What compound interest is
With compound interest you earn interest on your interest. Each time interest is added, the next period's interest is figured on a slightly larger balance. Over long periods this snowballs, which is why time matters so much in saving.
The formula is A = P(1 + r/n)nt, where P is the starting amount, r the annual rate, n how many times a year interest compounds, and t the number of years.
APY: the fair way to compare rates
Two accounts can both advertise 5% but pay different amounts if one compounds daily and the other yearly. The annual percentage yield (APY) converts any rate into what you'd actually earn in a year. US banks must show APY on savings accounts and CDs, so compare APYs, not rates.
This calculator also converts a rate to its equivalent at another frequency, which is handy for comparing a bond's semiannual yield with a monthly-compounding account.
Example
$10,000 at 5% compounded monthly grows to $16,470.09 after 10 years, an APY of 5.1162%. Compounded yearly, it would be $16,288.95; simple interest with no compounding would give $15,000.
Frequently asked questions
Does daily compounding make a big difference?
Less than you might think. Going from monthly to daily compounding at 5% raises the APY from about 5.116% to 5.127%. Going from yearly to monthly matters more.
What is the rule of 72?
Divide 72 by the annual rate to estimate how many years it takes money to double. At 6%, that's about 12 years.