金融学（博迪） 清华本科课件 chpt4

Chapter4:TimeValueofMoneyCopyright,2000PrenticeHall©AuthorNickBagley,bdellaSoft,Inc.ObjectiveExplaintheconceptofcompoundinganddiscountingandtoprovideexamplesofreallifeapplications1ValueofInvesting$1Continuinginthismanneryouwillfindthatthefollowingamountswillbeearnt:2Valueof$5InvestedMoregenerally,withaninvestmentof$5at10%weobtain3FutureValueofaLumpSum4Example:FutureValueofaLumpSumYourbankoffersaCDwithaninterestrateof3%fora5yearinvestments.Youwishtoinvest$1,500for5years,howmuchwillyourinvestmentbeworth?5PresentValueofaLumpSum6Example:PresentValueofaLumpSumYouhavebeenoffered$40,000foryourprintingbusiness,payablein2years.Giventherisk,yourequireareturnof8%.Whatisthepresentvalueoftheoffer?7SolvingLumpSumCashFlowforInterestRate8Example:InterestRateonaLumpSumInvestmentIfyouinvest$15,000fortenyears,youreceive$30,000.Whatisyourannualreturn?9ReviewofLogarithmsThebasicpropertiesoflogarithmsthatareusedbyfinanceare:10ReviewofLogarithmsThefollowingpropertiesareeasytoprovefromthelastones,andareusefulinfinance11SolvingLumpSumCashFlowforNumberofPeriods12EffectiveAnnualRatesofanAPRof18%13TheFrequencyofCompoundingNotethatasthefrequencyofcompoundingincreases,sodoestheannualeffectiverateWhatoccursasthefrequencyofcompoundingrisestoinfinity?14TheFrequencyofCompounding15TheFrequencyofCompounding16DerivationofPVofAnnuityFormula:Algebra.1of517DerivationofPVofAnnuityFormula:Algebra.2of518DerivationofPVofAnnuityFormula:Algebra.3of519DerivationofPVofAnnuityFormula:Algebra.4of520DerivationofPVofAnnuityFormula:Algebra.5of521PVofAnnuityFormula22PVAnnuityFormula:Payment23PVAnnuityFormula:NumberofPayments24AnnuityFormula:PVAnnuityDue25DerivationofFVofAnnuityFormula:Algebra26FVAnnuityFormula:Payment27FVAnnuityFormula:NumberofPayments28PerpetualAnnuities/PerpetuitiesRecalltheannuityformula:Letn->infinitywithi>0:29Mortgage:ThepaymentWewillexaminethisproblemusingafinancialcalculatorThefirstquantitytodetermineistheamountoftheloanandthepoints30CalculatorSolutionThisisthemonthlyrepayment31CalculatorSolutionOutstanding@60Months32SummaryofPaymentsThefamilyhasmade60payments=$2687.98*12*5=$161,878.64Theirmortgagerepayment= 450,000-418,744.61=$31,255.39Interest=payments-principlereduction=161,878.64-31,255.39=$130,623.253334353637$10,000$11,000¥1,000,000¥1,030,000¥Time10%$/$(direct)0.01$/¥3%¥/¥?$/¥U.S.A.Japan38$10,000$11,124$11,000¥1,000,000¥1,030,000¥Time10%$/$(direct)0.01$/¥3%¥/¥0.0108$/¥U.S.A.Japan39$10,000$10,918¥$11,000¥1,000,000¥1,030,000¥Time10%$/$(direct)0.01$/¥3%