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一蒙就对 · 2020年06月29日

问一道题：NO.PZ2017092702000006 [ CFA I ]

  1. CFA I
  2. Quantitative

问题如下：

For a lump sum investment of ¥250,000 invested at a stated annual rate of 3% compounded daily, the number of months needed to grow the sum to ¥1,000,000 is closest to:

选项：

A.

555.

B.

563.

C.

576.

解释：

A is correct.

The effective annual rate (EAR) is calculated as follows:

EAR = (1 + Periodic interest rate)m – 1   EAR = (1 + 0.03/365)365 – 1   EAR= (1.03045) – 1 = 0.030453 ≈ 3.0453%. Solving for N on a financial calculator results in (where FV is future value and PV is present value): (1 + 0,030453)N = FVN/PV = ¥1,000,000/¥250,000）So,N = 46.21 years, which multiplied by 12 to convert to months results in 554.5, or ≈ 555 months.

请问老师，IY不应该是0.03➗365么，为啥用EAR代表IY，我这个算出来的又是什么 感觉没有理解计算器这个IY是啥意思，我记得之前做题都是期间利率，用年化的除以滚多少次，做了这道题感觉懵了，希望得到您的耐心讲解。
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1 个答案

星星_品职助教 · 2020年06月30日

同学你好，

I/Y是期间利率的概念，这道题题干描述为“a stated annual rate of 3% compounded daily”，所以如果把一天设为一期的话，那么日利率就是3%/365。但由于I/Y的设置中，百分号是作为一个单位来处理的，不需要输入。所以输入计算器的I/Y就变成了3/365。

要注意“期间”是要对应的，所以如果I/Y期间设置为“天”，那么计算出来的N也就会是多少“天”，结果应该是16,867.2天。

但如果把“天”作为期间，这个时候就没法进行下去了，因为题干要求的是“the number of months needed ”，在没提示一个月是30还是31天的情况下，没法将天转化为“月”。

所以只能换其他的方法，即将期间设置为“年”，然后乘以12得到月数。这个时候就需要将“a stated annual rate of 3% compounded daily”转化成EAR= 3.0453%，去掉百分号后将3.0453输入成I/Y，然后此时得出来的N就是46.21年，进而可以得到最终答案。

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