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Nan🌞 · 2021年10月05日

先付年金的N是20还是21

  1. CFA I
  2. Quantitative

NO.PZ2015120604000011

问题如下：

An investor purchased an annuity many years ago. The first payment of the annuity is to be received today. Assume the payment of the annuity is $5,000 constanly , the period the payment is 20 years. and the discount rate is 12%, calculate the today' value of the annuity:

选项：

A.

$37,347.

B.

$403,493.

C.

$41,829.

解释：

C is correct.

Under the BGN mode.

N = 20; PMT = -5,000; I/Y =12; FV = 0; CPT PV = 41,828.89.

这道题说的是今天收到第一笔PMT，而这个年金的时间是20年，那么这道题中的今天指的是0时点还是1时点？这个表述很让人迷惑

我也可以理解为0时点就收到了第一笔5000元，然后用后付年金的功能计算的时候N就不是20，而应该是21不是吗？不然解释不通啊？

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1 个答案

星星_品职助教 · 2021年10月06日

同学你好，

“The first payment of the annuity is to be received today”说明：1）本题为先付年金；2）收到首笔PMT的时间为0时点。

先付年金的情况不能直接按照后付年金进行计算。最直接的方式是N=20，用BGN模式计算即可。

------

如果按照后付年金模式计算，N仍然是20，只是计算出来的结果需要乘以（1+r）进行调整。

可以自行计算验证一下，后付模式计算：N = 20; PMT = -5,000; I/Y =12; FV = 0; CPT PV =37,347.22，乘以1.12后得到先付年金模式下相同的值 41,828.8843

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