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广超 · 2023年07月19日

老师，这道题为什么不可以直接用计算器啊？N=10 I/Y=5，PMT=2000，用先付年金和后付都按一遍？

  1. CFA I
  2. Quantitative

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

PV=2000[1−1(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。

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1 个答案

星星_品职助教 · 2023年07月20日

同学你好，

这道题用计算器没有意义。后付年金的PV=15,443.47已经给出，不需要再按。有了后付年金PV后，利用关系式：

先付年金PV=后付年金PV×（1+r），

即可直接求得先付年金PV，完全没有必要非要通过计算器去调成BGN后再按出先付年金PV。

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2023-09-20 15:28 1 · 回答

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