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yfdhhc · 2022年05月16日

可以用这个公式吗FV=PV·〔1+r/m〕mn

  1. CFA I
  2. Quantitative

NO.PZ2017092702000006

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.

FV=PV·〔1+r/m〕mn


100万=25万*（1+0.03%/365）365n （365n次方）


求出来n是需要的年数，再转化成月份数


老师可以这样思路计算吗？

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星星_品职助教 · 2022年05月16日

同学你好，

列公式的思路不是考试的思路。列出来公式后就会发现n很难求。

对于求N的题目，最便捷的方法就是计算器直接搞定。本题的计算器解法可以是：

①选择转化为EAR得到3.0453%，此时计算器按键为：PV=-250000， I/Y=3.045，PMT=0，FV=1000000， CPT N=46.21（年），然后乘以12得到554.5月

②选择转化成日利率得到3%/365=0.0082%，此时计算器按键为：PV=-250000， I/Y=0.0082，PMT=0，FV=1000000， CPT N=16868（天），转化成16868/365=46.21年，再转化为554.5月

以上计算对于各个环节的四舍五入可能会导致结果细微差别。

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当PMT=0时，题目要计算PV或FV时，用你列的公式要比按计算器第三排五个键省事

yfdhhc · 2022年05月16日

明白了 谢谢老师

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