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Linda · 2022年11月13日

老师，compounding continuously求fv，用计算机是不是：n=4, i/y=3, pv=1,000,000 ,pmt=0, cpt fv?

  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。

老师，compounding continuously求fv，用计算机是不是：n=4, i/y=3, pv=1,000,000 ,pmt=0, cpt fv?

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3 个答案

星星_品职助教 · 2023年03月07日

@周建安

e是自然常数，约等于2.718。在连续复利（compounded continuously）转化EAR的公式中有用到。

e一般用计算器直接算，在最左列LN那个键的第二功能那里。

星星_品职助教 · 2022年11月16日

@Linda 学习加油~

星星_品职助教 · 2022年11月13日

同学你好，

continuous compounding的情况下需要用到公式，不能直接按计算器。

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。

-----

e的0.12次方的计算器按法为：先输入0.12，再按2nd，然后按最左列的LN键。按等号直接得到结果1.1275

Linda · 2022年11月16日

谢谢老师

周建安 · 2023年03月07日

老师请问这里的e代表什么

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