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Swan陈师雯 · 2021年03月29日

请问一下计算器应该怎么计算呢

  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.

请问一下计算器应该怎么计算呢

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1 个答案

星星_品职助教 · 2021年03月29日

同学你好，

提供两种按计算器的方法：

本题中“a stated annual rate of 3% compounded daily”，说明3%不能直接用，需要进行转化。

①可以选择转化为EAR得到3.0453%，此时计算器按键为：PV=-250000， I/Y=3.045，PMT=0，FV=1000000， CPT N=46.21（年），然后通过46.21×12=554.5≈555（月）得到正确选项A。

②也可以选择转化成日利率得到3%/365=0.0082%，此时计算器按键为：PV=-250000， I/Y=0.0082，PMT=0，FV=1000000， CPT N=16,867.27（天）。对于I/Y的四舍五入可能会导致结果细微差别。

然后首先将16,867.27天转化为16,867.27/365=46.21（年）。然后通过46.21×12=554.5≈555（月）

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