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vicki · 2022年07月23日

EAR算出与何老师的不一样呢？

  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。

老师好，连续复利EAR=（1+3%/4）4次方-1，我按计算器得出EAR=0.030339，哪里错了呢？

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2 个答案

星星_品职助教 · 2022年07月25日

@vicki

stated annual rate 3%除以的4，相当于EAR公式中的m，m是计息频率的意思，如果m=4次，说明按季度计息。

本题的compounded daily做转化时，需要用3%/ 365。无论题干给出的是4年还是6年还是100年，分母都只能是365.

星星_品职助教 · 2022年07月24日

同学你好，

这道题里要求计算的一个是“compounded continuously”，另一个是“compounded daily ”，并没有按季度复利（compounded quarter）这种情况

而你列出的计算式中，除以4就意味着按季度复利，和题干要求不符。

vicki · 2022年07月24日

老师，除以4不是4年的意思吗？还是我的ear公式弄错了？

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