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Lin · 2020年10月11日

问一道题：NO.PZ2016031001000110

  1. CFA I
  2. Fixed Income

问题如下：

An investor purchases a nine-year, 7% annual coupon payment bond at a price equal to par value. After the bond is purchased and before the first coupon is received, interest rates increase to 8%. The investor sells the bond after five years. Assume that interest rates remain unchanged at 8% over the five-year holding period.

Per 100 of par value, the future value of the reinvested coupon payments at the end of the holding period is closest to:

选项：

A.

35.00.

B.

40.26.

C.

41.07.

解释：

C is correct.

The future value of reinvested cash flows at 8% after five years is closest to 41.07per 100 of par value.

[(7×(1.08))4]+[7×(1.08)3]+[7×(1.08)2]+[7×(1.08)1]+7{\lbrack{(7\times{(1.08)})}^4\rbrack}+{\lbrack7\times{(1.08)}^3\rbrack}+{\lbrack7\times{(1.08)}^2\rbrack}+{\lbrack7\times{(1.08)}^1\rbrack}+7

= 41.0662

The 6.07 difference between the sum of the coupon payments over the five-year holding period (35) and the future value of the reinvested coupons (41.07) represents the "interest-on interest" gain from compounding.                                                          

老师，这题如果用计算器，为什么N=5呢，第一年末才收到第一次coupon，第五年就卖掉了，只有4个期间。麻烦老师解答一下，谢谢！

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1 个答案

WallE_品职答疑助手 · 2020年10月12日

我们这里算的是持有期（5年）中的coupon再投资收入，相当于是求一个第五年年末的FV。最后一年年末你还是能收到一份coupon，但在投资期限为0.

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NO.PZ2016031001000110问题如下investor purchases a nine-year, 7% annucoupon payment bona priequto pvalue. After the bonis purchaseanbefore the first coupon is receive interest rates increase to 8%. The investor sells the bonafter five years. Assume thinterest rates remain unchange8% over the five-yeholng perio Per 100 of pvalue, the future value of the reinvestecoupon payments the enof the holng periois closest to:A.35.00.B.40.26.C.41.07. C is correct.The future value of reinvestecash flows 8% after five years is closest to 41.07per 100 of pvalue. [(7×(1.08))4]+[7×(1.08)3]+[7×(1.08)2]+[7×(1.08)1]+7{\lbrack{(7\times{(1.08)})}^4\rbrack}+{\lbrack7\times{(1.08)}^3\rbrack}+{\lbrack7\times{(1.08)}^2\rbrack}+{\lbrack7\times{(1.08)}^1\rbrack}+7[(7×(1.08))4]+[7×(1.08)3]+[7×(1.08)2]+[7×(1.08)1]+7= 41.0662The 6.07 fferenbetween the sum of the coupon payments over the five-yeholng perio(35) anthe future value of the reinvestecoupons (41.07) represents the \"interest-on interest\" gain from compounng.考点Sourof return解析 题目让我们求的是持有到最后的FV。投资者在第五年末将债券卖了出去，对于他来说the enof the holng perio是第五年年末。所以我们这里算的是持有期（5年）中的coupon再投资收入，用到的不是剩余的年限。利用计算器求，那么相当于是求一个第五年年末的FV。N=5，PMT=7，I/Y=8，PV=0，求得FV=41.07，故C正确。 为什么pv=0 而不是100

2023-03-04 08:25 1 · 回答

NO.PZ2016031001000110 问题如下 investor purchases a nine-year, 7% annucoupon payment bona priequto pvalue. After the bonis purchaseanbefore the first coupon is receive interest rates increase to 8%. The investor sells the bonafter five years. Assume thinterest rates remain unchange8% over the five-yeholng perio Per 100 of pvalue, the future value of the reinvestecoupon payments the enof the holng periois closest to: A.35.00. B.40.26. C.41.07. C is correct.The future value of reinvestecash flows 8% after five years is closest to 41.07per 100 of pvalue. [(7×(1.08))4]+[7×(1.08)3]+[7×(1.08)2]+[7×(1.08)1]+7{\lbrack{(7\times{(1.08)})}^4\rbrack}+{\lbrack7\times{(1.08)}^3\rbrack}+{\lbrack7\times{(1.08)}^2\rbrack}+{\lbrack7\times{(1.08)}^1\rbrack}+7[(7×(1.08))4]+[7×(1.08)3]+[7×(1.08)2]+[7×(1.08)1]+7= 41.0662The 6.07 fferenbetween the sum of the coupon payments over the five-yeholng perio(35) anthe future value of the reinvestecoupons (41.07) represents the \"interest-on interest\" gain from compounng.考点Sourof return解析 题目让我们求的是持有到最后的FV。投资者在第五年末将债券卖了出去，对于他来说the enof the holng perio是第五年年末。所以我们这里算的是持有期（5年）中的coupon再投资收入，用到的不是剩余的年限。利用计算器求，那么相当于是求一个第五年年末的FV。N=5，PMT=7，I/Y=8，PV=0，求得FV=41.07，故C正确。 请再详细点分解开步骤的含义，谢谢

2023-01-26 10:49 1 · 回答

题目让求的是reinvest的FV，所以为什么不减掉5个coupon的价格，却直接用的是coupon和reinvest的FV总和呢

2020-11-03 15:33 2 · 回答

40.26. 41.07. C is correct. The future value of reinvestecash flows 8% after five years is closest to 41.07per 100 of pvalue. [(7×(1.08))4]+[7×(1.08)3]+[7×(1.08)2]+[7×(1.08)1]+7{\lbrack{(7\times{(1.08)})}^4\rbrack}+{\lbrack7\times{(1.08)}^3\rbrack}+{\lbrack7\times{(1.08)}^2\rbrack}+{\lbrack7\times{(1.08)}^1\rbrack}+7[(7×(1.08))4]+[7×(1.08)3]+[7×(1.08)2]+[7×(1.08)1]+7 = 41.0662 The 6.07 fferenbetween the sum of the coupon payments over the five-yeholng perio(35) anthe future value of the reinvestecoupons (41.07) represents the \"interest-on interest\" gain from compounng.                                                          老师，所以这道题问的其实就是第五年的账面价值………可是我理解的意思是第五年再买入这个债券，持有到第九年，FV是多少。然后我理解的是pv是第五年的卖出价，然后n=4 ，pmt7，iy 8 计算FV

2020-10-15 13:50 3 · 回答