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朵娜 · 2022年07月26日

compound daily的情况这样算为什么不对

  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。

compound daily的情况可否理解为pv=-1000000，pmt=0，I/Y=3/365=0.00829,n=365*4=1460,这样求出来的FV=1128657.624，为什么不对？

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星星_品职助教 · 2022年07月26日

同学你好，

提问中的列式是没问题的，这个按键组合得出的结果就是答案解析中的1,127,491,.292。

细微差异的原因在于I/Y的处理上。如果手动四舍五入，将I/Y录入成0.00829，就会得到你的那个结果。

更好的处理方式是用3/365得到结果后，不退出直接按I/Y进行录入。这样录入的I/Y是最准确的，也可以得到答案解析一致的结果。

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