The formula for interest compounded annually is FV = P(1+r)n, where P is the principal, or the amount deposited, r is the annual interest rate, and n is the number of years the money is in the bank. FV is the amount of money the depositor would have after n years, or the future value of that investment.
If a person deposits $1,000 at 5 percent annual interest, after 10 years he would have
FV = 1,000 x (1+0.05)10 or $1,647.01.
Compare this to a simple interest calculation. With simple interest, the depositor gets the same amount of interest each year, calculated on the initial deposit. Using the same numbers as the example above, the depositor would receive $50 in interest each year (the $1,000 initial deposit times 5 percent interest). At the end of 10 years, he would have $500 in interest for a total of $1,500. Compound interest gives him an additional $147.01 over 10 years.
The difference can also be explained in another manner. After the first year, both the simple interest depositor and the compound interest depositor have $1,050. In the second year, the simple interest depositor has once again earned 5 percent on his original $1,000, or $50. The compound interest depositor has earned $52.50, since he is earning 5 percent on his new balance of $1,050.