Time value of Money

TimeValueofMoneyTheTimeValueofMoneyTheInterestRateSimpleInterestCompoundInterestAmortizingaLoanObviously,$10,000today.YoualreadyrecognizethatthereisTIMEVALUETOMONEY!!TheInterestRateWhichwouldyouprefer--$10,000todayor$10,000in5years?TIMEallowsyoutheopportunitytopostponeconsumptionandearnINTEREST.TIMEalsoeatsawayyourmoneythroughINFLATIONTIMEhasanOPPORTUNITYCOSTWhyTIME?WhyisTIMEsuchanimportantelementinyourdecision?TypesofInterestCompoundInterestInterestpaid(earned)onanypreviousinterestearned,aswellasontheprincipalborrowed(lent).SimpleInterestInterestpaid(earned)ononlytheoriginalamount,orprincipalborrowed(lent).SimpleInterestFormulaFormulaSI=P0(i)(n)SI:SimpleInterestP0:Deposittoday(t=0)i:InterestRateperPeriodn:NumberofTimePeriodsSI=P0(i)(n)=$1,000(.07)(2)=$140SimpleInterestExampleAssumethatyoudeposit$1,000inanaccountearning7%simpleinterestfor2years.Whatistheaccumulatedinterestattheendofthe2ndyear?FV=P0+SI=$1,000+$140=$1,140FutureValueisthevalueatsomefuturetimeofapresentamountofmoney,oraseriesofpayments,evaluatedatagiveninterestrate.SimpleInterest(FV)WhatistheFutureValue(FV)ofthedeposit?ThePresentValueissimplythe$1,000youoriginallydeposited.Thatisthevaluetoday!PresentValueisthecurrentvalueofafutureamountofmoney,oraseriesofpayments,evaluatedatagiveninterestrate.SimpleInterest(PV)WhatisthePresentValue(PV)ofthepreviousproblem?050001000015000200001stYear10thYear20thYear30thYearFutureValueofaSingle1,000Deposit10%SimpleInterest7%CompoundInterest10%CompoundInterestWhyCompoundInterest?FutureValueAssumethatyoudeposit$1,000atacompoundinterestrateof7%for2years.FutureValueSingleDeposit(Graphic)012$1,000FV27%FV1=P0(1+i)1=$1,000(1.07)=$1,070CompoundInterestYouearned$70interestonyour$1,000depositoverthefirstyear.Thisisthesameamountofinterestyouwouldearnundersimpleinterest.FutureValueSingleDeposit(Formula)FV1=P0(1+i)1=$1,000(1.07)=$1,070FV2=FV1(1+i)1=P0(1+i)(1+i)=$1,000(1.07)(1.07)=P0(1+i)2=$1,000(1.07)2=$1,144.90YouearnedanEXTRA$4.90inYear2withcompoundoversimpleinterest.FutureValueSingleDeposit(Formula)FV1=P0(1+i)1FV2=P0(1+i)2GeneralFutureValueFormula:FVn=P0(1+i)norFVn=P0(FVIFi,n)--SeeTableGeneralFutureValueFormulaetc.FVIFi,nisfoundonTable.ValuationUsingTablePeriod6%7%8%11.0601.0701.08021.1241.1451.16631.1911.2251.26041.2621.3111.36051.3381.4031.469FV2=$1,000(FVIF7%,2)=$1,000(1.145)=$1,145[DuetoRounding]UsingFutureValueTablesPeriod6%7%8%11.0601.0701.08021.1241.1451.16631.1911.2251.26041.2621.3111.36051.3381.4031.469Rekhawantstoknowhowlargeherdepositof$10,000todaywillbecomeatacompoundannualinterestrateof10%for5years.StoryProblemExample012345$10,000FV510%CalculationbasedonTableFV5=$10,000(FVIF10%,5)=$10,000(1.611)=$16,110[DuetoRounding]StoryProblemSolutionCalculationbasedongeneralformula:FVn=P0(1+i)nFV5=$10,000(1+0.10)5=$16,105.10Wewillusethe“Rule-of-72”.DoubleYourMoney!!!Quick!Howlongdoesittaketodouble$5,000atacompoundrateof12%peryear(approx.)?Approx.YearstoDouble=72/i%72/12%=6Years[ActualTimeis6.12Years]The“Rule-of-72”Quick!Howlongdoesittaketodouble$5,000atacompoundrateof12%peryear(approx.)?Assumethatyouneed$1,000in2years.Let’sexaminetheprocesstodeterminehowmuchyouneedtodeposittodayatadiscountrateof7%compoundedannually.012$1,0007%PV1PV0PresentValueSingleDeposit(Graphic)PV0=FV2/(1+i)2=$1,000/(1.07)2=FV2/(1+i)2=$873.44PresentValueSingleDeposit(Formula)012$1,0007%PV0PV0=FV1/(1+i)1PV0=FV2/(1+i)2GeneralPresentValueFormula:PV0=FVn/(1+i)norPV0=FVn(PVIFi,n)--SeeTableGeneralPresentValueFormulaetc.PVIFi,nisfoundonTable.ValuationUsingTablePeriod6%7%8%1.943.935.9262.890.873.8573.840.816.7944.792.763.7355.747.713.681PV2=$1,000(PVIF7%,2)=$1,000(.873)=$873[DuetoRounding]UsingPresentValueTablesPeriod6%7%8%1.943.935.9262.890.873.8573.840.816.7944.792.763.7355.747.713.681Rekhawantstoknowhowlargeofadeposittomakesothatthemoneywillgrowto$10,000in5yearsatadiscountrateof10%.StoryProblemExample012345$10,000PV010%Calculationbasedongeneralformula:PV0=FVn/(1+i)nPV0=$10,000/(1+0.10)5=$6,209.21CalculationbasedonTable:PV0=$10,000(PVIF10%,5)=$10,000(.621)=$6,210.00[DuetoRounding]StoryProblemSolutionTypesofAnnuitiesOrdinaryAnnuity:Paymentsorreceiptsoccurattheendofeachperiod.AnnuityDue:Paymentsorreceiptsoccuratthebeginningofeachperiod.AnAnnuityrepresentsaseriesofequalpayments(orreceipts)occurringoveraspecifiednumberofequidistantperiods.ExamplesofAnnuitiesStudentLoanPaymentsCarLoanPaymentsInsurancePremiumsMortgagePaymentsRetirementSavingsPartsofanAnnuity0123$100$100$100(OrdinaryAnnuity)EndofPeriod1EndofPeriod2TodayEqualCashFlowsEach1PeriodApartEndofPeriod3PartsofanAnnuity0123$100$100$100(AnnuityDue)BeginningofPeriod1BeginningofPeriod2TodayEqualCashFlowsEach1PeriodApartBeginningofPeriod3FVAn=R(1+i)n-1+R(1+i)n-2+...+R(1+i)1+R(1+i)0OverviewofanOrdinaryAnnuity--FVARRR012nn+1FVAnR=PeriodicCashFlowCashflowsoccurattheendoftheperiodi%...FVA3=$1,000(1.07)2+$1,000(1.07)1+$1,000(1.07)0=$1,145+$1,070+$1,000=$3,215ExampleofanOrdinaryAnnuity--FVA$1,000$1,000$1,00001234$3,215=FVA37%$1,070$1,145CashflowsoccurattheendoftheperiodHintonAnnuityValuationThe