问一道题：NO.PZ2017092702000016 [ CFA I ]

问题如下：

A sports car, purchased for £200,000, is financed for five years at an annual rate of 6% compounded monthly. If the first payment is due in one month, the monthly payment is closest to:

选项：

£3,847.

£3,867.

£3,957.

解释：

B is correct,

calculated as follows (where A is annuity and PV is present value):

$A=\left[\frac{1-\frac1{(1+r_s/m)^{mN}}}{r_s/m}\right]$

${l}=(200,000)\left[\frac{1-{\displaystyle\frac1{(1+0.06/12)^{12\times5}}}}{0.06/12}\right]\\\;\;\;$

${l}=(200,000)/51.72556\\\;\;\;$

$=3,866.56$

为什么不用EAR,0.514

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1 个答案

星星_品职助教 · 2020年11月24日

同学你好，

这道题要求的是月度PMT，所以如果把N设置为每年为一期，然后用EAR的方式求出来的也是年度PMT，还需要再进一步转化才能得到月度PMT的结果。

所以这道题的做法是使用月度利率，把N设置为每个月一期，直接按计算器求出“monthly payment ”。

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NO.PZ2017092702000016 问题如下 A sports car, purchasefor £200,000, is financefor five years annurate of 6% compounmonthly. If the first payment is e in one month, the monthly payment is closest to: A.£3,847. B.£3,867. C.£3,957. B is correct,“the first payment is e in one month”是第一笔付款在第一个月的意思（t=1），所以是个后付年金问题。后付年金模式下，PV=-200,000, N=12*5， I/Y=6/12，FV=0 CPT PMT=3866.56 为什么不需要先计算EAR（6.17%），然后再代入PV=-200000，N=5*12，I/Y=6.17/12，FV=0，求PMT？

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2023-01-24 21:03 1 · 回答

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2022-09-07 22:11 1 · 回答

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问一道题：NO.PZ2017092702000016 [ CFA I ]

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