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1、CH511，13，18，19，2011.TofindthePVofalumpsum,weuse:PV=FV/(1+r)tPV=$1,000,000/(1.10)80=$488.1913.Toanswerthisquestion,wecanuseeithertheFVorthePVformula.Bothwillgivethesameanswersincetheyaretheinverseofeachother.WewillusetheFVformula,thatis:FV=PV(1+r)tSolvingforr,weget:r=(
2、FV/PV)1/t–1r=($1,260,000/$150)1/112–1=.0840or8.40%TofindtheFVofthefirstprize,weuse:FV=PV(1+r)tFV=$1,260,000(1.0840)33=$18,056,409.9418.TofindtheFVofalumpsum,weuse:FV=PV(1+r)tFV=$4,000(1.11)45=$438,120.97FV=$4,000(1.11)35=$154,299.40Betterstartearly!19.WeneedtofindtheF
3、Vofalumpsum.However,themoneywillonlybeinvestedforsixyears,sothenumberofperiodsissix.FV=PV(1+r)tFV=$20,000(1.084)6=$32,449.3320.Toanswerthisquestion,wecanuseeithertheFVorthePVformula.Bothwillgivethesameanswersincetheyaretheinverseofeachother.WewillusetheFVformula,thati
4、s:FV=PV(1+r)tSolvingfort,weget:t=ln(FV/PV)/ln(1+r)t=ln($75,000/$10,000)/ln(1.11)=19.31So,themoneymustbeinvestedfor19.31years.However,youwillnotreceivethemoneyforanothertwoyears.Fromnow,you’llwait:2years+19.31years=21.31yearsCH616，24，27，42，5816.Forthisproblem,wesimplyn
5、eedtofindtheFVofalumpsumusingtheequation:FV=PV(1+r)t17/17Itisimportanttonotethatcompoundingoccurssemiannually.Toaccountforthis,wewilldividetheinterestratebytwo(thenumberofcompoundingperiodsinayear),andmultiplythenumberofperiodsbytwo.Doingso,weget:FV=$2,100[1+(.084/2)]
6、34=$8,505.9324.ThisproblemrequiresustofindtheFVA.TheequationtofindtheFVAis:FVA=C{[(1+r)t–1]/r}FVA=$300[{[1+(.10/12)]360–1}/(.10/12)]=$678,146.3827.Thecashflowsareannualandthecompoundingperiodisquarterly,soweneedtocalculatetheEARtomaketheinterestratecomparablewiththeti
7、mingofthecashflows.UsingtheequationfortheEAR,weget:EAR=[1+(APR/m)]m–1EAR=[1+(.11/4)]4–1=.1146or11.46%AndnowweusetheEARtofindthePVofeachcashflowasalumpsumandaddthemtogether:PV=$725/1.1146+$980/1.11462+$1,360/1.11464=$2,320.3642.TheamountofprincipalpaidontheloanisthePVo
8、fthemonthlypaymentsyoumake.So,thepresentvalueofthe$1,150monthlypaymentsis:PVA=$1,150[(1–{1/[1+(.0635/12)]}360)/(.0635/12)]=$
