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1、November2001Course2InterestTheory,EconomicsandFinanceSocietyofActuaries/CasualtyActuarialSociety1.Erniemakesdepositsof100attime0,andXattime3.Thefundgrowsataforceof2tinterestd=,t>0.t100Theamountofinterestearnedfromtime3totime6isX.CalculateX.(A)385(B)485(C)585(
2、D)685(E)785Course2,November200122.Theproductionofagoodrequirestwoinputs,laborandcapital.Atitscurrentlevelofdailyoutput,acompetitivefirmemploys100machinehoursofcapitaland200laborhours.Themarginalproductofmachinehoursis10units.Themarginalproductoflaborhoursis5u
3、nits.Therentalrate,or“price,”ofcapitalis20permachinehour.Ifthefirmminimizesitscosts,whatisthehourlywagerate?(A)2.5(B)5.0(C)10.0(D)20.0(E)40.0Course2,November200133.Lastyear,acountry'soutputincreased2.6%.Thecountry’scapitalstockincreased4.0%whileitslaborhoursi
4、ncreased2.0%.Thelaborshareoftotalincomewas70%.Whatwasthecountry’stotalfactorproductivitygrowthlastyear?(A)–0.8(B)0.0(C)2.3(D)5.2(E)6.0Course2,November200144.Consideraprojectlastingoneyear.Theinitialoutlayis100,000atthebeginningoftheyearandtheexpectedinflowis1
5、20,000attheendoftheyear.Theopportunitycostofcapitalfortheprojectis20%,theborrowingrateis8%,andthemarginaltaxrateis35%.Calculatetheadjustedpresentvalueifthecompanyborrows54%oftheproject’srequiredinvestment.(A)800(B)1260(C)1400(D)3150(E)3500Course2,November2001
6、55.Mikebuysaperpetuity-immediatewithvaryingannualpayments.Duringthefirst5years,thepaymentisconstantandequalto10.Beginninginyear6,thepaymentsstarttoincrease.Foryear6andallfutureyears,thecurrentyear’spaymentisK%largerthanthepreviousyear’spayment.Atanannualeffec
7、tiveinterestrateof9.2%,theperpetuityhasapresentvalueof167.50.CalculateK,givenK<9.2.(A)4.0(B)4.2(C)4.4(D)4.6(E)4.8Course2,November200166.A10-yearloanof2000istoberepaidwithpaymentsattheendofeachyear.Itcanberepaidunderthefollowingtwooptions:(i)Equalannualpayment
8、satanannualeffectiverateof8.07%.(ii)Installmentsof200eachyearplusinterestontheunpaidbalanceatanannualeffectiverateofi.Thesumofthepaymentsunderoption(i)equalsthesumofthepaymentsunderoption
