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chuziyang · 2022年01月09日

關於PV與FV

  1. CFA I
  2. Quantitative

NO.PZ2018062016000013

问题如下：

You plan to set a saving account for 7 years which annual discount rate is 4% and compounded annually. Each year $500 cash is transferred into this account. What is the difference of account present value between transferring the cash at the beginning and at the end of each year?

选项：

A.

$500.00

B.

$120.04

C.

$115.42

解释：

B is correct. If the cash is transferred at the beginning, set the calculator in the BGN mode and input data: N=7, I/Y=4, PMT=500, FV=0, then PV=-3121.07. If the cash is transferred at the end, set the calculator in the END mode and input data: N=7, I/Y=4, PMT=500, FV=0, then PV=-3001.03. Therefore, the difference between the two methods is 3121.07-3001.03=$120.04.

老師您好，想請教兩個問題，1.是否只要題目無給出FV數值，FV 就按照“0”處理？就算給了PMT,每年存錢，最終FV也都是“0”？


2.題目要求計算 每年 ordinary annuity 與annuity due的差距，即是7年中，每年的差距其實都一樣？每年供$500不管供款幾年，兩者都差$120.04？謝謝。

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1 个答案

星星_品职助教 · 2022年01月09日

同学你好，

1）PMT和FV是不同的概念，是否给出PMT的值和FV的值不发生关系；

2）FV为期末时点单独的一笔独立金额，例如债券在期末需要偿还本金，此时FV就不为0。

3）题干没涉及到FV时，即FV为0

---------

其他条件相同的ordinary annuity和annuity due有固定差距。具体公式为：

1）annuity due的PV=ordinary annuity的PV×（1+r）

2）annuity due的FV=ordinary annuity的FV×（1+r）

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