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嘉轩0903 · 2022年10月22日

I/Y里的利率都是EAR是吗?

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[11(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?

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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