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oli · 2021年10月20日

请问本题为什么不能用求FV的方式来算两个不同计息方式的本息之和呢？为什么考虑到用的是EAR呢？

  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。

请问本题为什么不能用求FV的方式来算两个不同计息方式的本息之和呢？为什么考虑到用的是EAR呢？

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1 个答案

星星_品职助教 · 2021年10月21日

同学你好，

1）这道题答案解析即首先求出两种方式下的FV，进而计算出两种方式下的对应利息，进行相减得到答案。

2）可以用两个FV直接相减。

3）“ compounded daily”这种方式下，也可以使用日利率直接计算FV

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