What is the amount of an annuity if the size of each payment

What is the amount of an annuity if the size of each payment is $250, payable at the end of each quarter for five years at an interest rate of 16% compounded quarterly?

Solution

converting this all values to present value

nos of quarterly payment = 5*4 = 20

i = 16/4 = 4%

P = A * [(1+i)^n - 1]/[i*(1+i)^n]

P = 250 * [1.04^20 -1 ] / [0.04*1.04^20]

P = 3397.58..................(1)

Now lets say annuity is A,

n=5

i = 16%

then A = p * [ i * (1+i)^n]/[(1+i)^n -1]

A = 3397.58 * [ 0.16 * 1.16^5] / [1.16^5-1]

A = 1037.65$

Amount of annuity is 1037.65$