NO.PZ2017092702000013
问题如下:
At a 5% interest rate per year compounded annually, the present value (PV) of a 10-year ordinary annuity with annual payments of $2,000 is $15,443.47. The PV of a 10-year annuity due with the same interest rate and payments is closest to:
选项:
A.
$14,708.
B.
$16,216.
C.
$17,443.
解释:
B is correct.
The present value of a 10-year annuity (A) due with payments of $2,000 at a 5% discount rate is calculated as follows: PV = $16,215.64.
PV = $16,215.64. Alternatively, the PV of a 10-year annuity due is simply the PV of the ordinary annuity multiplied by 1.05: PV = $15,443.47 × 1.05 PV = $16,215.64.
无论是求PV还是FV,Annuity due的值都相当于对应期数的Ordinary Annuity的值再往后复利一期。即可以先求出Ordinary Annuity的PV,在乘以1+r,就是对应的Annuity due的PV。
对于本题而言,Ordinary Annuity的PV直接给出,所以就用给出的15,443.47*(1+0.05)即可得到对应annuity due的PV。即答案B。
比如按照年金的思路,后付年金的现值PV,折算出来相当于是后10年保险公司每年给我2000,按照利率5%每年,所以现在我要一次性存15443.47,那么如果同样的领取方式变成先付年金,由于保险公司在年初就付第一笔2000,按照货币的时间价值来说相当于我提前一年支付,所以目前我要用后付年金当年的现价乘上当年的利率折算出来为先付年金的现价?
就是怎么能去更好的在现实例子中理解先付年金现值等于后付年金现值✖️(1+r)?