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Poppy · 2022年06月24日

请问下老师为什么PMT是2.5？

NO.PZ2016031001000076

问题如下：

A 5-year, 5% semiannual coupon payment corporate bond is priced at 104.967 per 100 of par value. The bond’s yield-to-maturity, quoted on a semiannual bond basis, is 3.897%. An analyst has been asked to convert to a monthly periodicity. Under this conversion, the yield-to-maturity is closest to:

选项：

A.

3.87%.

B.

4.95%.

C.

7.67%.

解释：

A is correct.

The yield-to-maturity, stated for a periodicity of 12 (monthly periodicity), is 3.87%.The formula to convert an annual percentage rate (annual yield-to-maturity) from one periodicity to another is as follows:

${(1+\frac{APRm}m)}^m={(1+\frac{APRn}n)}^n$

${(1+\frac{0.03897}2)}^2={(1+\frac{APR12}{12})}^{12}$

${(1.01949)}^2={(1+\frac{APR12}{12})}^{12}$

$1.03935={(1+\frac{APR12}{12})}^{12}$

${(1.03935)}^{1/12}={\lbrack{(1+\frac{APR12}{12})}^{12}\rbrack}^{1/12}$

$1.00322={(1+\frac{APR12}{12})}$

$1.00322-1={(\frac{APR12}{12})}$

APR₁₂ = 0.00322 × 12 = 0.03865, or approximately 3.87%.

考点：APR的转换

解析：这里考查的是不同计息频率的收益率之间的转换。一年计息两次的年化收益率，即APR₂ ，转换到一年计息12次的APR₁₂ ，可以同时转换到一年计息一次（相当于一个过渡）。即(1+APR₂ /2)² =1+EAR=(1+APR₁₂ /12)¹² ，得到APR₁₂ 为3.87%。

请问下老师为什么PMT是2.5?

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吴昊_品职助教 · 2022年06月24日

嗨，从没放弃的小努力你好：

题干中有：5% semiannual coupon payment，债券是半年付息一次，所以coupon rate是需要去年化的。每一期的现金流PMT=100×5%/2=2.5

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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NO.PZ2016031001000076 问题如下 A 5-year, 5% semiannucoupon payment corporate bonis price104.967 per 100 of pvalue. The bons yielto-maturity, quoteon a semiannubonbasis, is 3.897%. analyst hbeen asketo convert to a monthly periocity. Unr this conversion, the yielto-maturity is closest to: A.3.87%. B.4.95%. C.7.67%. A is correct.The yielto-maturity, statefor a periocity of 12 (monthly periocity), is 3.87%.The formula to convert annupercentage rate (annuyielto-maturity) from one periocity to another is follows:(1+APRmm)m=(1+APRnn)n{(1+\frac{APRm}m)}^m={(1+\frac{APRn}n)}^n(1+mAPRm)m=(1+nAPRn)n(1+0.038972)2=(1+APR1212)12{(1+\frac{0.03897}2)}^2={(1+\frac{APR12}{12})}^{12}(1+20.03897)2=(1+12APR12)12(1.01949)2=(1+APR1212)12{(1.01949)}^2={(1+\frac{APR12}{12})}^{12}(1.01949)2=(1+12APR12)121.03935=(1+APR1212)121.03935={(1+\frac{APR12}{12})}^{12}1.03935=(1+12APR12)12(1.03935)1/12=[(1+APR1212)12]1/12{(1.03935)}^{1/12}={\lbrack{(1+\frac{APR12}{12})}^{12}\rbrack}^{1/12}(1.03935)1/12=[(1+12APR12)12]1/121.00322=(1+APR1212)1.00322={(1+\frac{APR12}{12})}1.00322=(1+12APR12)1.00322−1=(APR1212)1.00322-1={(\frac{APR12}{12})}1.00322−1=(12APR12)APR12 = 0.00322 × 12 = 0.03865, or approximately 3.87%.考点APR的转换解析这里考查的是不同计息频率的收益率之间的转换。一年计息两次的年化收益率，即APR2 ，转换到一年计息12次的APR12 ，可以同时转换到一年计息一次（相当于一个过渡）。即(1+APR2 /2)2 =1+EAR=(1+APR12 /12)12 ，得到APR12 为3.87%。请问APR是在哪里学过呢，怎么这一章我没有看到这个知识点呢？谢谢！

2023-04-27 05:08 1 · 回答

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2022-10-13 22:55 1 · 回答

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2022-07-28 08:19 1 · 回答

我用计算器这么按的 N=5*12=60 PV= -104.967 PMT= 100*5%/12=0.4167 FV=100 算出来 IY=0.3254这个应该是月化，我再乘以 12 得到对应的年化是 3.9，为什么这样是不对的呢？

2020-11-06 22:33 1 · 回答