Compounded Interest annually

Question

New members of a golf club are admitted at the start of each year and pay an initiation fee of $2,000 immediately. Thereafter, members pay an annual membership fee of $400, which falls due at the beginning of each year.

1) How much does the club make from a new member over the first 10 years, assuming an interest rate of 5.5% compounded annually. (Note: In answering this question you must use the formula for finding sums.

Answer 1

Two steps:

 

First, the initiation fee is 2,000 in "year 0".  No time value implications.

 

Second, the future value of an annuity of $400 for 10 years at 5.5%

 

Using either excel, a hand-held calculator or an online calculator like the one at:

 

http://www.ultimatecalculators.com/future_value_annuity_calculator.html

 

The $400 for 10 years will be equal to $5,150.14

 

So, $2,000 + $5,150.14 = $7,150.14