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Eliza · 2022年03月24日

本题按年求FV为什么用EAR的公式而不是直接用FV=(1+3%)^4的方式，我试了下，这两种计算方式的结果不一样欸

  1. CFA I
  2. Quantitative

NO.PZ2017092702000007

问题如下：

Given a €1,000,000 investment for four years with a stated annual rate of 3% compounded continuously, the difference in its interest earnings compared with the same investment compounded daily is closest to:

选项：

A.

€1.

B.

€6.

C.

€455.

解释：

B is correct.

The difference between continuous compounding and daily compounding is

€127,496.85 – €127,491.29 = €5.56, or ≈ €6, as shown in the following calculations. With continuous compounding, the investment earns (where PV is present value) PVersN - PV = €1,000,000e0.03(4) – €1,000,000

= €1,127,496.85 – €1,000,000 = €127,496.85 With daily compounding, the investment earns: €1,000,000(1 + 0.03/365)^365(4) – €1,000,000 = €1,127,491.29 – €1,000,000 = €127,491.29.

根据不同的计息频率来计算两个利息。第一个是“.... compounded continuously”，第二个是“ compounded daily”，分别计算出利息后做差即可。

1000000*e^(0.03*4)=1127496.85

(1+3%)^4=1125508.81


这两种计算方式算得的结果差很多欸

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1 个答案

星星_品职助教 · 2022年03月24日

同学你好，

3%是“stated annual rate”，不能直接使用，需要根据题干中的“compounded daily”进行转化。

公式的正确形式为：

1,000,000×(1+3% / 365)^（4×365）=1,127,491.292

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