You want to purchase an annuity that will pay you $1,200 a quarter for 15 years and earn a return of 5.5 percent, compounded quarterly. What is the most you should pay to purchase this annuity

Value of annuity is $48,811

Explanation:

A fix Payment for a specified period of time is called annuity. The discounting of these payment on a specified rate is known as present value of annuity. The value of the annuity is also determined by the present value of annuity payment.

Formula for Present value of annuity is as follow

PV of annuity = P x [ (1 - (1 + r) ^-n) / r ]

Where

P = Annual payment = $1,200

r = rate of return = 5.5% / 4 = 1.375%

n = number of period = 15 years x 4 quarters per year = 60 quarters

PV of annuity = $1,200 x [ (1 - (1 + 0.01375) ^-60) / 0.01375 ]

PV of Annuity = $48,811.2