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如此_AnnieCcc · 2020年03月17日

问一道题：NO.PZ2017092702000006 [ CFA I ]

  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.

我看了答案 第一步 算EAR= 3.04% 我明白  第二步 我确实看不懂 为什么 （1+EAR）的n次方= FV除以PV  我想说 FV除以PV不是等于（ 1+r除以m）的m次方吗？
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1 个答案

星星_品职助教 · 2020年03月17日

同学你好，

这个的原理其实就是1块钱投资一年，按年计息的利率为r，1年后的结果就是1×（1+r），n年后的结果就是1×（1+r）^n

这个转化为抽象的公式就是1年后的FV=PV×(1+r)，n年后的FV=PV×（1+r）^n

和你的问题相关联后，这里面EAR就是上面公式里的“r”，也就是一年的实际投资利率。你写的公式就相当于一年的情况，即FV=PV×(1+EAR)，如果是n年的情况就是FV=PV×（1+EAR）^n

 

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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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