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snow666_6 · 2021年04月27日

用月这种方法，问题出在哪里了？

  1. CFA I
  2. Quantitative

NO.PZ2017092702000006

问题如下：

For a lump sum investment of ¥250,000 invested at a stated annual rate of 3% compounded daily, the number of months needed to grow the sum to ¥1,000,000 is closest to:

选项：

A.

555.

B.

563.

C.

576.

解释：

A is correct.

The effective annual rate (EAR) is calculated as follows:

EAR = (1 + Periodic interest rate)m – 1   EAR = (1 + 0.03/365)365 – 1   EAR= (1.03045) – 1 = 0.030453 ≈ 3.0453%. Solving for N on a financial calculator results in (where FV is future value and PV is present value): (1 + 0,030453)N = FVN/PV = ¥1,000,000/¥250,000）So,N = 46.21 years, which multiplied by 12 to convert to months results in 554.5, or ≈ 555 months.

250000(1 + 0.03/365)30*n=1000000 直接算出N (月数） ，是B，问题出在哪里了？
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星星_品职助教 · 2021年04月28日

同学你好，

这个提问重复了，复制回复如下：

1）250000(1 + 0.03/365)^30*n=1000000 这个式子中，0.03/365算的是日利率，之后应该乘方为“365×N”次方，算出来的N是年数不是月数。按照你公式的逻辑，N=30×月数n，这又涉及到另外一个问题，即每月并非30天，否则每年就是360天了，和此前计算使用的365天不一致。

2）这种求n的题目直接用计算器计算即可，不用公式。计算器直接短平快就按出来了。

--------------------

提供两种计算器的按法：

本题中“a stated annual rate of 3% compounded daily”，说明3%不能直接用，需要进行转化。

1）可以选择转化为EAR得到3.0453%，此时计算器按键为：PV=-250000， I/Y=3.045，PMT=0，FV=1000000， CPT N=46.21（年），然后乘以12得到554.5月

2）也可以选择转化成日利率得到3%/365=0.0082%，此时计算器按键为：PV=-250000， I/Y=0.0082，PMT=0，FV=1000000， CPT N=16868（天），转化成16868/365=46.21年，再转化为554.5月

以上计算对于各个环节中的四舍五入可能会导致结果细微差别。

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