Question

The time value of money concept can be applied in various situations and is a fundamental concept underlying other financial concepts.

Consider the following example of the application of this concept.

Eileen is a divorce attorney who practices law in Detroit. She wants to join the American Divorce Lawyers Association (ADLA), a professional organization for divorce attorneys. The membership dues for the ADLA are $500 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 $4,500 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 8.5%. What is the minimum number of years that Eileen must remain a member of the ADLA so that the lifetime membership is cheaper (on a present value basis) than paying $500 in annual membership dues? (Note: Round your answer up to the nearest year.)

13 years

15 years

19 years

20 years

Answer 1

Number of years will be such that lifetime membership becomes cheaper than annual membership

Let number of years be x

4500 = 500 + 500*PVAF(8.5%, x-1 years)

PVAF(8.5%, x -1 years) = 8

Hence, x-1 = 14 years as PVAF(8.5%, 14 years) = 8.0101

Hence, x = 15 years

Hence, the answer is 15 years