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尼克内姆 · 2020年06月25日

问一道题：NO.PZ2017092702000007 [ CFA I ]

  1. CFA I
  2. Quantitative

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.

请问老师，我的做法错在哪里？？

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1 个答案

星星_品职助教 · 2020年06月28日

同学你好，

题干中提示“a stated annual rate of 3% compounded continuously”，所以是连续复利的EAR转化，你的做法相当于将计息频率转化为了每日计息，这个结果算出来的利息是比连续复利情况下要小的

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