问题如下图：
老师，能麻烦讲解下题目和计算逻辑吗？没看懂
选项：
A. 
B. 
C. 
解释：
星星_品职助教 · 2019年09月10日
同学你好，
这道题考察的是Ordinary Annuity和Annuity due之间的联系。
有两个思路，建议优先使用这一种：就是无论是求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。关于这种思路，上课视频里是有详述的，可以再回去看一看。
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。这也就是答案解析中最后的那一句“Alternatively，….”所说的内容。
第二种描述Ordinary Annuity和Annuity due之间的联系的思路是：一个10期的Annuity due的现值可以在0时点分解为两项之和：1.0时点的PMT=2000；2. 不考虑0时点的PMT后，剩余9期PMT按照Ordinary Annuity的方式计算在0时点的PV。这就是答案解析中看似很复杂的公式的方法。第二种思路比较绕，没有第一种思路那么简单直接，所以建议优先掌握第一种。
其实这道题直接计算也可以，将计算器调成BGN模式，然后直接输入N=10，I/Y=5，PMT=2000，FV=0，CPT PV，也可以算出答案。但这个并不是题目想考察的方向。
两种年金之间关系的这个知识点也很重要，不过这是个独立知识点，数量这个科目之外应用的不多。
这个问题和上一个EAR的问题都属于基础知识。建议一定要确保完全掌握了一个知识点后，再推进到下一个知识点，不然容易乱，还得重头回来学。
加油
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
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？
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。即答案没有理解这题，能不能具体讲一遍
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 CFA一级
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。即答案老师，请问为什么是先付年金的PV x （1+r）呢？没太理解这个公式。谢谢