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Asker · 2020年10月05日

问一道题：NO.PZ2017092702000006

  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.

这个题把 0.03 除以 12 或者除以 365 按月份，天数 求 EAR 都可以得到 555 的正确结果，但是按年度求次方为啥不对：


250000*((1+0.03)^(555/12))=980983

250000*((1+0.03)^(563/12))=1000506


按年算的话是 563 更合理啊

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已采纳答案

星星_品职助教 · 2020年10月08日

同学你好，

这道题不能用3%除以365来做，这样求出来的N是天数，在不知道一个月有多少天的前提下无法转化为月份。只能算EAR求出年份再乘以12. 这样直接就可以算出答案，不需要用选项反向代入。

sarahjia · 2020年11月16日

hi 星星老师我又从头再来了😂想问下这里 (1 + 0.03/365)^365 这个计算器要怎么按呢

星星_品职助教 · 2020年11月16日

@sarahjia

首先检查一下计算器是不是AOS模式的。（2nd+最下面一行的“·”，调用“format”功能，然后连续按向下箭头直至看到“AOS”或者“Chn”，如果是后者就需要按2nd+“ENTER”键调用“SET”功能给调成AOS模式）

AOS模式就是正常的运算模式，不管按键顺序如何，都是先算乘除，再算加减。而Chn模式是按照按键顺序进行计算。

然后按公式顺序直接输入1+0.03/365就可以，输入完了以后先按“=”，得到1.000082，然后按“yx”“365”，再按“=”即可得到结果1.030453

加油~

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