Find the present value of an ordinary annuity with deposits

Find the present value of an ordinary annuity with deposits of $20,369 quarterly for 5.2 % compound quantity. What is the present value?

Solution

The formula for the present value of an annuity is P = p [ 1- { 1/(1 +r)ⁿ } ]/ r , where , P is the present value of the annuity, p is the peridic payment, n is the number of periods, and r is the rate of interest per period in decimals. Here, p = $ 20369, r = (5.2/100)*1/4 = 5.2/400 = 0.013 , and n = 5*4 = 20. Then P = 20369 [ 1 - ( 1/1.013)²⁰ ] /0.013 = 20369(1 – 0.772344561)/0.013 = 20369*0.226755439/0.013 = $ 356701.05