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Emily2329 · 2023年06月02日

不太会算这题

  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。

我daily算出来是12.74%，连续复利是e的0.003*4=4.4228不知道哪里有问题。。。

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1 个答案

星星_品职助教 · 2023年06月03日

同学你好，

1）daily compounding计算如下：

PV= -1,000,000； N=365×4； I/Y=3/365； PMT=0； CPT FV=1,127,491.29。

（如果结果有细微差异，则来自于I/Y的四舍五入）

2）连续复利，

1,000,000×e^(3%×4)=1,127,496.85。其中应为e的0.03*4，即e的0.12次方，这个数字算出来应为1.127496，再乘以本金，即可得到最终结果。

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