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小胖嘟 · 2021年01月14日

问一道题：NO.PZ2017092702000006 [ CFA I ]

  1. CFA I
  2. Quantitative

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.

为什么算出天数以后不能直接除以30算月数呢
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1 个答案

星星_品职助教 · 2021年01月15日

同学你好，

按照你提到的做法，首先要算出一共有多少天

I/Y=3/365=0.0082（注意这一步）， PV=-250,000，PMT=0，FV=1,000,000，CPT N=16,867.27（天）

如果这个时候直接用16,867.27除以30，相当于默认每个月只有30天。这就相当于1年只有12×30=360天。这就和最开始转化利率时用的每年365天（I/Y=3/“365”）矛盾了。

所以这个时候应该将16,867.27天按照365天首先转化为16,867.27/365=46.21（年），这种计算方式和最初的利率转化就是一致的了。然后通过46.21×12=554.5≈555年得到正确选项A。

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