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婉婷 · 2022年06月05日

为什么不用(1+6%/12)^1的EAR公式计算有效年利率呢，不是每月复利一次吗

  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

为什么不用(1+6%/12)^1的EAR公式计算有效年利率呢，不是每月复利一次吗，然后再用这个利率算年金的PV

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3 个答案

张小橙🍊 · 2022年08月15日

因为EAR是折算后的年化有效利率，折算后不能再复利了。但永续年金公式本质意义在于每月现金流用折算前的discount rate 往前折算现值，所以并不用把题目给定的利率再换算成有效利率

袁园_品职助教 · 2022年06月06日

嗨，爱思考的PZer你好：


是啊，年金的问题，就是年金的公式求PV哦，这个就是考点，永续年金的PV=A/r其实就是根据(1+6%/12)推导出来的。只不过这个折现后面是无穷无尽的，然后再通过（1+r)相乘的变形后相减直接推导出来的。

你说的EAR算，你是想怎么算呢，就直接换算成1年，然后再除一年吗？

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袁园_品职助教 · 2022年06月05日

嗨，从没放弃的小努力你好：


不可以，这道题给了条件，这个就是a perpetuity of £2,000，永续年金就要按照永续年金的公式来算，因为你自己虽然没有持有到永久，但是永续年金现在的定价必须要反应这个永续的含义，所以必须用永续年金的公式。

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婉婷 · 2022年06月05日

没明白，是年金问题，就不需要用到EAR的算法吗？

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