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书珧 · 2022年08月29日

这道题是什么意思？ 麻烦翻译一下

  1. CFA I
  2. Quantitative

NO.PZ2018062016000019

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

是说：问题1. 1的 每一个季度的利率是3%,那么年利率就是3*4么？

问题2. 2的每年的利率是2.5% 对么

问题3。这个人一次性把30，000都给了2，并且把每年的利息都给了1 对么，最后是问1的账户里还剩多少钱么？


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1 个答案

星星_品职助教 · 2022年08月29日

同学你好，

1）stated annual rate是名义上的年利率，这个利率是由实际的期间利率乘以期数得到的。即期间利率×4=3%，实际季度利率=4%/3；

2）对的， compounded annually相当于每年计息一次，所以此时就是以年为计息周期，每年的年利率就是2.5%/ 1=2.5%；

3）这个人把30,000一次性给2，每当2产生利息后，就把利息拿出来给1，在1里进行复利计息。

由于2是按年计息，所以相当于一年给Account 1一次利息，即30,000×2.5%=750.

最后问的是：财富管理有两种方式：第一种是上面说的这种，另一个选择是不在两个账户之间倒腾，直接就把30,000就放在Account 2里复利。问这两种方式最终的终值差多少。

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