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rabbit · 2021年02月18日

EAR

  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.

250000(1 + 0.03/365)365*n=1000000 直接算出N (年数） 乘以12个月，算出多少个月。老师，这样有误吗？如果无误，什么情况下用EAR 什么情况下直接计算？谢谢

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3 个答案

星星_品职助教 · 2021年04月28日

@snow666_6

1）250000(1 + 0.03/365)^30*n=1000000 这个式子中，0.03/365算的是日利率，之后应该乘方为“365×N”次方，算出来的N是年数不是月数。按照你公式的逻辑，N=30×月数n，这又涉及到另外一个问题，即每月并非30天，否则每年就是360天了，和此前计算使用的365天不一致。

2）这种求n的题目直接用计算器计算即可，不用公式。计算器直接短平快就按出来了。


snow666_6 · 2021年04月27日

250000(1 + 0.03/365)30*n=1000000 直接算出N (月数） ，为啥是B啊，问题出在哪了老师？

星星_品职助教 · 2021年02月18日

同学你好，

这个思路没问题。在你的列式中就已经含了转化EAR的过程了，过程中的(1 + 0.03/365)^365就是1+EAR。EAR=3.045%

这个步骤和用计算器输入：PV=-250000， I/Y=3.045，PMT=0，FV=1000000， CPT N=46.21（年）是一样的。

货币时间价值问题里求N次方的题目都建议用计算器第三排直接CPT N的方法来求，不建议用公式来算。

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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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