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雷雷12322 · 2023年01月25日

解释下题目的具体含义和递延年金概念,还有两个步骤的具体含义

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.

麻烦解释下题目的含义以及递延年金的概念,还有两个计算步骤的具体含义,题目中第13年年末才发生第一笔现金流,那不应该是14年年初吗?

第一步计算的PV不应该是13这个时间点的吗?12 13 14这几个时间节点要怎么区分呢

1 个答案

星星_品职助教 · 2023年01月27日

同学你好,

本题为求 在13时间点发生第一笔现金流,连续发生20期的年金 的现值。

正常的后付年金是1时点发生第一笔现金流,折现折到0时点。本题是13时点发生第一笔现金流,相当于将1时点递延到了13时点。所以此时折现需要折现到12时点(步骤1)。然后再从12时点折现回0时点得到最终的现值(步骤2)即可。

-----

“to be received at the end of thirteenth years”指首笔现金流于13年末收到,在时间轴上即为13这个时间点,以此为首笔现金流一直持续20期。

虽然13年末也是14年初,但不需要考虑年初的情况,只需要考虑在时间轴上是哪个点。

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