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Jiarong · 2021年10月16日

题目含义

  1. CFA I
  2. Quantitative

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an immediate lump sum payment of £350,000是什么意思，是一个什么样的产品？

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1 个答案

星星_品职助教 · 2021年10月16日

同学你好，

“an immediate lump sum payment of £350,000”指的就是现在马上（immediate）就一次性（lump sum payment）给£350,000这么多钱。或者理解为这种付款方式的PV就是£350,000

假设本题的永续年金的现值计算出来小于了350,000，就应该选择PV更大的£350,000。原则就是选择PV更大的。

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