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mitmit · 2020年02月16日

问一道题: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%)

用计算器N=6,算出年利率等于8.148375%。然后这个和题目问的有什么区别吗。。。

1 个答案
已采纳答案

星星_品职助教 · 2020年03月08日

同学你好(修改下之前的笔误),

这么算也可以。由于计算器上的I/Y指的都是期间利率,如果N设定为6,那么算出来的就是(有效)年利率。

所以这道题就转化成了哪种stated annual rate和计息频率的组合可以等价于这个有效年利率。C选项计算EAR=(1+8%/2)^2 -1 =8.16%.

同理,A选项是7.79%,B选项是8%。相对而言C选项和EAR=8.1484接近一些。

这题选项设置的有点相近,考试的时候一般会差的比较大,比如A算出来是6.5%,B算出来是6.8%这样的

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