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Dang.D · 2022年09月21日

想问下题目不是已经说了annual rate of 3% compounded daily，为啥还要换算成EAR的形式呢？

  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.

为啥不能直接在计算器里I/Y带入3%/365

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星星_品职助教 · 2022年09月22日

同学你好，

1）换算成EAR可以直接求出N的年数，然后乘以12得到题目问的月份数；

2）不换算EAR，用3/365求出的是N的天数，然后除以365得到年，再乘以12得到月份数。

以上两种做法都可以。

星星_品职助教 · 2022年09月22日

@Dang.D

不可以。这种做法相当于是每年有30×12=360天，而实际复利用的天数是365天。

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