为什么这道题换成先付年金后的N还是等于10而不是9？

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