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Jane Z · 2020年07月28日

问一道题：NO.PZ2018062016000019

  1. CFA I
  2. Quantitative

问题如下：

Clark opens two bank accounts. Account 1 is compounded quarterly with stated annual rate of 3%, while Account 2 is compounded annually with annual interest rate of 2.5%. Clark put the principal of $30,000 to Account 2 and annual interest to Account 1 as long as he received. After three years, what is the difference between Clark’s current wealth planning and leaving all the money in Account 2?

选项：

A.

$13.50

B.

$12.24

C.

$16.12

解释：

B is correct.

Annual interest received from Account 2 is $30,000*2.5%=$750.

After three years, Clark’s current wealth planning:

Leave all the money in Account 2: $30,000*(1+2.5%)3=$32306.71

The difference is $32318.95-$32306.71=12.24

如果把钱全放在Account 2， 最后的受益应该是Fv=30000*(1+2.5%)^3=32307, 如果按Clerk现在的plan, 我算PV=0， PMT=750，I/Y=3%/4 N=3, FV=2266.9 32307-（2266.9+30000）=40，请问这样为什么不对？

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2 个答案

星星_品职助教 · 2020年08月19日

@yd08qg

同学你好，计算无误，我上面的解答也是这么算的。

2318.16是account 1里的投资，还需要加上一开始account里的30,000，最后结果是32318.95。这就是本金30,000放在account 2里，但把每期利息都拿出来放在account 1里投资后的总FV。

拿这个FV去和钱全放在account 2里直接投资所得到的32306.71进行对比就可以得到答案12.24

星星_品职助教 · 2020年07月29日

同学你好，

钱全放在a/c 2的计算无误。

之后a/c 1的计算器按键里，PMT，N和I/Y的期间不一致，PMT是“年”现金流，N是3“年”，但I/Y是“季度”利率。把I/Y转化成年利率即EAR就可以了。

如果按照这种思路算，I/Y=3.03，最后FV=2318.95。最终结果为32306.71-（2318.95+30000）=-12.24，选择B选项

yd08qg · 2020年08月19日

EAR=3.03，PMT=750，N=3，PV=0 算出来是 2318.86 是哪里出错了吗？没有想明白

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NO.PZ2018062016000019问题如下Clark opens two bank accounts. Account 1 is compounquarterly with stateannurate of 3%, while Account 2 is compounannually with annuinterest rate of 2.5%. Clark put the principof $30,000 to Account 2 anannuinterest to Account 1 long he receive After three years, whis the fferenbetween Clark’s current wealth planning anleaving all the money in Account 2?A.$13.50B.$12.24C.$16.12B is correct.Annuinterest receivefrom Account 2 is $30,000*2.5%=$750.After three years, Clark’s current wealth planning:Leave all the money in Account 2: $30,000*(1+2.5%)3=$32306.71The fferenis $32318.95-$32306.71=12.24我想得比较复杂，本金在账户2里面不需要按照2.5%复利吗

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