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Sophie · 2020年06月17日

问一道题:NO.PZ2017092702000007 [ CFA I ]

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!
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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