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Allez😃Sea · 2020年04月13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 = 4 So,N = 46.21 years”


求助老师，翻遍了讲义和google，计算机怎么求开根号的N次方等于几？如果像这类题目都没有提示的话，真的只能靠蒙了。。。


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星星_品职助教 · 2020年04月14日

同学你好，

我理解你说的是如果a^X=Y, 不知道如何去求X。这种问题有两种思路，首先是（不推荐）传统的对数函数的思路X=log a Y，然后通过换底公式得到log a Y=LnY/Lna。计算器是可以求LnY和Lna的，但这种方法不推荐，极度麻烦，对数函数也不是CFA的考点和要求。

推荐的是如果涉及到了对数函数，就要看看有没有其他的渠道来求。例如这道题，公式虽然是这么列的，但是并没有必要去解这个公式，而是可以通过计算器的一排5个键直接CPT N就可以了。

 

zhuzhu123 · 2020年05月06日

还是不太理解，可以写出计算器怎么按键还有推理过程么，关于n 的计算

星星_品职助教 · 2020年05月06日

这道题目正常按计算器即可。首先根据公式算出EAR=3.0453%，进而按计算器PV=-250,000,PV=1,000,000，PMT=0，I/Y=3.0453. CPT N，得出46.21年后乘以12即可得到月份数

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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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