300.SolveforFV=$1,725.22.

Annuitydue:

300300300300300

Withafinancialcalculator,switchto“BEG”andenterthefollowing:

N=5,I/YR=7,PV=0,andPMT=300.SolveforFV=$1,845.99.Don’tforgettoswitchbackto“END”mode.

8%

4-70123456

|||||||

100100100200300500

PV=?

FV=?

Usingafinancialcalculator,enterthefollowing:

CF0=0;

CF1=100;

Nj=3;

CF4=200（NotecalculatorwillshowCF2onscreen.）;

CF5=300（NotecalculatorwillshowCF3onscreen.）;

CF6=500（NotecalculatorwillshowCF4onscreen.）;

andI/YR=8.SolveforNPV=$923.98.

TosolvefortheFVofthecashflowstreamwithacalculatorthatdoesn’thavetheNFVkey,dothefollowing:

EnterN=6,I/YR=8,PV=-923.98,andPMT=0.SolveforFV=$1,466.24.

4-8Usingafinancialcalculator,enterthefollowing:

N=60,I/YR=1,PV=20000,andFV=0.SolveforPMT=$444.89.

EAR=

–1.0

=（1.01）12–1.0

=12.68%.

Alternatively,usingafinancialcalculator,enterthefollowing:

NOM%=12andP/YR=12.SolveforEFF%=12.6825%.RemembertochangebacktoP/YR=1onyourcalculator.

6%

4-9a.01

||$500（1.06）=$530.00.

-500FV=?

6%

b.012

|||$500（1.06）2=$561.80.

-500FV=?

c.01

||$500（1/1.06）=$471.70.

500

d.012

|||$500（1/1.06）2=$445.00.

500

4-10a.012345678910$500（1.06）10=$895.42.

|||||||||||

-500FV=?

b.012345678910$500（1.12）10=$1,552.92.

c.012345678910

|||||||||||$500（1/1.06）10=$279.20

d.012345678910

|||||||||||$500（1/1.12）10=$160.99

500

4-11a.?

||

-200400

Withafinancialcalculator,enterI/YR=7,PV=-200,PMT=0,andFV=400.ThenpresstheNkeytofindN=10.24≈10.

b.?

||

-200400.

Withafinancialcalculator,enterI/YR=107,PV=-200,PMT=0,andFV=400.ThenpresstheNkeytofindN=7.27≈7.

18%

c.?

Withafinancialcalculator,enterI/YR=18,PV=-200,PMT=0,andFV=400.ThenpresstheNkeytofindN=4.19≈4.

d.100%?

Withafinancialcalculator,enterI/YR=100,PV=-200,PMT=0,andFV=400.ThenpresstheNkeytofindN=1.00≈1.

4-12

a.012345678910

400400400400400400400400400400

FVA10=?

Withafinancialcalculator,enterN=10,I/YR=10,PV=0,andPMT=-400