Question

New members of a tennis club are admitted at the start of each year and pay an initiation fee of $5,000 immediately. Thereafter, members pay an annual membership fee of $600, which falls due at the beginning of each year. How much does the club make from a new member over the first 10 years, assuming an interest rate of 5.5% compounded annually? Use the formula for finding sums.

Answer 1

R = 5.5%

Since the annual membership fee is paid at the beginning of the year, then it is a case of annuity due.

Payment in present time = $5000

Annual payment at the beginning of each year = $600

Time = 10 years

So,

Present value of payments = 5000 + (600*(1-1/(1+5.5%)^10)/.055)*(1+5.5%)

Present value of payments = $9771.32

---------

If future value is concerned,

Then,

Future value of payments = 5000*(1+5.5%)^10 + (600*(1.055^10 - 1)/.055)*(1+5.5%)

Future value of payments = $16690.82