How it works
With compound interest, each period's interest is added to the balance, so the next period earns interest on a bigger amount. The more often it compounds, the slightly faster it grows.
A = P × (1 + r/n)n×t
P is the starting amount, r the annual rate as a decimal, n the compounding periods per year and t the number of years. Monthly contributions are added at the end of each month and grow at the same rate from then on.
Real returns vary. Savings accounts change their rates, and investments can lose value. Taxes and fees aren't included.
Worked example
You invest $10,000 at 5% a year for 10 years.
Compounded yearly: 10,000 × 1.0510 = $16,288.95. Compounded monthly: 10,000 × (1 + 0.05/12)120 = $16,470.09.
Starting from $0 and adding $100 a month at 6% compounded monthly for 10 years gives $16,387.93, of which $12,000 is your deposits and $4,387.93 is interest.
Frequently asked questions
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.
Is daily compounding much better than monthly?
Only a little. At 5% for 10 years, $10,000 grows to $16,470 with monthly compounding and about $16,486 with daily compounding.
What's the difference between APR and APY?
APR is the stated yearly rate. APY includes the effect of compounding, so it's a little higher. A 5% rate compounded monthly is about a 5.12% APY.
Does this work for debt too?
Yes. Credit card balances compound the same way, which is why unpaid balances grow so quickly.