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anyewumian · 2020年09月05日

问一道题:NO.PZ2016031001000075

问题如下:

The annual yield-to-maturity, stated for with a periodicity of 12, for a 4-year, zero coupon bond priced at 75 per 100 of par value is closest to:

选项:

A.

6.25%.

B.

7.21%.

C.

7.46%.

解释:

B is correct.

The annual yield-to-maturity, stated for a periodicity of 12, is 7.21%. It is calculated as follows:

PV=FV(1+r)NPV=\frac{FV}{{(1+r)}^N}

75=(100(1+r)4×12)75={(\frac{100}{{(1+r)}^{4\times12}})}

10075=(1+r)48\frac{100}{75}=(1+r)^{48}

1.33333 =(1+r)48

[1.33333]1/48 = [(1+r)48]1/48

1.3333302083= (1 + r)

1.00601 = (1 + r)

1.00601−1 = r

0.00601 = r

r × 12 = 0.07212, or approximately 7.21%

老师,这道题能否解释一下,没有理解

1 个答案

WallE_品职答疑助手 · 2020年09月06日

就是让你求年化的收益率,这个债券每年复利12次,复利4年,从75块钱变成了100.

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NO.PZ2016031001000075 问题如下 The annuyielto-maturity, statefor with a periocity of 12, for a 4-year, zero coupon bonprice75 per 100 of pvalue is closest to: A.6.25%. B.7.21%. C.7.46%. B is correct.The annuyielto-maturity, statefor a periocity of 12, is 7.21%. It is calculatefollows:PV=FV(1+r)NPV=\frac{FV}{{(1+r)}^N}PV=(1+r)NFV​75=(100(1+r)4×12)75={(\frac{100}{{(1+r)}^{4\times12}})}75=((1+r)4×12100​)10075=(1+r)48\frac{100}{75}=(1+r)^{48}75100​=(1+r)481.33333 =(1+r)48[1.33333]1/48 = [(1+r)48]1/481.3333302083= (1 + r)1.00601 = (1 + r)1.00601−1 = r0.00601 = rr × 12 = 0.07212, or approximately 7.21%考点bonvaluation解析利用计算器PV= -75,FV=100,PMT=0,N=4×12=48,求得I/Y=0.601×12=7.21,故B正确。 计算求解过程明白了, 问两个表述是什么意思1. statefor a periocity of 12 的periocity 是什么含义, 分12期计息吗 2. 题干最后一句怎么看出是让求YTM的,75 of100是什么意思

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