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Quadradinho · 2019年11月18日

问一道题：NO.PZ2017092702000013

  1. CFA I
  2. Quantitative

问题如下：

At a 5% interest rate per year compounded annually, the present value (PV) of a 10-year ordinary annuity with annual payments of $2,000 is $15,443.47. The PV of a 10-year annuity due with the same interest rate and payments is closest to:

选项：

A.

$14,708.

B.

$16,216.

C.

$17,443.

解释：

B is correct.

The present value of a 10-year annuity (A) due with payments of $2,000 at a 5% discount rate is calculated as follows: PV = $16,215.64.

PV=A[1−1(1+r)Nr]+2000PV=A{\lbrack\frac{1-\frac1{{(1+r)}^N}}r\rbrack}+2000

PV=2000[1−1(1+0.05)90.05]+2000PV=2000{\lbrack\frac{1-\frac1{{(1+0.05)}^9}}{0.05}\rbrack}+2000

PV = $16,215.64. Alternatively, the PV of a 10-year annuity due is simply the PV of the ordinary annuity multiplied by 1.05: PV = $15,443.47 × 1.05 PV = $16,215.64.

请问为什么FV=0呢？ 并没有给这个条件呀...

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1 个答案

星星_品职助教 · 2019年11月18日

同学你好，

回忆一下年金的定义，是一系列等额等间距的现金流，也就是说，无论是先付还是后付年金，在期初和期末都没有单独的，另外的一笔大额现金流出现。以后付年金为例，在0时刻没有任何现金流，在最后一期的N时刻也没有“另外的”现金流（有PMT，但PMT属于年金本身的一部分，不是另外的独立现金流）。所以这种情况下，求PV时则FV为0。求FV时则PV为0。本质都是在0时刻和N时刻没有除PMT外的单独现金流存在。

举一个有FV的例子，例如求债券的PV，除了1时刻开始每一期固定的PMT外，最后一期除了有PMT，还会有一个par value的返还，这个Par 的返还就是一笔另外的单独现金流，所以算债券现值的时候FV不为0，而是要输入FV=par。

对比来看，纯年金在期末并不存在类似par value一样的这种现金流，所以FV=0。加油

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