Glossary
Compound Interest
Interest earned on both the original principal and on interest already earned, so growth accelerates over time.
Compound interest is interest calculated on a balance that already includes earlier interest. Instead of earning the same dollar amount each year, the balance earns a return on a growing base, so the yearly gain gets bigger every year. Over long periods this "interest on interest" does more of the work than the original deposit.
The formula
Compounding more often helps a little: the same 6% compounded monthly ends near $60,226. The rate and the number of years matter far more than the frequency.
The rule of 72
A quick mental shortcut: divide 72 by the annual rate in percent to estimate how many years it takes money to double. At 6%, that is about 12 years; at 9%, about 8. The rule is an approximation that works best between roughly 4% and 12%.
What to keep in mind
Compounding works against you as well. Credit-card debt at 24% doubles in about three years if unpaid, and fund fees compound too: a 1% yearly expense ratio takes a noticeably larger bite after 30 years than 1% of the starting balance suggests. Investment returns also compound only on average; real portfolios swing from year to year.