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1、英国精算师协会英国精算师协会考试真题CT2导读：就爱阅读网友为您分享以下“英国精算师协会考试真题CT2”的资讯，希望对您有所帮助，感谢您对92to的支持!13(i)(ii)(iii)Page8Loan=200(Da)+2,000aat9%=200??20-a?è0.09÷?+2,000a=200??20-9.1285?è0.09÷?+2,000′9.1285=42,415.89Loanoutstandingafter7thpayment=200(Da)+2000aat9%=200??13-7.4869
2、?è0.09÷?+2,000′7.4869=27,225.13Hence,YearLoano/satstartPaymentInterestelement827225.1346002450.26925075.3944002256.79Loano/safter9thpayment=25075.39-2143.21=22932.18Let10thpaymentbeX+2200Then22932.18=200(Da)+Xaat7%=200??11-a?è0.07÷?+Xa=200??11-7.4987?è0
3、.07÷?+7.4987X=10003.71+7.4987XTX=1724.09T10thpayment=1724.09+2200=￡3,924.09Capitalelement2149.742143.2114(i)Let(Va)=v+4v2+9v3+...+n2vnThenv.(Va)=v2+4v3+...+n2vn+1T(1-v)(Va)=v+3v2+5v3+...+(2n-1)vn-n2vn+1=2v+4v2+6v3+...+2nvn-a-n2vn+1T(Va)=2(Ia)-a-n2vn+11-
4、v(ii)(a)Workin￡000’sPVofliabilities=95a+5(Ia)at7%=95′10.5940+5′????-20v20ai?11.3356-20′0.25842?=1006.43+5′?÷0.07è?=1446.94Numeratorofduration=95(Ia)+5(1.v+2.2v2+...+20.20v20)=95′88.1029+52(Ia)-a-400v211-v{}=8369.78+5{2′88.1029-10.5940-400′0.24151}0.0654
5、2=8369.78+5274.21=13,643.99Hence,durationofliabilities=13643.99=9.43years1446.94Page9(b)Page10Letnominalamountof25-yearstockbeAandnominalamountof12-yearstockbeB.ThenPVofassets=Av25+B′0.08′a+Bv12(=PVofliabilities=1446.94)(1)anddurationofassets=(25Av25+B′
6、0.08′(Ia)12+12Bv12)/1446.94(=durationofliabilities=13643.991446.94)(2)From(1),1446.94=A′0.18425+B′0.08′7.9427+B′0.44401T1446.94=0.18425A+1.07943B(3)From(2),13643.99=25′0.18425′A+éê?0.08′??1.07′7.9427-12′0.44401?è0.07÷?+12′0.44401ùú?′BT13643.99=4.60625A+
7、(3.62351+5.32812)B=4.60625A+8.95163B(4)Now,4.606250.18425′(3)T36173.50=4.60625A+26.98575BT22529.51=18.03412BTB=1249.27A=534.27Hence,amountinvestedineachsecurityis:StockA:534.27v25=98.44(=￡98,440)StockB:1249.27′0.08′a+1249.27v12=1249.27′1.07943=1348.50(=
8、￡1,348,500)Page11FacultyofActuariesInstituteofActuariesEXAMINATIONS19April2000(pm)Subject102—FinancialMathematicsTimeallowed:ThreehoursINSTRUCTIONSTOTHECANDIDATE1.2.3.Writeyoursurnameinfull,theinitialsofyourothernamesandyourCandi
