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Sissiwonglx · 2022年08月18日

如题

NO.PZ2017092702000013

问题如下:

At a 5% interest rate per year compounded annually, the present value (PV) of a 10-year ordinary annuity with annual payments of $2,000 is $15,443.47. The PV of a 10-year annuity due with the same interest rate and payments is closest to:

选项:

A.

$14,708.

B.

$16,216.

C.

$17,443.

解释:

B is correct.

The present value of a 10-year annuity (A) due with payments of $2,000 at a 5% discount rate is calculated as follows: PV = $16,215.64.

PV=A[11(1+r)Nr]+2000PV=A{\lbrack\frac{1-\frac1{{(1+r)}^N}}r\rbrack}+2000

PV=2000[11(1+0.05)90.05]+2000PV=2000{\lbrack\frac{1-\frac1{{(1+0.05)}^9}}{0.05}\rbrack}+2000

PV = $16,215.64. Alternatively, the PV of a 10-year annuity due is simply the PV of the ordinary annuity multiplied by 1.05: PV = $15,443.47 × 1.05 PV = $16,215.64.

无论是求PV还是FV,Annuity due的值都相当于对应期数的Ordinary Annuity的值再往后复利一期。即可以先求出Ordinary Annuity的PV,在乘以1+r,就是对应的Annuity due的PV。

对于本题而言,Ordinary Annuity的PV直接给出,所以就用给出的15,443.47*(1+0.05)即可得到对应annuity due的PV。即答案B。

这道题如何使用计算器啊

1 个答案

星星_品职助教 · 2022年08月18日

同学你好,

本题不需要用计算器计算。

可参见中文答案解析,只需要在已知的后付年金PV的基础上乘以(1+r),就可以得到先付年金的PV。

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