What Is Compound Interest?

Compound interest is interest that is calculated on the initial amount of money and also on the interest that has already been added. In other words, interest earns interest. Over long periods, this effect can make savings and investments grow much faster than with simple interest, and it can also make debts grow quickly.

Simple versus compound

Suppose you deposit 1,000 at 5 percent a year.

• Simple interest: you earn 50 each year, so after 10 years you have 1,500.
• Compound interest: the first year you earn 50, and in the second year interest is calculated on 1,050, and so on. After 10 years you have about 1,629.

The difference widens with time and higher rates.

The formula

Future value = principal multiplied by (1 + r divided by n) raised to the power n times t, where r is the annual interest rate as a decimal, n is the number of compounding periods per year and t is the number of years. With regular contributions, the formula includes the added payments.

The rule of 72

A quick way to estimate how long it takes for money to double is to divide 72 by the annual interest rate in percent. At 6 percent, money doubles in about 12 years. At 9 percent, it takes about 8 years. The rule is approximate.

Why starting early matters

Time is the strongest factor. A person who saves a small amount from age 20 may end up with more than a person who starts later and saves more, because the early contributions have longer to compound. This is why retirement advice stresses starting early.

Compound interest and debt

Borrowing costs also compound. Credit cards and some loans add unpaid interest to the balance, so you pay interest on interest. Paying more than the minimum, and paying off high-interest debt early, limits this effect. See our entry on interest capitalization for student loans.

Rates and inflation

Real growth depends on the interest rate compared with inflation. If prices rise faster than your savings grow, your purchasing power falls. Investments may offer higher returns but carry risk.

Practical tips

• Start saving early, even small amounts.
• Use tax-advantaged accounts where available.
• Reinvest earnings.
• Compare rates and fees.
• Avoid high-interest debt.
• Use online calculators to see scenarios.

Related terms

See APR, interest capitalization, inflation, 401(k) and credit utilization.