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曲轩宏 · 2022年01月16日

何时是考察EAR呢

  1. CFA I
  2. Quantitative

NO.PZ2018062016000005

问题如下：

John receive a gift from his grandpa about $1.2 million. He plans to buy a house in five years later, which price is expected to be $250,000 at that time. How much should John deposit now if the stated annual rate is 3% and compounded monthly?

选项：

A.

$215,652

B.

$215,217

C.

$242,620

解释：

B is correct. Present value * (1+3%/12)12*5=$250,000, therefore, John should deposit $215,217 currently.

老师，这道题给了stated annual rate， 这里不需要想到EAR的问题么，虽然计息频率是12个月？

如果通过计息频率判断得知无法用EAR，那么什么情况下需要考虑EAR的换算呢

请老师点拨，谢谢老师啦

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星星_品职助教 · 2022年01月16日

同学你好，

1）只要给出了stated annual rate+计息频率，就必须要进行利率转化，不能直接用stated annual rate；

2）这道题转化为EAR（此时N=5）或者直接转化为月利率（此时N=60）都可以得到相同的PV，但转化为EAR多一步计算过程，会浪费时间；

3）进一步总结：计算PV或FV时，可以直接使用期间利率，此时N需要调整为相应的期数。

4）计算PMT时，I/Y要和题目问题保持一致。即如果有题目要求年度的PMT，I/Y就需要是EAR，N也必须要是年份数；但如果求的是月度PMT，此时I/Y必须是月利率，此时N也必须要调为月份数。

5）如果要计算N，原则同4）。

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NO.PZ2018062016000005问题如下John receive a gift from his grana about $1.2 million. He plans to buy a house in five years later, whipriis expecteto $250,000 thtime. How mushoulJohn posit now if the stateannurate is 3% ancompounmonthly?A.$215,652B.$215,217C.$242,620B is correct. Present value * (1+3%/12)12*5=$250,000, therefore, John shoulposit $215,217 currently.老师您好，为什么可以判断n是5而不是4啊？five years later 是说第五年年初还是年底呢

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