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Mandy · 2020年04月21日

问一道题：NO.PZ2017092702000006

  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.

1）算出了EAR=3.0453%， 然后列出公式 （1+3.0453%）^N= 4 后怎么算N呢

2）另外尝试用计算器上面的5个按键，N算出来不对，input数值哪里错了呢？ I/Y=3.0453%, PV=-250000, FV=1000000, PMT=0 然后按CPT N=

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3 个答案

星星_品职助教 · 2020年08月08日

@vko

你也可以把PV写成正的，对应FV为负就可以

星星_品职助教 · 2020年07月07日

@GS

同学你好，你这个思路的按键应为：I/Y=3/365, PV=-250000, FV=1000000, PMT=0， CPT N=16,867.27（天）

最终要求的月份数=16,867.27/365×12=554.54（月），故选择A选项

 

vko · 2020年08月08日

为什么PV要写负的

星星_品职助教 · 2020年04月21日

同学你好，

这道题用（1+3.0453%）^N= 4解公式算N很麻烦，不要求掌握。用计算器是正确的方法。

 I/Y=3.0453, PV=-250000, FV=1000000, PMT=0， CPT N=46.21这个过程是正确的。要注意I/Y，N和PMT都是“期间”的概念，即期间利率，多少期，期间PMT，由于I/Y已经折算成有效“年”利率了，所以对应算出来的N也是多少“年”，这道题要求求多少个月，再乘以12即可。

GS · 2020年07月07日

为什么用以下方式算，结果不对呢？ I/Y = 3/365, PV=-250000, FV= 1000000 then CPT PMT / 365 * 12

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