问一道题：NO.PZ2017092702000013 [ CFA I ]

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：

$14,708.

$16,216.

$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.

$PV=A{\lbrack\frac{1-\frac1{{(1+r)}^N}}r\rbrack}+2000$

$PV=2000{\lbrack\frac{1-\frac1{{(1+0.05)}^9}}{0.05}\rbrack}+2000$

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.

你好，老师。能否画一下同样的从0时刻开始，先付年金和后付年金的pv在时间轴的哪个位置？谢谢

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星星_品职助教 · 2020年10月08日

同学你好，

无论是先付还是后付年金，PV都一定在时间轴的0时点。

有区别的是现金流（PMT），先付年金的第一笔PMT在0时点，而后付年金的第一笔PMT在1时点。

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NO.PZ2017092702000013 问题如下 a 5% interest rate per yecompounannually, the present value (PV) of a 10-yeornary annuity with annupayments of $2,000 is $15,443.47. The PV of a 10-yeannuity e with the same interest rate anpayments is closest to: A.$14,708. B.$16,216. C.$17,443. B is correct. The present value of a 10-yeannuity (e with payments of $2,000 a 5% scount rate is calculatefollows: PV = $16,215.64.PV=A[1−1(1+r)Nr]+2000PV=A{\lbrack\frac{1-\frac1{{(1+r)}^N}}r\rbrack}+2000PV=A[r1−(1+r)N1]+2000PV=2000[1−1(1+0.05)90.05]+2000PV=2000{\lbrack\frac{1-\frac1{{(1+0.05)}^9}}{0.05}\rbrack}+2000PV=2000[0.051−(1+0.05)91]+2000PV = $16,215.64. Alternatively, the PV of a 10-yeannuity e is simply the PV of the ornary annuity multiplie1.05: PV = $15,443.47 × 1.05 PV = $16,215.64.无论是求PV还是FV，Annuity e的值都相当于对应期数的Ornary Annuity的值再往后复利一期。即可以先求出Ornary Annuity的PV，在乘以1+r，就是对应的Annuity e的PV。对于本题而言，Ornary 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 e的PV。即答案这道题不应该先用N=10,I/Y=5,PMT=2000,PV = 15443.47 求出FV再转换成先付年金用求出来的FV算PV不是这样吗

2023-09-20 15:28 1 · 回答

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2023-09-12 08:04 1 · 回答

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2023-09-09 16:39 1 · 回答

2023-07-19 11:03 1 · 回答

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2023-06-06 11:40 1 · 回答

问一道题：NO.PZ2017092702000013 [ CFA I ]

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