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怿冉 · 2020年09月24日

问一道题:NO.PZ2017092702000018

问题如下:

Given the  discount rate of 4% a year compounded annually, the present value (PV)of 50,000, as of the end of Year 5 (PV5 ), of the cash flow received at the end of Year 20 is closest to:

选项:

A.

$22,819.

B.

$27,763.

C.

$28,873.

解释:

B is correct.

The PV in Year 5 of a $50,000 lump sum paid in Year 20 is $27,763.23 (where FV is future value): PV = FVN(1 + r)N PV = $50,000(1 + 0.04)15 PV = $27,763.23

这个题目每次都看不懂,确实不知道说的什么意思,老师能讲解一下吗?

1 个答案

星星_品职助教 · 2020年09月24日

同学你好,

这道题描述的比较复杂。其实如果拿掉题干描述中的插入语和修饰词,本质上题干就是在问:the PV is closet to:也就是求PV的问题。

所以其实就是求一笔发生在未来第20年,价值5w的现金流在未来第5年的现值是多少。实质上就是已知FV求PV的问题,要注意由于是求在第5年的PV,所以期限n=20-5=15。

由于PV=FV/[(1+r)^n],所以这个PV就等于50,000/1.04的15次方,即选择B选项。

 

 

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