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杨大发 · 2021年08月16日

问题

  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.

老师，我把abc换算成天，分别得到a=15650，b=16890，c=17280，然后用250000*（1+3%/365）n=1000000这个公式，把abc分别带入计算得到n=16890的时候等式成立，然后选了b，请问我这个计算方式为什么会选错呢？
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1 个答案

星星_品职助教 · 2021年08月16日

同学你好，

这个计算的问题在于直接默认一个月有30天，这样一年被默认为了360天，和后续计算中的“3%/365”不符。

但这种解题思路本身是有问题的。这种问题应该使用计算器直接按出结果，而不是代入公式手算。


提供两种按计算器的思路，以后直接这么做就可以：

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的四舍五入可能会导致结果细微差别。


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