问一道题：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：

$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.

老师你好我有点搞混，已经给出的后付年金的PV是15443.47，现在不是要求0'时刻的PV ，那不是应该往前折现一年吗，谢谢

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星星_品职助教 · 2021年03月13日

@sarahjia @Yanshu

同学你好，这道题出现了一个笔误，感谢@Yanshu的提醒，重新回复如下：

-----------------------------

这道题要计算先付年金的PV，这笔先付年金除了是“先付”以外，其他条件和题干给出后付年金都相同。

后付年金的特点是PMT从N=1时点开始一直到N=10，一共10笔PMT，算PV时是计算到0时点的。只要是算PV，都是计算到0时点，因为只有0时点才是“present”即现在。

先付年金的特点是PMT从N=0开始一直到N=9，也是一共10笔PMT，算PV也是计算到0时点的。

所以可以看出，两个年金唯一的差别就是先付年金往前提前了一期（相当于一个提前了一期的后付年金），所以可以直接记忆规律，无论是求PV还是FV，先付年金的值都等于后付年金的对应值×（1+r）。

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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

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。即答案题目哪里能看出是先付年金啊？后面那个e那里就是后付年金的意思吗？所以普通年金都是先付年金？

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

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