Question

Bob 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 $550 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 $5,000 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 7.5%. What is the minimum number of years that Bob must remain a member of the ADLA so that the lifetime membership is cheaper (on a present value basis) than paying $550 in annual membership dues? (Note: Round your answer up to the nearest year.)

12 years

14 years

18 years

21 years

Answer 1

At around 13.90 years present value of $550 payments is equal to 5000

	Present value of annuity due=	P* [ [1- (1+r)-(n-1) ]/r ] + P
P=	Periodic payment	550.00
r=	Rate of interest per period:
	Annual rate of interest	7.50000%
	Frequency of payment	once in every 12 months
	Payments per year	12/ 12=	1
	Interest rate per period	0.075/1=	7.500%
n=	number of payments:
	Number of years	13.9
	Payments per year	1
	number of payments	13.9
	Present value of annuity=	550* [ [1- (1+0.075)^-(13.9-1)]/0.075 ] +550
	Present value of annuity=	4,998.42

Answer is 14 years.