2025年金融計(jì)算考試試題及答案解析考試時(shí)間：______分鐘總分：______分姓名：______一、某投資者計(jì)劃在5年后獲得100,000元，用于購買一輛汽車。假設(shè)銀行存款年利率為4%，且每年復(fù)利計(jì)息一次。為在5年末達(dá)到目標(biāo)金額，該投資者從現(xiàn)在起每年需要存入多少等額資金？二、假設(shè)某公司發(fā)行面值為1,000元的5年期債券，票面年利率為6%，每年付息一次。投資者甲以1,050元的價(jià)格買入該債券，持有到期。請計(jì)算投資者甲的持有期收益率（持有至到期時(shí)的總收益率）。三、某投資者購買了一只股票，預(yù)計(jì)未來三年每年的股利分別為每股1.00元、1.10元和1.20元。預(yù)計(jì)第三年末股票的出售價(jià)格為每股15元。如果該投資者的預(yù)期收益率為12%，那么該股票的現(xiàn)在價(jià)值（內(nèi)在價(jià)值）應(yīng)為多少？該投資者是否應(yīng)該購買（僅從價(jià)值角度判斷）？四、假設(shè)某公司股票的預(yù)期收益率是15%，市場組合的預(yù)期收益率是10%，無風(fēng)險(xiǎn)利率是5%。根據(jù)資本資產(chǎn)定價(jià)模型（CAPM），該公司股票的Beta系數(shù)是多少？五、某公司正在考慮一個(gè)投資項(xiàng)目，初始投資額為200,000元。預(yù)計(jì)項(xiàng)目壽命期為4年，每年產(chǎn)生的凈現(xiàn)金流分別為：Year1:80,000元；Year2:70,000元；Year3:60,000元；Year4:50,000元。假設(shè)該項(xiàng)目的必要回報(bào)率（或折現(xiàn)率）為8%。請計(jì)算該項(xiàng)目的凈現(xiàn)值（NPV）。六、一項(xiàng)投資的標(biāo)準(zhǔn)差為0.15（15%）。如果投資組合中只包含這項(xiàng)資產(chǎn)，并且投資者持有100%的該資產(chǎn)，那么該投資組合的預(yù)期收益率和標(biāo)準(zhǔn)差分別是多少？七、A、B兩種資產(chǎn)的預(yù)期收益率和標(biāo)準(zhǔn)差如下：資產(chǎn)A：預(yù)期收益率=12%，標(biāo)準(zhǔn)差=10%；資產(chǎn)B：預(yù)期收益率=8%，標(biāo)準(zhǔn)差=12%。假設(shè)A、B兩種資產(chǎn)的協(xié)方差為0。如果投資者將資金按70%的比例投資于A資產(chǎn)，30%的比例投資于B資產(chǎn)，請計(jì)算該投資組合的預(yù)期收益率和標(biāo)準(zhǔn)差。八、解釋什么是“復(fù)利”，并說明與單利相比，在相同條件下復(fù)利對投資者而言意味著什么。九、簡述凈現(xiàn)值（NPV）指標(biāo)在資本預(yù)算決策中的作用及其決策規(guī)則。十、為什么投資者需要承擔(dān)風(fēng)險(xiǎn)？簡述風(fēng)險(xiǎn)與預(yù)期收益率之間的關(guān)系。試卷答案一、P=A*[(1+i)^n-1]/[i*(1+i)^n]Where:P=FutureValue=100,000i=Interestrateperperiod=4%=0.04n=Numberofperiods=5A=Periodicpayment(whatweneedtofind)100,000=A*[(1+0.04)^5-1]/[0.04*(1+0.04)^5]100,000=A*[1.2166529-1]/[0.04*1.2166529]100,000=A*[0.2166529]/[0.0486661]100,000=A*4.4519A=100,000/4.4519A≈22,414.84Theinvestorneedstodepositapproximately22,414.84yuanannually.二、YieldtoMaturity(YTM)=[(C+(F-P)/n)/((F+P)/2)]*100%Where:C=Annualcouponpayment=1,000*6%=60F=Facevalue=1,000P=Purchaseprice=1,050n=Yearstomaturity=5YTM=[(60+(1,000-1,050)/5)/((1,000+1,050)/2)]*100%YTM=[(60-10/5)/(2,050/2)]*100%YTM=[(60-2)/1,025]*100%YTM=[58/1,025]*100%YTM≈5.66%Theholdingperiodyield(YTM)isapproximately5.66%.三、PV=[D1/(1+r)^1]+[D2/(1+r)^2]+[D3/(1+r)^3]+[P3/(1+r)^3]Where:D1=DividendYear1=1.00D2=DividendYear2=1.10D3=DividendYear3=1.20P3=SellingpriceatYear3=15r=Requiredrateofreturn=12%=0.12PV=Currentvalue(whatweneedtofind)PV=[1.00/(1+0.12)^1]+[1.10/(1+0.12)^2]+[1.20/(1+0.12)^3]+[15/(1+0.12)^3]PV=[1.00/1.12]+[1.10/1.2544]+[1.20/1.4049]+[15/1.4049]PV≈0.8929+0.8763+0.8540+10.6768PV≈12.3999Theintrinsicvalueofthestockisapproximately12.40yuan.Sincetheintrinsicvalue(12.40)isgreaterthantheexpectedfutureprice(15),basedsolelyonvalue,theinvestorshouldbuythestock.四、RequiredRateofReturn(k)=Risk-FreeRate(Rf)+Beta(β)*[MarketReturn(Rm)-Risk-FreeRate(Rf)]Where:k=15%=0.15Rf=5%=0.05Rm=10%=0.10β=Betacoefficient(whatweneedtofind)0.15=0.05+β*(0.10-0.05)0.15=0.05+β*0.050.15-0.05=β*0.050.10=β*0.05β=0.10/0.05β=2TheBetacoefficientforthecompany'sstockis2.五、NPV=Σ[CashFlow_t/(1+r)^t]-InitialInvestmentWhere:InitialInvestment=200,000CashFlowYear1=80,000CashFlowYear2=70,000CashFlowYear3=60,000CashFlowYear4=50,000r=Discountrate=8%=0.08t=TimeperiodNPV=[80,000/(1+0.08)^1]+[70,000/(1+0.08)^2]+[60,000/(1+0.08)^3]+[50,000/(1+0.08)^4]-200,000NPV=[80,000/1.08]+[70,000/1.1664]+[60,000/1.2597]+[50,000/1.3605]-200,000NPV≈74,074.07+59,860.14+47,630.92+36,751.50-200,000NPV≈218,316.63-200,000NPV≈18,316.63TheNetPresentValue(NPV)oftheprojectisapproximately18,316.63yuan.六、Iftheportfolioconsistsonlyofoneasset(100%invested),theportfolio'sexpectedreturnisequaltotheexpectedreturnofthatsingleasset,andtheportfolio'sstandarddeviationisequaltothestandarddeviationofthatsingleasset.ExpectedReturn(Portfolio)=ExpectedReturn(Asset)=15%StandardDeviation(Portfolio)=StandardDeviation(Asset)=15%Theexpectedreturnandstandarddeviationoftheportfolioareboth15%.七、PortfolioExpectedReturn(E(Rp)):E(Rp)=w_A*E(R_A)+w_B*E(R_B)Where:w_A=WeightofAssetA=70%=0.70w_B=WeightofAssetB=30%=0.30E(R_A)=ExpectedReturnofA=12%=0.12E(R_B)=ExpectedReturnofB=8%=0.08E(Rp)=0.70*0.12+0.30*0.08E(Rp)=0.084+0.024E(Rp)=0.108Theexpectedreturnoftheportfoliois10.8%.PortfolioStandardDeviation(σp):σp=√[w_A^2*σ_A^2+w_B^2*σ_B^2+2*w_A*w_B*Cov(A,B)]Where:σ_A=StandardDeviationofA=10%=0.10σ_B=StandardDeviationofB=12%=0.12Cov(A,B)=CovariancebetweenAandB=0σp=√[(0.70)^2*(0.10)^2+(0.30)^2*(0.12)^2+2*0.70*0.30*0]σp=√[0.49*0.01+0.09*0.0144+0]σp=√[0.0049+0.001296+0]σp=√[0.006196]σp≈0.0787Thestandarddeviationoftheportfolioisapproximately7.87%.八、Compoundinterestistheprocessofcalculatinginterestontheinitialprincipal,whichalsoincludesalloftheaccumulatedinterestfrompreviousperiods.Inotherwords,interestearnsinterest.SingleInterestcalculation:Interest=Principal*Rate*TimeCompoundInterestcalculation:FutureValue=Principal*(1+Rate)^TimeInthesameconditions(sameprincipal,rate,time),compoundinterestresultsinahigherfuturevaluecomparedtosimpleinterestbecausetheinterestcalculationbasegrowslargerwitheachperiod.Compoundinterestmeansthatthereturnonaninvestmentgrowsatanincreasingrateovertimeduetothereinvestmentofearnings.Thismakesinvestmentswithcompoundinterestmorebeneficialforinvestorscomparedtoinvestmentswithsimpleinterestoverlongerperiods.九、NetPresentValue(NPV)isacapitalbudgetingtechniqueusedtoevaluatetheprofitabilityofaprojectorinvestment.Itcalculatesthepresentvalueofallexpectedfuturecashinflowsminusthepresentvalueofallexpectedfuturecashoutflows,discountedattheproject'srequiredrateofreturnorcostofcapital.ThedecisionruleforNPVis:*IfNPV>0,theprojectisexpectedtoaddvaluetothefirmandshouldbeaccepted.*IfNPV<0,theprojectisexpectedtodestroyvalueandshouldberejected.*IfNPV=0,theprojectisexpectedtobreakevenandisgenerallyconsideredacceptable,althoughotherfactorsmightbeconsidered.NPVhelpsmanagersdecidewhethertoproceedwithaninvestmentbyprovidingadirectmeasureoftheexpectedincreaseinfirmvalue.十、Investorsneedtobearriskbecausetheyexpecttobecompensatedfortakingonuncertainty.Withoutthepossibilityofearninghigherreturns,investorswouldnotinvest