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Alicess · 2020年06月22日

问一道题：NO.PZ2018062016000019 [ CFA I ]

  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

account2怎知不是复利呢？每年利息都是750？
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1 个答案

星星_品职助教 · 2020年06月22日

同学你好，

Account 2是以复利计息的。

题干中说明“while Account 2 is COMPOUNDED annually with annual interest rate of 2.5%”，所以account 2是以复利而不是单利计息的。由于复利的计息频率恰好是一年，所以也没有必要去做EAR的转化。

复利的概念是“利滚利”，也就是说产生的利息也会在下一期作为本金的一部分继续计息，所以本金会越变越大达到滚雪球的效果。但在本题中，account 2每年产生的750一出来就被拿走投放到account 1里了，所以这个设置就使得Account 2中的利滚利不再存在了，虽然account 2还是以复利计息的，但是本金一直就是期初的30,000，因为新增的利息全部都被直接拿走了。

 

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