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英诺森吃覅消 · 2020年08月22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 + 0,030453)N = FVN/PV = ¥1,000,000/¥250,000）这个在计算器上怎么求出N？

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3 个答案

星星_品职助教 · 2021年02月10日

@010****0328

同学你好，

1）用计算器第三排五个键的时候，符号只代表方向。PV，FV，PMT三者不能同号，不然计算器会显示“ERROR”

这道题PMT=0，可以不用考虑符号。

如果从投资者的角度出发，起初投入了250,000，这是一个现金的流出，所以PV设置为-250,000。而期末这笔投资会带来1,000,000的收入，这是一个现金的流入，所以FV设置为+1,000,000.

但如果将PV设置为+250,000，FV设置为-1,000,000也不会影响计算的结果，这时候就是收钱方的角度出发考虑了，期初收到了250,000，期末要给出1,000,000。

符号只代表现金流的方向，不代表大小。符号方向可以根据“从谁的角度出发”来自己设置，

2）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。

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）

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）

此后将（无论哪种方法计算）得出的结果转化成月份数即可。

010****0328 · 2021年02月09日

请问这里的pv为什么是负值、I/Y为什么是3/365呢

星星_品职助教 · 2020年08月22日

同学你好，

这种情况计算器求解很麻烦。也不建议这么做，直接按计算器就可以很容易的得到答案。

PV=-250000， I/Y=3/365，PMT=0，FV=1000000， CPT N，得到N=16868天后再换算成16878/365=46.21年，即555个月

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NO.PZ2017092702000006 问题如下 For a lump sum investment of ¥250,000 investea stateannurate of 3% compounily, the number of months neeto grow the sum to ¥1,000,000 is closest to: A.555. B.563. C.576. A is correct. The effective annurate (EAR) is calculatefollows: E= (1 + Perioc interest rate)m – 1   E= (1 + 0.03/365)365 – 1   EAR= (1.03045) – 1 = 0.030453 ≈ 3.0453%. Solving for N on a financicalculator results in (where FV is future value anPV is present value): (1 + 0,030453）N = FVN/PV = (¥1,000,000/¥250,000）So,N = 46.21 years, whimultiplie12 to convert to months results in 554.5, or ≈ 555 months. 这题我EAR已经算出来是3.045，带入计算器知四求一不知道为什么算出来是46.21.

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