What compound interest is
Simple interest is paid only on the money you put in. Compound interest is also paid on the interest you've already earned. Each period's interest joins the balance, and the next period's interest is figured on that bigger number. Over short periods the difference is small. Over decades it does most of the work.
The formula
P is the starting amount, r the annual rate as a decimal, n the number of times interest compounds per year and t the number of years. This calculator works month by month: it converts the rate to an equivalent monthly rate for the compounding you choose, applies it, then adds your deposit at the end of the month.
A quick shortcut is the Rule of 72: divide 72 by the interest rate to estimate how many years it takes money to double. At 7%, that's about 10 years.
Worked example
Start with $10,000, add $200 a month and earn 7% compounded monthly. After 20 years the balance is about $144,572.72. You deposited $58,000.00; the other $86,572.72 is interest.
Without the monthly deposits, the $10,000 alone would grow to about $40,387.39. The effective annual yield of 7% compounded monthly is 7.229%.
Keep in mind
- Rates aren't guaranteed. Savings account rates change with the market, and investment returns vary from year to year. Treat any long-term rate as an assumption.
- Inflation reduces buying power. To see results in today's dollars, subtract an inflation estimate from the rate.
- Taxes and fees are not included. Interest in a regular taxable account is usually taxed each year, while retirement accounts follow different rules.