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嘉轩0903 · 2022年10月22日

I/Y里的利率都是EAR是吗？

  1. CFA I
  2. Quantitative

NO.PZ2017092702000014

问题如下：

Grandparents are funding a newborn’s future university tuition costs, estimated at $50,000/year for four years, with the first payment due as a lump sum in 18 years. Assuming a 6% effective annual rate, the required deposit today is closest to:

选项：

A.

$60,699.

B.

$64,341.

C.

$68,201.

解释：

B is correct.

First, find the present value (PV) of an ordinary annuity in Year 17 that represents the tuition costs: 50,000[1−1(1+0.06)40.06]50,000{\lbrack\frac{1-\frac1{{(1+0.06)}^4}}{0.06}\rbrack} = $50,000 × 3.4651 = $173,255.28. Then, find the PV of the annuity in today’s dollars (where FV is future value):

PV0=FV(1+0.06)17=173,255.28(1+0.06)17PV_0=\frac{FV}{{(1+0.06)}^{17}}=\frac{173,255.28}{{(1+0.06)}^{17}}

PV0 = $64,340.85 ≈ $64,341.

I/Y里的利率都是EAR是吗？如果什么都没描述，就给了个6%，按半年复利，一共18年，是不是要先算EAR=（1+6%/2）^18*2-1得出EAR，再代入公式？算出来利率很大，如果不是，那题目中给的EAR为什么可以直接代入？如果是半年的话，是不是要EAR/2？

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1 个答案

星星_品职助教 · 2022年10月22日

同学你好，

1）I/Y中的利率为实际的利率。如果计算是以年为单位的，则要输入的是实际年利率，即EAR。如果是以其他期间计算，则要输入相对应的期间利率，例如月利率，日利率等。

2）提问中的公式为stated annual rate转化EAR的公式，此时stated annual rate后会跟着计息频率，需要根据计息频率将stated annual rate转化为实际的期间利率，如果需要转化为实际年利率，则需套用EAR的公式。此点可以在做题碰到后，结合具体的题目来问。

3）本题直接给出了EAR，所以直接代入I/Y即可，不需要后续转化。

4）需要除以计息频率的是stated annual rate，EAR不能再除以2.

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NO.PZ2017092702000014 问题如下 Granarents are funng a newborn’s future university tuition costs, estimate$50,000/yefor four years, with the first payment e a lump sum in 18 years. Assuming a 6% effective annurate, the requireposit toy is closest to: A.$60,699. B.$64,341. C.$68,201. B is correct. First, finthe present value (PV) of ornary annuity in Ye17 threpresents the tuition costs: 50,000[1−1(1+0.06)40.06]50,000{\lbrack\frac{1-\frac1{{(1+0.06)}^4}}{0.06}\rbrack}50,000[0.061−(1+0.06)41​​] = $50,000 × 3.4651 = $173,255.28. Then, finthe PV of the annuity in toy’s llars (where FV is future value):PV0=FV(1+0.06)17=173,255.28(1+0.06)17PV_0=\frac{FV}{{(1+0.06)}^{17}}=\frac{173,255.28}{{(1+0.06)}^{17}}PV0​=(1+0.06)17FV​=(1+0.06)17173,255.28​PV0 = $64,340.85 ≈ $64,341. 173255.28我能算出来 但为什么下一步时间是17 不是18

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