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Dancy · 2021年05月02日

n 在连续复利时为多少

  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.

连续复利时计算公式：I/Y 用 特殊EAR公式，n 为多少？才能用四个键计算出来
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1 个答案

星星_品职助教 · 2021年05月02日

同学你好，

计算器第三排5个键不能用于计算连续复利的情况。

连续复利的情况比较简单，直接代入公式计算即可。应该就是你提到的“特殊EAR公式”

以本题为例，1+EAR=e^0.03，可以得到EAR=3.0455%。但是对于本题而言，仅计算EAR没有意义，要计算的是连续复利下的利息，所以最后列式应该是：

1,000,000×[e(0.03×4) – 1]=127,496.85



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