Question

Find the amount and the present value of an annuity of P540 payable every end ofthe month at 7% compounded monthly for 4 years and 5 months.

Answer 1

We have to find the present value of a annuity of $540 payable every end of the month at 7% compounded monthly for 4 years and 5 months.

We can express the present value PV as:

`PV=M\cdot([1-(1+r\/m)^(-n\cdot m)])/(r\/m)`

where M: monthly payment (M = 540), r: annual nominal rate (r = 0.07), m: number of subperiods of compounding per year (m = 12) and n: number of years (n = 4+5/12).

We can replace the variables with its value and calculate PV as:

`\begin{gathered} PV=540\cdot([1-(1+(0.07)/(12))^(-53)])/((0.07)/(12)) \\ PV\approx540\cdot([1-(1.005833)^(-53)])/(0.005833) \\ PV\approx540\cdot(1-0.7347)/(0.005833) \\ PV\approx540\cdot(0.2653)/(0.005833) \\ PV\approx540\cdot45.4826 \\ PV\approx24560.60 \end{gathered}`

Answer: The present value of teh annuity is P 24560.60.