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What is compound interest?

Compound interest is interest earned on both your original money and on the interest it has already earned. Each period, the interest is added to your balance, and the next period's interest is calculated on that larger balance. Over time this snowball effect accelerates, which is why Albert Einstein is often (probably apocryphally) said to have called it the eighth wonder of the world. The longer your money compounds, the more dramatic the curve becomes.

The compound interest formula

The core formula is A = P(1 + r/n)^nt, where P is the principal, r is the annual rate (as a decimal), n is the number of times interest compounds per year, and t is the number of years. When you add regular contributions, each deposit compounds for the remaining time, so the calculator sums the growth of every contribution as well as the starting principal.

Compound vs. simple interest

Simple interest is calculated only on the original principal, so it grows in a straight line. Compound interest grows on an ever-larger base, so it curves upward. On short horizons the difference is small, but over decades it is enormous: the gap between the two lines on the chart above is the entire reason long-term investing works.

How compounding frequency changes the result

The more often interest compounds (annually, monthly, daily), the more you earn, because interest starts earning interest sooner. The jump from annual to monthly is meaningful; the jump from daily to continuous is tiny. The effective annual rate (EAR) expresses the true yearly return once compounding is included, which is why a "6% compounded monthly" account actually returns slightly more than 6% per year.

The Rule of 72

For a quick estimate, divide 72 by your annual return to approximate the years it takes to double your money. At 8%, that is about 9 years; at 6%, about 12 years. It is a back-of-the-envelope shortcut, but it builds intuition for why even a couple of extra percentage points of return matter so much over a lifetime.

Projections assume a constant rate and are for illustration only. This is not financial advice; real returns vary.