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为了求职冲呀 · 2022年02月21日

请问这道题目的解题思路是什么？

  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.

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


1）先求出EAR，然后带入的是fv=pv*（1+r/m）^m这个公式吗？


2）不知道怎么算n的结果，能麻烦老师列一下求n的解题步骤吗



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2 个答案

星星_品职助教 · 2022年08月17日

@Marissa

这里相当于把“百万”作为一个单位，1就代表1（百万）。

只要PV、FV和PMT三者都用百万来衡量，最后结果就是不变的。

星星_品职助教 · 2022年02月22日

同学你好，

1）最终解题是基于fv=pv*（1+r/m）^m这个公式的，但通过公式直接手算N很麻烦，所以统一都按计算器来CPT N；

2）提供两种按计算器的思路：

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=0.006849，CPT N=10,120.295（天），此处I/Y的四舍五入可能会造成结果的细微差别。

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。

Marissa · 2022年08月17日

老师请问，这里的PV和FV，计算时都可以简化成1，而不是输入一百万吗？

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