Chapter6Calculators DiscountedCashFlowValuationMcGraw-Hill/IrwinCopyright?2013byTheMcGraw-HillCompanies,Inc.Allrightsreserved.公司理財?shù)谑鍼PTChap006-Calc Chapter6McGraw-Hill/IrwinCo1KeyConceptsandSkillsBeabletocomputethefuturevalueofmultiplecashflowsBeabletocomputethepresentvalueofmultiplecashflowsBeabletocomputeloanpaymentsBeabletofindtheinterestrateonaloanUnderstandhowinterestratesarequotedUnderstandhowloansareamortizedorpaidoff6C-2公司理財?shù)谑鍼PTChap006-CalcKeyConceptsandSkillsBeable2ChapterOutlineFutureandPresentValuesofMultipleCashFlowsValuingLevelCashFlows:AnnuitiesandPerpetuitiesComparingRates:TheEffectofCompoundingLoanTypesandLoanAmortization6C-3公司理財?shù)谑鍼PTChap006-CalcChapterOutlineFutureandPres3MultipleCashFlows–FutureValueExample6.1Findthevalueatyear3ofeachcashflowandaddthemtogetherToday’s(year0)CF:3N;8I/Y;-7,000PV;CPTFV=8817.98Year1CF:2N;8I/Y;-4,000PV;CPTFV=4,665.60Year2CF:1N;8I/Y;-4,000PV;CPTFV=4,320Year3CF:value=4,000Totalvaluein3years=8,817.98+4,665.60+4,320+4,000=21,803.58Valueatyear4:1N;8I/Y;-21,803.58PV;CPTFV=23,547.876C-4公司理財?shù)谑鍼PTChap006-CalcMultipleCashFlows–FutureV4MultipleCashFlows–FVExample2Supposeyouinvest$500inamutualfundtodayand$600inoneyear.Ifthefundpays9%annually,howmuchwillyouhaveintwoyears?Year0CF:2N;-500PV;9I/Y;CPTFV=594.05Year1CF:1N;-600PV;9I/Y;CPTFV=654.00TotalFV=594.05+654.00=1,248.056C-5公司理財?shù)谑鍼PTChap006-CalcMultipleCashFlows–FVExamp5MultipleCashFlows–Example2ContinuedHowmuchwillyouhavein5yearsifyoumakenofurtherdeposits?Firstway:Year0CF:5N;-500PV;9I/Y;CPTFV=769.31Year1CF:4N;-600PV;9I/Y;CPTFV=846.95TotalFV=769.31+846.95=1,616.26Secondway–usevalueatyear2:3N;-1,248.05PV;9I/Y;CPTFV=1,616.266C-6公司理財?shù)谑鍼PTChap006-CalcMultipleCashFlows–Example6MultipleCashFlows–FVExample3Supposeyouplantodeposit$100intoanaccountinoneyearand$300intotheaccountinthreeyears.Howmuchwillbeintheaccountinfiveyearsiftheinterestrateis8%?Year1CF:4N;-100PV;8I/Y;CPTFV=136.05Year3CF:2N;-300PV;8I/Y;CPTFV=349.92TotalFV=136.05+349.92=485.976C-7公司理財?shù)谑鍼PTChap006-CalcMultipleCashFlows–FVExamp7MultipleCashFlows–PresentValueExample6.3FindthePVofeachcashflowandaddthemYear1CF:N=1;I/Y=12;FV=200;CPTPV=-178.57

Year2CF:N=2;I/Y=12;FV=400;CPTPV=-318.88

Year3CF:N=3;I/Y=12;FV=600;CPTPV=-427.07

Year4CF:N=4;I/Y=12;FV=800;CPTPV=-508.41

TotalPV=178.57+318.88+427.07+508.41=1,432.936C-8公司理財?shù)谑鍼PTChap006-CalcMultipleCashFlows–Present8Example6.3Timeline01234200400600800178.57318.88427.07508.411,432.936C-9公司理財?shù)谑鍼PTChap006-CalcExample6.3Timeline01234200409MultipleCashFlowsUsingaSpreadsheetYoucanusethePVorFVfunctionsinExceltofindthepresentvalueorfuturevalueofasetofcashflowsSettingthedataupishalfthebattle–ifitissetupproperly,thenyoucanjustcopytheformulasClickontheExceliconforanexample6C-10公司理財?shù)谑鍼PTChap006-CalcMultipleCashFlowsUsingaSp10MultipleCashFlows–PVAnotherExampleYouareconsideringaninvestmentthatwillpayyou$1,000inoneyear,$2,000intwoyearsand$3,000inthreeyears.Ifyouwanttoearn10%onyourmoney,howmuchwouldyoubewillingtopay?N=1;I/Y=10;FV=1,000;CPTPV=-909.09N=2;I/Y=10;FV=2,000;CPTPV=-1,652.89N=3;I/Y=10;FV=3,000;CPTPV=-2,253.94PV=909.09+1,652.89+2,253.94=4,815.936C-11公司理財?shù)谑鍼PTChap006-CalcMultipleCashFlows–PVAnoth11MultipleUnevenCashFlows–UsingtheCalculatorAnotherwaytousethefinancialcalculatorforunevencashflowsistousethecashflowkeysPressCFandenterthecashflowsbeginningwithyear0.Youhavetopressthe“Enter”keyforeachcashflowUsethedownarrowkeytomovetothenextcashflowThe“F”isthenumberoftimesagivencashflowoccursinconsecutiveperiodsUsetheNPVkeytocomputethepresentvaluebyenteringtheinterestrateforI,pressingthedownarrow,andthencomputingtheanswerClearthecashflowworksheetbypressingCFandthen2ndCLRWork6C-12公司理財?shù)谑鍼PTChap006-CalcMultipleUnevenCashFlows–U12Decisions,DecisionsYourbrokercallsyouandtellsyouthathehasthisgreatinvestmentopportunity.Ifyouinvest$100today,youwillreceive$40inoneyearand$75intwoyears.Ifyourequirea15%returnoninvestmentsofthisrisk,shouldyoutaketheinvestment?UsetheCFkeystocomputethevalueoftheinvestmentCF;CF0=0;C01=40;F01=1;C02=75;F02=1NPV;I=15;CPTNPV=91.49No–thebrokerischargingmorethanyouwouldbewillingtopay.6C-13公司理財?shù)谑鍼PTChap006-CalcDecisions,DecisionsYourbroke13SavingForRetirementYouareofferedtheopportunitytoputsomemoneyawayforretirement.Youwillreceivefiveannualpaymentsof$25,000eachbeginningin40years.Howmuchwouldyoubewillingtoinvesttodayifyoudesireaninterestrateof12%?Usecashflowkeys:CF;CF0=0;C01=0;F01=39;C02=25,000;F02=5;NPV;I=12;CPTNPV=1,084.716C-14公司理財?shù)谑鍼PTChap006-CalcSavingForRetirementYouareo14SavingForRetirementTimeline012…394041424344000…025K25K25K25K25KNoticethattheyear0cashflow=0(CF0=0)Thecashflowsinyears1–39are0(C01=0;F01=39)Thecashflowsinyears40–44are25,000(C02=25,000;F02=5)6C-15公司理財?shù)谑鍼PTChap006-CalcSavingForRetirementTimeline15QuickQuiz–PartISupposeyouarelookingatthefollowingpossiblecashflows:Year1CF=$100;Years2and3CFs=$200;Years4and5CFs=$300.Therequireddiscountrateis7%.Whatisthevalueofthecashflowsatyear5?Whatisthevalueofthecashflowstoday?Whatisthevalueofthecashflowsatyear3?6C-16公司理財?shù)谑鍼PTChap006-CalcQuickQuiz–PartISupposeyou16AnnuitiesandPerpetuitiesDefinedAnnuity–finiteseriesofequalpaymentsthatoccuratregularintervalsIfthefirstpaymentoccursattheendoftheperiod,itiscalledanordinaryannuityIfthefirstpaymentoccursatthebeginningoftheperiod,itiscalledanannuityduePerpetuity–infiniteseriesofequalpayments6C-17公司理財?shù)谑鍼PTChap006-CalcAnnuitiesandPerpetuitiesDef17AnnuitiesandPerpetuities–BasicFormulasPerpetuity:PV=C/rAnnuities:6C-18公司理財?shù)谑鍼PTChap006-CalcAnnuitiesandPerpetuities–B18AnnuitiesandtheCalculatorYoucanusethePMTkeyonthecalculatorfortheequalpaymentThesignconventionstillholdsOrdinaryannuityversusannuitydueYoucanswitchyourcalculatorbetweenthetwotypesbyusingthe2ndBGN2ndSetontheTIBA-IIPlusIfyousee“BGN”or“Begin”inthedisplayofyourcalculator,youhaveitsetforanannuitydueMostproblemsareordinaryannuities6C-19公司理財?shù)谑鍼PTChap006-CalcAnnuitiesandtheCalculatorYo19Annuity–Example6.5YouborrowmoneyTODAYsoyouneedtocomputethepresentvalue.48N;1I/Y;-632PMT;CPTPV=23,999.54($24,000)Formula:6C-20公司理財?shù)谑鍼PTChap006-CalcAnnuity–Example6.5Youborro20Annuity–SweepstakesExampleSupposeyouwinthePublishersClearinghouse$10millionsweepstakes.Themoneyispaidinequalannualend-of-yearinstallmentsof$333,333.33over30years.Iftheappropriatediscountrateis5%,howmuchisthesweepstakesactuallyworthtoday?30N;5I/Y;333,333.33PMT;CPTPV=5,124,150.296C-21公司理財?shù)谑鍼PTChap006-CalcAnnuity–SweepstakesExampleS21BuyingaHouseYouarereadytobuyahouse,andyouhave$20,000foradownpaymentandclosingcosts.Closingcostsareestimatedtobe4%oftheloanvalue.Youhaveanannualsalaryof$36,000,andthebankiswillingtoallowyourmonthlymortgagepaymenttobeequalto28%ofyourmonthlyincome.Theinterestrateontheloanis6%peryearwithmonthlycompounding(.5%permonth)fora30-yearfixedrateloan.Howmuchmoneywillthebankloanyou?Howmuchcanyouofferforthehouse?6C-22公司理財?shù)谑鍼PTChap006-CalcBuyingaHouseYouarereadyto22BuyingaHouse-ContinuedBankloanMonthlyincome=36,000/12=3,000Maximumpayment=.28(3,000)=84030*12=360N.5I/Y-840PMTCPTPV=140,105TotalPriceClosingcosts=.04(140,105)=5,604Downpayment=20,000–5,604=14,396TotalPrice=140,105+14,396=154,5016C-23公司理財?shù)谑鍼PTChap006-CalcBuyingaHouse-ContinuedBank23AnnuitiesontheSpreadsheet-ExampleThepresentvalueandfuturevalueformulasinaspreadsheetincludeaplaceforannuitypaymentsClickontheExcelicontoseeanexample6C-24公司理財?shù)谑鍼PTChap006-CalcAnnuitiesontheSpreadsheet-24QuickQuiz–PartIIYouknowthepaymentamountforaloan,andyouwanttoknowhowmuchwasborrowed.Doyoucomputeapresentvalueorafuturevalue?Youwanttoreceive5,000permonthinretirement.Ifyoucanearn0.75%permonthandyouexpecttoneedtheincomefor25years,howmuchdoyouneedtohaveinyouraccountatretirement?6C-25公司理財?shù)谑鍼PTChap006-CalcQuickQuiz–PartIIYouknowt25FindingthePaymentSupposeyouwanttoborrow$20,000foranewcar.Youcanborrowat8%peryear,compoundedmonthly(8/12=.66667%permonth).Ifyoutakea4-yearloan,whatisyourmonthlypayment?4(12)=48N;20,000PV;.66667I/Y;CPTPMT=488.266C-26公司理財?shù)谑鍼PTChap006-CalcFindingthePaymentSupposeyou26FindingthePaymentonaSpreadsheetAnotherTVMformulathatcanbefoundinaspreadsheetisthepaymentformulaPMT(rate,nper,pv,fv)ThesamesignconventionholdsasforthePVandFVformulasClickontheExceliconforanexample6C-27公司理財?shù)谑鍼PTChap006-CalcFindingthePaymentonaSprea27FindingtheNumberofPayments–Example6.6Thesignconventionmatters!!!1.5I/Y1,000PV-20PMTCPTN=93.111months=7.75yearsAndthisisonlyifyoudon’tchargeanythingmoreonthecard!6C-28公司理財?shù)谑鍼PTChap006-CalcFindingtheNumberofPayments28FindingtheNumberofPayments–AnotherExampleSupposeyouborrow$2,000at5%,andyouaregoingtomakeannualpaymentsof$734.42.Howlongbeforeyoupayofftheloan?Signconventionmatters!!!5I/Y2,000PV-734.42PMTCPTN=3years6C-29公司理財?shù)谑鍼PTChap006-CalcFindingtheNumberofPayments29FindingtheRateSupposeyouborrow$10,000fromyourparentstobuyacar.Youagreetopay$207.58permonthfor60months.Whatisthemonthlyinterestrate?Signconventionmatters!!!60N10,000PV-207.58PMTCPTI/Y=.75%6C-30公司理財?shù)谑鍼PTChap006-CalcFindingtheRateSupposeyoubo30Annuity–FindingtheRateWithoutaFinancialCalculatorTrialandErrorProcessChooseaninterestrateandcomputethePVofthepaymentsbasedonthisrateComparethecomputedPVwiththeactualloanamountIfthecomputedPV>loanamount,thentheinterestrateistoolowIfthecomputedPV<loanamount,thentheinterestrateistoohighAdjusttherateandrepeattheprocessuntilthecomputedPVandtheloanamountareequal6C-31公司理財?shù)谑鍼PTChap006-CalcAnnuity–FindingtheRateWit31QuickQuiz–PartIIIYouwanttoreceive$5,000permonthforthenext5years.Howmuchwouldyouneedtodeposittodayifyoucanearn0.75%permonth?Whatmonthlyratewouldyouneedtoearnifyouonlyhave$200,000todeposit?Supposeyouhave$200,000todepositandcanearn0.75%permonth.Howmanymonthscouldyoureceivethe$5,000payment?Howmuchcouldyoureceiveeverymonthfor5years?6C-32公司理財?shù)谑鍼PTChap006-CalcQuickQuiz–PartIIIYouwant32FutureValuesforAnnuitiesSupposeyoubeginsavingforyourretirementbydepositing$2,000peryearinanIRA.Iftheinterestrateis7.5%,howmuchwillyouhavein40years?Rememberthesignconvention!!!40N7.5I/Y-2,000PMTCPTFV=454,513.046C-33公司理財?shù)谑鍼PTChap006-CalcFutureValuesforAnnuitiesSup33AnnuityDueYouaresavingforanewhouseandyouput$10,000peryearinanaccountpaying8%.Thefirstpaymentismadetoday.Howmuchwillyouhaveattheendof3years?2ndBGN2ndSet(youshouldseeBGNinthedisplay)3N-10,000PMT8I/YCPTFV=35,061.122ndBGN2ndSet(besuretochangeitbacktoanordinaryannuity)6C-34公司理財?shù)谑鍼PTChap006-CalcAnnuityDueYouaresavingfor34AnnuityDueTimeline012310000100001000032,46435,016.126C-35公司理財?shù)谑鍼PTChap006-CalcAnnuityDueTimeline035Perpetuity–Example6.7Perpetuityformula:PV=C/rCurrentrequiredreturn:40=1/rr=.025or2.5%perquarterDividendfornewpreferred:100=C/.025C=2.50perquarter6C-36公司理財?shù)谑鍼PTChap006-CalcPerpetuity–Example6.7Perpet36QuickQuiz–PartIVYouwanttohave$1milliontouseforretirementin35years.Ifyoucanearn1%permonth,howmuchdoyouneedtodepositonamonthlybasisifthefirstpaymentismadeinonemonth?Whatifthefirstpaymentismadetoday?Youareconsideringpreferredstockthatpaysaquarterlydividendof$1.50.Ifyourdesiredreturnis3%perquarter,howmuchwouldyoubewillingtopay?6C-37公司理財?shù)谑鍼PTChap006-CalcQuickQuiz–PartIVYouwantt37WorktheWebExampleAnotheronlinefinancialcalculatorcanbefoundatMoneyChimpClickonthewebsurferandworkthefollowingexampleChoosecalculatorandthenannuityYoujustinherited$5million.Ifyoucanearn6%onyourmoney,howmuchcanyouwithdraweachyearforthenext40years?Moneychimpassumesannuitydue!!!Payment=$313,497.816C-38公司理財?shù)谑鍼PTChap006-CalcWorktheWebExampleAnotheron38Table6.26C-39公司理財?shù)谑鍼PTChap006-CalcTable6.26C-39公司理財?shù)谑鍼PTChap0039GrowingAnnuityAgrowingstreamofcashflowswithafixedmaturity6C-40公司理財?shù)谑鍼PTChap006-CalcGrowingAnnuityAgrowingstrea40GrowingAnnuity:ExampleAdefined-benefitretirementplanofferstopay$20,000peryearfor40yearsandincreasetheannualpaymentbythree-percenteachyear.Whatisthepresentvalueatretirementifthediscountrateis10percent?6C-41公司理財?shù)谑鍼PTChap006-CalcGrowingAnnuity:ExampleAdefi41GrowingPerpetuityAgrowingstreamofcashflowsthatlastsforever6C-42公司理財?shù)谑鍼PTChap006-CalcGrowingPerpetuityAgrowingst42GrowingPerpetuity:ExampleTheexpecteddividendnextyearis$1.30,anddividendsareexpectedtogrowat5%forever.Ifthediscountrateis10%,whatisthevalueofthispromiseddividendstream?6C-43公司理財?shù)谑鍼PTChap006-CalcGrowingPerpetuity:ExampleThe43EffectiveAnnualRate(EAR)Thisistheactualratepaid(orreceived)afteraccountingforcompoundingthatoccursduringtheyearIfyouwanttocomparetwoalternativeinvestmentswithdifferentcompoundingperiods,youneedtocomputetheEARandusethatforcomparison.6C-44公司理財?shù)谑鍼PTChap006-CalcEffectiveAnnualRate(EAR)Thi44AnnualPercentageRateThisistheannualratethatisquotedbylawBydefinitionAPR=periodratetimesthenumberofperiodsperyearConsequently,togettheperiodratewerearrangetheAPRequation:Periodrate=APR/numberofperiodsperyearYoushouldNEVERdividetheeffectiveratebythenumberofperiodsperyear–itwillNOTgiveyoutheperiodrate6C-45公司理財?shù)谑鍼PTChap006-CalcAnnualPercentageRateThisis45ComputingAPRsWhatistheAPRifthemonthlyrateis.5%?.5(12)=6%WhatistheAPRifthesemiannualrateis.5%?.5(2)=1%WhatisthemonthlyrateiftheAPRis12%withmonthlycompounding?12/12=1%6C-46公司理財?shù)谑鍼PTChap006-CalcComputingAPRsWhatistheAPR46ThingstoRememberYouALWAYSneedtomakesurethattheinterestrateandthetimeperiodmatch.Ifyouarelookingatannualperiods,youneedanannualrate.Ifyouarelookingatmonthlyperiods,youneedamonthlyrate.IfyouhaveanAPRbasedonmonthlycompounding,youhavetousemonthlyperiodsforlumpsums,oradjusttheinterestrateappropriatelyifyouhavepaymentsotherthanmonthly 6C-47公司理財?shù)谑鍼PTChap006-CalcThingstoRememberYouALWAYSn47ComputingEARs-ExampleSupposeyoucanearn1%permonthon$1investedtoday.WhatistheAPR?1(12)=12%Howmuchareyoueffectivelyearning?FV=1(1.01)12=1.1268Rate=(1.1268–1)/1=.1268=12.68%Supposeyouputitinanotheraccountandearn3%perquarter.WhatistheAPR?3(4)=12%Howmuchareyoueffectivelyearning?FV=1(1.03)4=1.1255Rate=(1.1255–1)/1=.1255=12.55%6C-48公司理財?shù)谑鍼PTChap006-CalcComputingEARs-ExampleSuppos48EAR-FormulaRememberthattheAPRisthequotedrate,andmisthenumberofcompoundingperiodsperyear6C-49公司理財?shù)谑鍼PTChap006-CalcEAR-FormulaRememberthatthe49Decisions,DecisionsIIYouarelookingattwosavingsaccounts.Onepays5.25%,withdailycompounding.Theotherpays5.3%withsemiannualcompounding.Whichaccountshouldyouuse?Firstaccount:EAR=(1+.0525/365)365–1=5.39%Secondaccount:EAR=(1+.053/2)2–1=5.37%Whichaccountshouldyouchooseandwhy?6C-50公司理財?shù)谑鍼PTChap006-CalcDecisions,DecisionsIIYouare50Decisions,DecisionsIIContinuedLet’sverifythechoice.Supposeyouinvest$100ineachaccount.Howmuchwillyouhaveineachaccountinoneyear?FirstAccount:365N;5.25/365=.014383562I/Y;100PV;CPTFV=105.39SecondAccount:2N;5.3/2=2.65I/Y;100PV;CPTFV=105.37Youhavemoremoneyinthefirstaccount.6C-51公司理財?shù)谑鍼PTChap006-CalcDecisions,DecisionsIIContin51ComputingAPRsfromEARsIfyouhaveaneffectiverate,howcanyoucomputetheAPR?RearrangetheEARequationandyouget:6C-52公司理財?shù)谑鍼PTChap006-CalcComputingAPRsfromEARsIfyo52APR-ExampleSupposeyouwanttoearnaneffectiverateof12%andyouarelookingatanaccountthatcompoundsonamonthlybasis.WhatAPRmusttheypay?6C-53公司理財?shù)谑鍼PTChap006-CalcAPR-ExampleSupposeyouwant53ComputingPaymentswithAPRsSupposeyouwanttobuyanewcomputersystemandthestoreiswillingtoallowyoutomakemonthlypayments.Theentirecomputersystemcosts$3,500.Theloanperiodisfor2years,andtheinterestrateis16.9%withmonthlycompounding.Whatisyourmonthlypayment?2(12)=24N;16.9/12=1.408333333I/Y;3,500PV;CPTPMT=-172.886C-54公司理財?shù)谑鍼PTChap006-CalcComputingPaymentswithAPRsSu54FutureValueswithMonthlyCompoundingSupposeyoudeposit$50amonthintoanaccountthathasanAPRof9%,basedonmonthlycompounding.Howmuchwillyouhaveintheaccountin35years?35(12)=420N9/12=.75I/Y50PMTCPTFV=147,089.226C-55公司理財?shù)谑鍼PTChap006-CalcFutureValueswithMonthlyCom55PresentValuewithDailyCompoundingYouneed$15,000in3yearsforanewcar.IfyoucandepositmoneyintoanaccountthatpaysanAPRof5.5%basedondailycompounding,howmuchwouldyouneedtodeposit?3(365)=1,095N5.5/365=.015068493I/Y15,000FVCPTPV=-12,718.566C-56公司理財?shù)谑鍼PTChap006-CalcPresentValuewithDailyCompo56ContinuousCompoundingSometimesinvestmentsorloansarefiguredbasedoncontinuouscompoundingEAR=eq–1TheeisaspecialfunctiononthecalculatornormallydenotedbyexExample:Whatistheeffectiveannualrateof7%compoundedcontinuously?EAR=e.07–1=.0725or7.25%6C-57公司理財?shù)谑鍼PTChap006-CalcContinuousCompoundingSometime57QuickQuiz–PartVWhatisthedefinitionofanAPR?Whatistheeffectiveannualrate?Whichrateshouldyouusetocomparealternativeinvestmentsorloans?Whichratedoyouneedtouseinthetimevalueofmoneycalculations?6C-58公司理財?shù)谑鍼PTChap006-CalcQuickQuiz–PartVWhatisthe58PureDiscountLoans–Example6.12Treasurybillsareexcellentexamplesofpurediscountloans.Theprincipalamountisrepaidatsomefuturedate,withoutanyperiodicinterestpayments.IfaT-billpromisestorepay$10,000in12monthsandthemarketinterestrateis7percent,howmuchwillthebillsellforinthemarket?1N;10,000FV;7I/Y;CPTPV=-9,345.796C-59公司理財?shù)谑鍼PTChap006-CalcPureDiscountLoans–Example59Interest-OnlyLoan-ExampleConsidera5-year,interest-onlyloanwitha7%interestrate.Theprincipalamountis$10,000.Interestispaidannually.Whatwouldthestreamofcashflowsbe?Years1–4:Interestpaymentsof.07(10,000)=700Year5:Interest+principal=10,700Thiscashflowstreamissimilartothecashflowsoncorporatebonds,andwewilltalkaboutthemingreaterdetaillater.6C-60公司理財?shù)谑鍼PTChap006-CalcInterest-OnlyLoan-ExampleCo60AmortizedLoanwithFixedPrincipalPayment-ExampleConsidera$50,000,10yearloanat8%interest.Theloanagreementrequiresthefirmtopay$5,000inprincipaleachyearplusinterestforthatyear.ClickontheExcelicontoseetheamortizationtable6C-61公司理財?shù)谑鍼PTChap006-CalcAmortizedLoanwithFixedPrin61AmortizedLoanwithFixedPayment-Example