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为了求职冲呀 · 2022年02月21日

请问这个公式是怎么求n的？

  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.

(1 + 0,030453）N = FVN/PV = (¥1,000,000/¥250,000）So,N = 46.21 


能麻烦老师列一下详细的解题步骤吗，是如何解出n=46.21的呢？这个是需要用到log和Ln吗？请问log和Ln是那个章节的知识点呀？

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1 个答案

星星_品职助教 · 2022年02月22日

同学你好，

货币时间价值问题中的N统一用计算器来求，数量科目里没有专门讲过Ln的运算法则。

计算器方法如下：

本题中“a stated annual rate of 3% compounded daily”，说明3%不能直接用，需要进行转化。

①可以选择转化为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也可以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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