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phoebeqp · 2023年05月26日

No.PZ2017092702000010 存量重复计算的问题

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。

题干里给的是每年年末的deposit。第一年4000,第二年8000,第二年8000里面不会有4000已经compound到第四年年末了吗?再计算8000的compound为什么没有重复计算的问题?

1 个答案

星星_品职助教 · 2023年05月26日

同学你好,

1)8,000指的是在第二年末又单独存入8,000。这个8,000直接复利两年(即复利4个半年,也就是复利4期)到第四年末,和之前的4,000没有联系。

2)之前的4,000直接复利了三年(即复利6期)复利到第四年末了,不需要在第二年(即又存入8,000的时候)和8,000一起共同去复利。

总结一下,就是8,000和4,000是两笔独立的现金流,彼此没有联系。分别各自、独立的去复利到了第四年末。


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