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西华 · 2020年11月24日

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:

A.

£3,847.

B.

£3,867.

C.

£3,957.

解释:

B is correct,

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

A=[11(1+rs/m)mNrs/m]A=\left[\frac{1-\frac1{(1+r_s/m)^{mN}}}{r_s/m}\right]

l=(200,000)[11(1+0.06/12)12×50.06/12]      {l}=(200,000)\left[\frac{1-{\displaystyle\frac1{(1+0.06/12)^{12\times5}}}}{0.06/12}\right]\\\;\;\;

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

=3,866.56=3,866.56

为什么不用EAR,0.514
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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