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188****7003 · 2021年02月17日

老师好用公式fv/pv=(1+r/m)m次方的公式算出,为什么是r/2,代入半年计息一次不应该是12么,就是最后一步没看懂

NO.PZ2017092702000011

问题如下:

An investment of €500,000 today that grows to €800,000 after six years has a stated annual interest rate closest to:

选项:

A.

7.5% compounded continuously.

B.

7.7% compounded daily.

C.

8.0% compounded semiannually.

解释:

C is correct,

as shown in the following (where FV is future value and PV is present value): If: FVN = PV(1 + rs/m)mN, Then: (800,000500,000)12×61=rs2{(\frac{800,000}{500,000})}^\frac1{2\times6}-1=\frac{r_s}2    rs = 0.07988 (rounded to 8.0%)

老师好用公式fv/pv=(1+r/m)m次方的公式算出,为什么是r/2,代入半年计息一次不应该是12么,就是最后一步没看懂

1 个答案

星星_品职助教 · 2021年02月18日

同学你好,

fv/pv=(1+r/m)^m这个公式是用来计算EAR即有效“年”利率的。其中,“r”是stated annual rate,“m”指的是计息频率。

本题C选项中,计息频率是“compounded semiannually”,即每半年计息一次,一年计息2次。所以m=2。

但这道题用的公式实际上是上述公式的一个拓展,即fv/pv=(1+r/m)^(m×N),其中N是按年计息时,一共有多少年。本题中,一共有6年(...after six years...),所以N=6。这是最后一步中2×6=12次方的由来。12是m和N的乘积,但m本身还是等于2的。

所以r/m只能是r/2,不能是r/12.

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