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乔。 · 2022年09月19日

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

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.

请问计算器N怎么按出来的?

2 个答案
已采纳答案

星星_品职助教 · 2022年09月19日

同学你好,

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=0.006849,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。

乐笙 · 2022年10月03日

他问的是 通过这个方程 $1million*(1+0.02531)N =$2million, 如何在计算器上求出N?我也有同问。

星星_品职助教 · 2022年10月04日

@乐笙

原回复中已经强调,这类求N的题目都通过计算器来解,并不用公式来求。

通过公式无法直接求出N。需要方程两边同时取Ln进行转换,这并不是这类题目的常规解题思路。

下列内容仅供参考,实际中并不这样去做。

(答案的细微差别来自四舍五入)



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