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婉婷 · 2022年06月03日

为什么I/Y的算法不是直接用3/365,算出天数，再÷30算月数呢？

  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.

为什么I/Y的算法不是直接用3/365,算出天数，再÷30算月数呢？

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1 个答案

袁园_品职助教 · 2022年06月05日

嗨，爱思考的PZer你好：


也可以这么做，但是最后换算成月的时候就不能除以30了哦，因为你对I/Y是除以365的，如果最后按30来换算，你就默认了一年是30*12=360天，会导致计算出来有误差。所以应该除以（365/12）来计算才能得到正确答案哦。

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