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倩仔 · 2022年11月18日

第一步PV计算没有理解,还请老师解惑

NO.PZ2015120604000013

问题如下:

An annuity of $2,000 per year will be received for twenty years. The first payment is to be received at the end of thirteenth years. Assume the discount rate is 7% over next years, calculate the today's present value of the annuity

选项:

A.

$8,792.

B.

$9,408.

C.

$10,066.

解释:

B is correct.

  1. Calculate the PV of annuity at the end of the twentieth years : N = 20; I/Y = 7; PMT = -2,000; FV = 0; CPT PV = 21,188.03. ;
  2. Calculate the PV today: N = 12; PMT = 0; FV = -21,188.03; I/Y = 7; CPT PV = 9,407.74.

请问第一步算the end of the thirteenth year的PV的时候为什么N=20而不是12?first payment at the thirteenth year是把所有的钱都给我了吗?还是先付前13年的,后面再每年两千?

3 个答案
已采纳答案

zhouanne · 2022年11月19日

这道题的意思是从第13年开始之后的20年每年有pmt

所以要先算后20年的pv啊 所以n就是20,然后再算前面12年的pv

是要分段算的

星星_品职助教 · 2022年11月19日

@zhouanne

思路是对的。改了一个字。

因为是第13年年末付的pmt 所以我们先用后付模式算出13年初的pv(也就是12年末的fv) 再根据13年的pv(12年末的fv)折到0时间点 也就是折12年。

分析现金流时,建议全部都转化为用年末数,没必要用年初数。

星星_品职助教 · 2022年11月19日

同学你好,

上面的同学解释正确。本题是递延年金,相当于把一笔20年期的年金递延到了13时点才支付第一笔现金流。

具体而言,不递延的年金从0时点开始,1时点付首笔现金流;本题的年金递延到了12时点才开始,13时点付首笔现金流。

所以要先折现回12时点,再折现回0时点,才能得到最终的现值。

zhouanne · 2022年11月19日

老师 我再确认一下,因为是第13年年末付的pmt 所以我们先用后付模式算出13年初的pv(也就是12年末的fv) 再根据13年末的pv(12年末的fv)折到0时间点 也就是折12年

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