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Sophie · 2020年06月17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.

请问下老师什么时后出现state rate 的时候需要转换成EAR来算呢？什么时候不用呢？我自己觉得是compound daily/monthly/quarterly/semiannually 的时候需要转换，但似乎有时候做到类似自字眼的题又不需要转换，直接用state rate就行，有些疑惑，请老师解下疑，谢谢！
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1 个答案

星星_品职助教 · 2020年06月17日

同学你好，

首先要明确一个结论，就是stated annual rate无论在什么情况下都不能直接使用，因为这是一个“假的”名义上的利率，并不代表真实能获得的利息。

如果看到题干中有类似“a stated annual rate of 3%（名义上的利率）+ compounded continuously（计息频率）”的时候，就一定要做转化。

需要区分的在于：1. 有可能是需要直接代公式转化为EAR；2. 也有可能是不用专门转化为EAR，而是只求出期间利率（“I/Y”）就可以，再配合上期数（“N”）和期间现金流（“PMT”）后直接用计算器求解。

 

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