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红豆生南国 · 2019年11月03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

老师 请解释一下这个题目 谢谢

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1 个答案

星星_品职助教 · 2019年11月03日

同学你好，

这道题的意思是clark有两种投资方式，第一种是把3w放在account 2里面，本金不动，每年把利息750拿出来放到account 1里面，将利息单独以3%名义利率季度结息的方式进行再投资。第二种方法是把3w放在account 2里面，直接以利率2.5%的复利投三年。问这两种方法的收益之差是多少。

所以第一种方法3w的本金始终在account 2里面不动，每年会产生750的利息后拿出来投到account 1中，第一笔750投到account 1后又复利了两年，最后收益为 750*(1+3%/4)^(4*2)=796.2，以此类推，第二笔750相当于只在account 1里面放了1年，最后变为772.75，第三笔750由于就是在第三年产生的，所以没有复利效果还是750。最终这种投资方式获得的本息和为3w+796.2+772.75+750=32318.95。

而第二种方式就比较容易，直接就是3w*(1+2.5%)3=$32306.71。两种方式收益做差即可，加油。

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