房地产市场与金融PVFVPMTRATE计算

第三讲利率因素,复利/资金时间价值复利终值/现值年金/偿债基金因子收益率,RealEstateFinanceandInvestments,WuYuzhe,ZJU,Interest,兴趣与利息如果年初个人在银行存10000元，年利率为6%，年末这笔存款为多少？解答须明白四个基本成分：1.Aninitialdeposit2.Aninterestrate3.Time4.Valueatsomespecifiedfutureperiod,RealEstateFinanceandInvestments,WuYuzhe,ZJU,CompoundInterest,PV=presentvaluei=interestrate,discountrate,rateofreturnI=dollaramountofinterestearnedFV=futurevaluesFV=PV+IExhibit3-1,3-2,RealEstateFinanceandInvestments,WuYuzhe,ZJU,Formulaforcompoundinterest,FV=PV(1+i)nn=numberofperiodsi=interestratePV=presentvalueordepositPMT=paymentFV=futurevalue,RealEstateFinanceandInvestments,WuYuzhe,ZJU,FutureValueofaSingleLumpSum,Example:assumeAstuteinvestorinvests$1,000todaywhichpays10percent,compoundedannually.Whatistheexpectedfuturevalueofthatdepositinfiveyears?=1000*(1+0.1)5Solution=$1,610.51,RealEstateFinanceandInvestments,WuYuzhe,ZJU,Annualinterestrate(i),FV=PV(1+i)nNumberofyearsCompounding:interestoninterestOtherCompoundingintervalsMonthly,quarterly,semiannual,RealEstateFinanceandInvestments,WuYuzhe,ZJU,Effectiveannualyield(EAY),n=1时Equivalentnominalannualrate(ENAR)i?如果有效年利率为5%，按季度计算复利，等价的名义年利率为多少？,RealEstateFinanceandInvestments,WuYuzhe,ZJU,TheFinancialCalculator,n=numberofperiodsi=interestratePV=presentvalue,deposit,ormortgageamountPMT=paymentFV=futurevaluen,i,andPMTmustcorrespondtothesameperiod:Monthly,quarterly,semiannualoryearlyWhenusingthefinancialcalculatorthreevariablesmustbepresentinordertocomputethefourthunknown.PVorPMTmustbeenteredasanegative,RealEstateFinanceandInvestments,WuYuzhe,ZJU,PresentValueofaFutureSum,PV=FV1/(1+i)nThediscountingprocessistheoppositeofcompoundingThesamerulesmustbeappliedwhendiscountingn,iandPMTmustcorrespondtothesameperiodMonthly,quarterly,semi-annually,andannually,RealEstateFinanceandInvestments,WuYuzhe,ZJU,Annuities,OrdinaryAnnuityendofperiod(e.g.,mortgagepayment)AnnuityDuebeginofperiod(e.g.,amonthlyrentalpayment),RealEstateFinanceandInvestments,WuYuzhe,ZJU,FutureValueofanAnnuity,FVA=P(1+i)n-1+P(1+i)n-2.+P,RealEstateFinanceandInvestments,WuYuzhe,ZJU,PresentValueofanAnnuity,PVA=R1/(1+i)1+R1/(1+i)2.R1/(1+i)n,RealEstateFinanceandInvestments,WuYuzhe,ZJU,SinkingFundFactor,偿债基金因子？,RealEstateFinanceandInvestments,WuYuzhe,ZJU,FutureValueofanAnnuity,Example:assumeAstuteinvestorinvests$1,000attheendofeachyearinaninvestmentwhichpays10percent,compoundedannually.Whatistheexpectedfuturevalueofthatinvestmentinfiveyears?Solution=$6,105.10,RealEstateFinanceandInvestments,WuYuzhe,ZJU,SinkingFundPayment,Example:assumeAstuteinvestorwantstoaccumulate$6,105.10infiveyears.AssumeMs.Investorcanearn10percent,compoundedannually.Howmuchmustbeinvestedeachyeartoobtainthegoal?Solution=$1,000.00,RealEstateFinanceandInvestments,WuYuzhe,ZJU,PresentValueofaSingleLumpSum,Example:assumeAstuteinvestorhasanopportunitythatprovides$1,610.51attheendoffiveyears.IfMs.Investorrequiresa10percentannualreturn,howmuchcanastutepaytodayforthisfuturesum?Solution=$1,000,RealEstateFinanceandInvestments,WuYuzhe,ZJU,PaymenttoAmortizeMortgageLoan,Example:assumeAstuteinvestorwouldlikeamortgageloanof$100,000at10percentannualinterest,paidmonthly,amortizedover30years.Whatistherequiredmonthlypaymentofprincipalandinterest?Solution=$877.57,RealEstateFinanceandInvestments,WuYuzhe,ZJU,思考?,WhatisIRR?,RealEstateFinanceandInvestments,WuYuzhe,ZJU,作业1,计算3月定期整存整取，6月定期整存整取，2年期的整存整取，5年期的整存整取年实际收益率，并于1年期整存整取比较,RealEstateFinanceandInvestments,WuYuzhe,ZJU,作业2：RemainingLoanBalanceCalculation,Example:determinetheremainingbalanceofamortgageloanof$100,000at10percentannualinterest,paidmonthly,amortize