參考答案

(1)甲債券的價值=1000×10%/2×(P/A, 6%,6)+1000×(P/F,6%,6)=950.87(元)乙債券的價值=1000×(1+5×10%)÷(1+12%×3)=1102.94(元)丙債券的價值=1000×(P/F,12%,3)=711.8(元)由于只有甲債券的目前市價低于其價值,所以,甲、乙、丙三種債券中只有甲債券值得購買。
(2)令半年的到期實際收益率為i,則1000×10%/2×(P/A,i,4)+1000×(P/F,i,4)=1020i=5%時,1000×10%/2×(P/A,i,4)+1000×(P/F,i,4)=1000i=4%時,1000×10%/2×(P/A,i,4)+1000×(P/F,i,4)=1036.30利用內插法解得:半年的期間利率=4.45%,有效年利率=(4.45%+1)×(4.45%+1)-1=9.1%
(3) 2013年3月1日甲債券的價值=[50×(P/A,6%,3)+50+1000×(P/F,6%,3)]×(P/F, 6%, 2/3)=984.26(元)如果價格低于984.26元,則可以投資。
(4)設投資收益率為K,則有:80×(P/A, K,2)+1060×(P/F, K,2)=1041K=9%時,80×(P/A, K,2)+1060×(P/F, K,2)=1032.93K=8%時,80×(P/A, K,2)+1060×(P/F, K,2)=1051.40利用內插法解得:投資收益率=8.56%English answers:
(1) The value of bond Jia=1000×10%/2×(P/A, 6%,6)+1000×(P/F, 6%,6)=950.87(元)The value of bond Yi=1000×(1+5×10%)÷(1+12%×3)=1102.94(元)The value of bond Bing=1000×(P/F, 12%,3)=711.8(元)Because only the market price of bond Jia is lower than its value, so only bond Jia should be
(2) Assuming the yield to maturity of the half year as i,then1000×10%/2×(P/A,i,4)+1000×(P/F,i,4)=1020i=5%, 1000×10%/2×(P/A,i,4)+1000×(P/F,i,4)=1000i=4%, 1000×10%/2×(P/A,i,4)+1000×(P/F,i,4)=1036.30By interpolation method:Period interest of the half year=4.45%,Effective interest of the year=(4.45%+1)×(4.45%+i) -1=9.1%
(3) The value of bond Jia in March, lst, 2013=[50×(P/A, 6%,3)+50+1000×(P/F,6%,3)]×(P/F, 6%, 2/3)=984.26(元)If the market price is lower than 984.26元,it is suitable to invest.
(4) Assuming the return on investment as K, then80×(P/A, K,2)+1060×(P/F, K,2)=1041K=9%,80×(P/A, K,2)+1060×(P/F, K,2)=1032.93K=8%,80×(P/A, K,2)+1060×(P/F, K,2)=1051.40By interpolation method: return on investment=8.56%