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yingbao · 2023年06月24日

没看明白前六年的PV是怎么算的

  1. CFA I
  2. Quantitative

NO.PZ2018062016000014

问题如下：

Tom has twin daughters Lucy and Lily at 12 years old. Six years later, both will study in a famous university in California for four years with a tuition fee of $6,000 paid at the beginning of each year per person. Assume the annual discount rate is 5%, today Tom should prepare:

选项：

A.

$16,670

B.

$33,340

C.

$31,753

解释：

B is correct. Six years later, Tom will pay tuition fee of $12,000 each year and last for 4 years, as he has two daughters. The payment is paid in the front, therefore set the calculator at BGN mode and input: N=4, I/Y=5%, PMT=12,000, FV=0, then PV=44678.98. The value of tuition fund at year 6 is $44,678.98, so the present value is $44,678.98/(1+5%)6=$33,340.

为什么前六年不用利率除以6加一‘而是直接加上百分之五

什么情况下用EAR、 什么时候括号外是每年次数乘以年数 、什么时候不用除以次数直接相加利滚利

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1 个答案

星星_品职助教 · 2023年06月24日

同学你好，

1）折现的公式为 PV= FV /（1+r）^n . 本题中折现率为r=5%。直接代入即可，没有其他的算法和公式。

2）r的选择要和n的期限一致，如果N的期限是以年为单位，则r需要选择EAR。如果N是其他的期限，则也需要选择对应的期限。

3）（1+r）的次方数对应的是期限，如果r为年，则括号外就是多少年；如果r为月，则括号外就是多少个月。

4）不确定“不用除以次数直接相加利滚利”是什么，可以在对应的题目下相应提问。

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