Question

Antonio is a divorce attorney who practices law in New York City. He wants to join the American Divorce Lawyers Association (ADLA), a professional organization for divorce attorneys. The membership dues for the ADLA are $800 per year and must be paid at the beginning of each year. For instance, membership dues for the first year are paid today, and dues for the second year are payable one year from today. However, the ADLA also has an option for members to buy a lifetime membership today for $8,500 and never have to pay annual membership dues. Obviously, the lifetime membership isn't a good deal if you only remain a member for a couple of years, but if you remain a member for 40 years, it's a great deal. Suppose that the appropriate annual interest rate is 7.6%. What is the minimum number of years that Antonio must remain a member of the ADLA so that the lifetime membership is cheaper (on a present value basis) than paying $800 in annual membership duas? (Note: Round your answer up to the nearest year.) O 13 years O 14 years 16 years O 19 years

Answer 1

Let number of years be x

8500 = 800 + 800*PVAF(7.6%, x-1 years)

PVAF(7.6%, x -1 years) = 9.625

Hence, x-1 = 18 years as PVAF(7.6%, 18 years) = 9.637

Hence, x = 19 years

The answer is trend between present and future value

Rest all factors are relevant as Future value = Present value*(1+Interest rate)^Number of periods