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ryanno1 · 2021年05月05日

请问前面的127,496.85是怎么算的

  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.

请问前面的127,496.85是怎么算的

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2 个答案

星星_品职助教 · 2021年05月17日

@🍡GrayBubble

同学你好，

1+EAR=e的3%次方，如果用e的3%次方减1的话，计算出来的是EAR本身。即对于求EAR的题型要减1.

但这道题要算的是本息和，即本金×（1+EAR）。所以这个时候单独计算EAR没有意义，直接计算1+EAR就可以了。

否则计算出EAR后，还要再加上1.

星星_品职助教 · 2021年05月05日

同学你好，

127,496.85是continuous compounding的情况。

对于连续复利而言，1+EAR=e的3%次方，所以最终本息和为 1,000,000×e^(3%×4)=1,127,496.85

🍡GrayBubble · 2021年05月17日

老师 为什么算出来不再减一呢

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