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苏·Xu · 2021年01月17日

问一道题：NO.PZ2015120604000013 [ CFA I ]

  1. CFA I
  2. Quantitative

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.

这道题题目的表达很容易有歧义吧？字面意思不是一共20年，从第13年开始吗？所以此后的应该是7年？
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1 个答案

星星_品职助教 · 2021年01月17日

同学你好，

这道题的表达是：

1. An annuity of $2,000 per year WILL be received for twenty years。有一笔持续20年的年金“即将”被收到

2. The first payment is to be received at the end of thirteenth years。这笔即将发生的年金的首笔现金流发生在第13年末（即N=13时间点）

所以是从N=13这个时间点开始有连续20笔的现金流。注意折现的话是需要首先折到N=12时间点的，并不是直接折到N=13时间点。然后再从N=12时间点折现回0时间点即可。

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