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欲溺之鱼 · 2018年04月13日

问一道题:NO.PZ2017092702000013 [ CFA I ]

问题如下图:

选项:

A.

B.

C.

解释:

没看懂,这是计算年金的题目吗?
1 个答案

源_品职助教 · 2018年04月13日

本题考察的是,其他条件相同的情况下,后付年金现值如何转化为先付年金现值,

只要将其后付年金现值乘以每期的利率即可。

即解答最后一步,15443.47×1.05=16215.64

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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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