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喧嚣 · 2023年03月08日

不懂这个计算

NO.PZ2017092702000010

问题如下:

A saver deposits the following amounts in an account paying a stated annual rate of 4%, compounded semiannually:

At the end of Year 4, the value of the account is closest to:

选项:

A.

$30,432

B.

$30,447

C.

$31,677

解释:

B is correct.

To solve for the future value of unequal cash flows, compute the future value of each payment as of Year 4 at the semiannual rate of 2%, and then sum the individual future values, as follows:

根据上表所示,首先计算每笔存款的FV,但是需使用semiannual rate 2%,然后将FV相加求和。

我的想法:每一年分开算,如第一年,N=2,I/Y=2%,pv=题目中的,然后能算出来FV 第二年,N和I/Y不变,PV=第一年算出来的值,PMT=题目给的第二年的投资,算FV 第三年,N和I/Y不变,PV=第二年算出来的值,PMT=题目给的第三年的投资,算Fv 这个FV就是答案。 请问老师我这个思路有什么问题吗?

1 个答案

星星_品职助教 · 2023年03月08日

同学你好,

1)每年给出的deposit不能作为PMT,PMT是一系列的现金流,不是单一现金流。例如把第二年的8,000设为PMT,就相当于要付N个8,000,这显然不对;

2)I/Y是不变的,但N是改变的。由于要算到第四年末,所以第一年的N要等于3,到第二年时,N就需要等于2,以此类推;

3)上述不是解这种题目的常规思路,常规的解法就是将每笔现金流都复利到4时点后,将FV相加。其中对于FV的计算可以如答案解析一样的通过公式解,也可以用计算器按。这种解法是需要掌握的。其余的思路只了解即可。

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