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书茜 · 2022年01月04日

不理解

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.

1、第六年开始上大学交学费,通过N-4,FV=2.,PMT=6000,I/Y=5,求得PV=22339.48,这个PV应该是第五年的价值吧?

2、第五年的价值22339.48元相当于FV5,通过N=5,I/Y=5,PMT=0,求得PV =17503.56,然后乘以2,求得结果为35007.13元

1 个答案

星星_品职助教 · 2022年01月04日

同学你好,

根据题干中的“six years later”,这道题的四笔学费现金流应在6,7,8,9这四个时点。

如果要将PV算到5时点,列式应为 END模式下的N=4,I/Y=5,PMT=-6,000,FV=0,结果为21,275.7,这个结果就是5时点的PV

然后再将此结果折现5期回到0时点,可直接用21,275.7除以1.05的5次方,或者列式N=5,I/Y=5,PMT=0,FV=-21,275.7,CPT PV。最后结果为16670.07,乘以2即得到答案结果。

-----

你的第一步列式为根据BGN模式算出的PV,如果这样计算,这就是在6时点的PV,第二步就需要除以1.05的6次方。同样也能得到结果。但这种算法不是协会常规算法,上面的算法是比较常用的。

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