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77 · 2021年02月03日

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  1. CFA I
  2. Quantitative

NO.PZ2018062016000006

问题如下：

Lucy believes that after retirement she will need about $2 million totally for her daily expenses. At present, she has $1million investment at a stated annual interest rate of 2.5%. Assuming compounded daily, how long does it take for Lucy to have enough money for retirement life?

选项：

A.

27.73 years

B.

28.07 years

C.

26.48 years

解释：

A is correct.

EAR=(1+0.025/365)365-1=0.02531

$1million*(1+0.02531)N =$2million, N=27.73 years.

最后一步的1.0253的n次方=2，需要怎么按计算器才能算出来n?我用代入试错法，前两个选项都约等于2。。。

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星星_品职助教 · 2021年02月03日

同学你好，

这道题不建议按照公式里的顺序去“硬算”N。这样需要用到LN做转化，麻烦还容易错。用计算器可以很简单的解决这个问题，提供两种思路：

①由于选项中给的都是多少“年”，所以可以先把I/Y也转化成“年”的形式

EAR=(1+0.025/365)^365-1=0.02531，即I/Y=2.531

PV=-1，PMT=0，FV=2，I/Y=2.531，CPT N=27.7268直接得到答案A。

②也可以把期限设置成天来计算，然后再转化到年。这样的好处是可以不用去计算一个EAR

PV=-1，FV=2，PMT=0，I/Y=2.5/365=0.0068，CPT N=10,120.295（天）

转化成年就是10,120.295/365=27.7268（年）。

这类求N的题目都可以这样去用计算器来处理。

丫丫12512 · 2021年08月19日

请问老师，为什么PMT是0？无论按照年、还是按照日，都产生了利息收益的啊？

星星_品职助教 · 2021年08月19日

@丫丫12512

同学你好，

需要明确“PMT”的概念。这个指的是期限固定，金额固定的持续现金流。题目中没有这个条件，所以默认为0处理。

产生的利息已经反应在I/Y和N里了。

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