Question

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 $750 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 $8,000 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 7.9%. 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 $750 in annual membership dues? ( Not e : Round your answer up to the nearest year.)

0   20 years

0    14 years

0   15 years

0   17 years

Answer 1

Both the options are equal when the PV of 750 is equal to $8000.

Equating the two, we have

8000 = 750*PVIFA(7.9,n) where n is the number of years for which

PV of 750 equals 8000.

Solving for n, we have

8000/750 = PVIFA(7.9,n) = 10.6667

Using an online PVIFA calculator

PVIFA for 7.9% and n = 20 = 10.6731

for 19 it is 10.4373

Hence, n is near to 20 years.

Answer: 20 years