为什么用先付年金

问题如下：

QuestionA financial contract offers to pay €1,200 per month for five years with the first payment made immediately. Assuming an annual discount rate of 6.5%, compounded monthly the present value of the contract is closest to:

选项：

A.€ 63,731.00

B.€ 61,330.00

C.€ 61,663.00

解释：

Solution

C is correct. Using a financial calculator: N = 60; the discount rate (I/Y) = (6.5%/12) = 0.54166667; PMT = €1,200; Future value = €0; Mode = Begin; Calculate present value (PV): PV = €61,662.62.

Alternatively: Treat the stream as an ordinary annuity of 59 periods and add the current value of €1,200 to the derived answer. Using a financial calculator: N = 59; the discount rate (I/Y) = (6.5%/12) = 0.54166667; PMT = €1,200; Future value = €0; Mode = End; Calculate PV: PV = €60,462.62; Total PV = €1,200 + €60,462.62 = €61,662.62.

A is incorrect. This is the PV of an annuity due of 5 periods, 6.5% interest, and payments of 14,400 (1,200 × 12): N = 5; the discount rate (I/Y) = 6.5; PMT = 14,400; FV = 0; Mode = Begin; Calculate PV = 63,731.49.

B is incorrect. This is the PV of a 60-month ordinary annuity. N = 60, the discount rate (I/Y) = 6.5/12; PMT = 1,200, FV = 0. Mode = End; Calculate PV: PV = 61,330.41.