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哩ooo · 2022年04月18日

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NO.PZ2017092702000012

问题如下:

A sweepstakes winner may select either a perpetuity of £2,000 a month beginning with the first payment in one month or an immediate lump sum payment of £350,000. If the annual discount rate is 6% compounded monthly, the present value of the perpetuity is:

选项:

A.

less than the lump sum.

B.

equal to the lump sum.

C.

greater than the lump sum.

解释:

C is correct.

As shown below, the present value (PV) of a £2,000 per month perpetuity is worth approximately £400,000 at a 6% annual rate compounded monthly. Thus, the present value of the annuity (A) is worth more than the lump sum offer. A = £2,000 r = (6%/12) = 0.005 PV = (A/r) PV = (£2,000/0.005) PV = £400,000

the present value of the“perpetuity”--永续年金,带入永续年金的公式 PV=A/r即可:

A=2,000, r=(6%/12)=0.005, PV=A/r=400,000

请问什么时候需要从T1折现到T0,什么时候不需要?

1 个答案

星星_品职助教 · 2022年04月18日

同学你好,

不确定你提问中的“T1和T0”是什么意思。

对于普通的后付年金而言,PMT现金流都是在第一期的期末开始。例如PMT从1时点开始,但折现是折到0时点的。如果是两次折现问题,例如首笔付款从5时间点开始,则先折现到4时点算出PV1,再把PV1折现回0时点得到最终的PV。



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