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Victoriazhang · 2022年04月09日

按年算和按日算为什么不对

  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。

按年算：pv=1000000 pmt=0 i/y=3 n=4 求fv-1000000为年的利息差；按日算：pv=1000000 pmt=0 i/y=3/365 n=4*365求fv-1000000,然后求两个算法的差值，这个思路为什么不对呢

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1 个答案

星星_品职助教 · 2022年04月09日

同学你好，

本题没有按年算的情况（compounded annually），需要计算的是连续复利（compounded continuously）下的情况。

然后再和按日计息的这种情况做差。

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