Lloyd is a divorce attorney who practices law in Florida. He wants to join the American Divorce Lawyers Association (ADLA), a professional organization for divorce attorneys. The membership dues for the ADLA are $650 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 $7,000 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 5.9%. What is the minimum number of years that Lloyd must remain a member of the ADLA so that the lifetime membership is cheaper (on a present value basis) than paying $650 in annual membership dues? (Note: Round your answer up to the nearest year.)
a. 16 years
b. 21 years
c. 19 years
d. 14 years

We must determine the net present value of the annual payments in a similar way to calculating the present value of annuities. We can use an excel spreadsheet and the present value formula with a 5.9% interest rate and then subtract the lifetime fee ($7,000):

Present value 14 years = $6,079 - $7,000 = -$921

Present value 16 years = $6,614 - $7,000 = -$386

Present value 19 years = $7,310 - $7,000 = $310

Present value 21 years = $7,711 - $7,000 = $711

*present value 18 years = $7,091 - $7,000 = $91, but 18 years was not an option.