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holicess · 2023年05月28日

老师，为什么不能用(1+3%/365)^(m*30)=4%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.

不能用上面这个去试，是因为不能默认每个月30天么？谢谢

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1 个答案

星星_品职助教 · 2023年05月28日

同学你好，

是的。复利计算时一年为365天。EAR等均基于365计算。

如果用了每月30天，相当于设置了每年为30×12=360天。两者就矛盾了。

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NO.PZ2017092702000006 问题如下 For a lump sum investment of ¥250,000 investea stateannurate of 3% compounily, the number of months neeto grow the sum to ¥1,000,000 is closest to: A.555. B.563. C.576. A is correct. The effective annurate (EAR) is calculatefollows: E= (1 + Perioc interest rate)m – 1   E= (1 + 0.03/365)365 – 1   EAR= (1.03045) – 1 = 0.030453 ≈ 3.0453%. Solving for N on a financicalculator results in (where FV is future value anPV is present value): (1 + 0,030453）N = FVN/PV = (¥1,000,000/¥250,000）So,N = 46.21 years, whimultiplie12 to convert to months results in 554.5, or ≈ 555 months. 这题我EAR已经算出来是3.045，带入计算器知四求一不知道为什么算出来是46.21.

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