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王予彤 · 2020年04月01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

关于ACCOUNT 1我这样算哪个地方出错了？有点没想明白

第一年 Pv=750, N=4,I/Y=3%/4 ,PMT=0 第一年FV=772.754

第二年PV=772.754+750 N=4 I/Y=3%/4 ,PMT=0 第二年FV=1568.953

第三年 PV=750

本金30000

sum=33091.7


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2 个答案

星星_品职助教 · 2020年11月19日

@sarahjia

现金流的符号只代表方向，所以无所谓750是正号还是负号。如果750是负号，算出来的FV就是正号。如果750是正号，算出来的FV就是负号。因为我们看的是绝对值，所以怎么计算都可以。

星星_品职助教 · 2020年04月01日

同学你好，

不要用你计算的那个思路，比较麻烦，也不是规范的方法。正确的思路应该是计算三笔现金流的FV，然后相加，不要一年一年的加。

Account 1第一笔现金流由1时间点进入Account 1，持续两年，按季度结息；

即 PV=-750，N=4×2=8，I/Y=3/4=0.75，PMT=0，CPT FV=796.1991

同理，Account 1第二笔现金流：PV=-750，N=4，I/Y=3/4=0.75，PMT=0，CPT FV=772.7544

Account 1第三笔现金流FV=750，三个FV相加即可。

-------

这些看一下就行，不要这么去算：

你的那种列式中，不能把第一年的FV=772.754和后两笔的FV直接相加，这三笔现金流不在同一个时点上，第一年的FV=772.54是在N=2这个时点上，而后两笔FV（1568.953和750）都在N=3这个时点上。其中1568.953已经包含了772.54的内容。所以算N=3时点的总FV就是1568.953+750=2318.95，不需要额外再包含一个772.54.

解题时并不需要这么计算，统一把3笔现金流的FV都计算到N=3时点然后相加即可。

 

sarahjia · 2020年11月19日

对于account1来说这个750不是流入吗为啥是负号呢，谢谢老师

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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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