Smith wishes to buy an annuity that will Provide 15 annual p

Smith wishes to buy an annuity that will Provide 15 annual payments. the 1st payment of 200 will be made one year from today. The payments increase such that each payment is 3% greater than the preceding payment It the effective annual interest rate is 7.12%, find the price of this annuity. PV = 200 v + 200 (1.03) v^2 + 200 (1.03)^2 v^3 + ... + 200 (1.03)^14 v^15 = 200 v [1 + 1.03 v + (1.03)^2 v^2 + (1.03)^3 v^3]+... (1.03)^14 v^14] = 200 v [1- (1.03)^15/1- (1.03] = 2159

Solution

in present value calculation 1.03 has to be divided not multiplied so final answer is 200 *[1 - (1/1.03)^15]/[1-1/1.03] = 2459.21