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为了求职冲呀 · 2022年02月20日

老师为什么在many years后的今天“today”是后付年金啊？

  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.

An investor purchased an annuity many years ago. The first payment of the annuity is to be received today. 


老师看了您给其他学生的解答说是received today所以是0时刻，但是题目不是说很多年前就买了这个annuity，那么买的时候就应该是0时刻？然后今天才付钱，今天付钱的时刻不应该是1了吗？先买后付，不应该是ordinary annuity吗？

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2 个答案

星星_品职助教 · 2022年09月13日

@Gretchen

对的，这就是题目所表述的意思。

星星_品职助教 · 2022年02月21日

同学你好，

“... purchased an annuity many years ago”这句话没有用，无论年金是在什么时候买的，过去的已经过去了。年金的价值是未来的现金流折现求和。

换而言之，年金的现值求的就是“today”的值，而不是“many years ago”的值。

对于未来的现金流来说，首笔就是在今天付的，所以就是先付年金的形式。如果首笔是在一年后 / at the end of the first year时付的，就是后付年金。


Gretchen · 2022年09月12日

老师，你的意思是，这个年金是在过去买的，但是是从今天开始支付首笔款，连续支付20年，求现值？

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