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zhouanne · 2022年11月22日

这道题为什么必须要求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.

我直接就是计算器计算的 I/Y是3÷365 pmt=0 然后分别代入pv和fv

最后求出是16867

再除以三十天 是562.24

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星星_品职助教 · 2022年11月22日

同学你好，

1）本题不一定非要使用EAR；

2）算出16867天后，不能除以30。除以30相当于将每年天数设置为了30×12=360天，和前面的3/365矛盾。

3）算出16867天后，需要除以365得到年数，然后乘以12得到月数。这和直接用EAR计算出年数后再得到月数是一致的。

zhouanne · 2022年11月22日

现在回头做数量的题又有一些懵 不知道啥时候需要算ear 啥时候可以直接用计算器那一行直接算呀 是不是只要题目中没说求ear的 基本都可以用计算器直接算啊

卓娅 · 2023年05月15日

我用I/Y是3/12，代入算出来直接是555.21，这样算对么？

星星_品职助教 · 2023年05月16日

@卓娅

同学你好，不能这样计算。除以12相当于以月度计息。和题干中的“compounded daily”是冲突的。

星星_品职助教 · 2022年11月22日

@zhouanne

是的，除非是求EAR的特定题目，否则大部分的题目都可以用期间利率直接计算，不用专门去转化一步EAR。

只有一类题目除外，就是题干给出的条件都是以年度为单位的，例如给出的是年度的PMT。这种情况下，I/Y就也必须得是一致的年利率，不能用普通的期间利率了。


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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.

2023-06-02 16:31 1 · 回答

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. 不能用上面这个去试，是因为不能默认每个月30天么？谢谢

2023-05-28 15:18 1 · 回答

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. 为什么用 FVN/PV

2023-03-14 11:28 1 · 回答

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. (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.请问这一步是什么意思，是怎么求得的46.21呢。我算到日利率为0.030453就不知道怎么往下算了

2022-11-11 06:02 3 · 回答