What Is Compound Interest?

What Is Compound Interest?

Compound interest is interest calculated on both the original principal and the accumulated interest from prior periods. Unlike simple interest, which accrues only on the principal, compound interest generates returns or costs that grow exponentially over time. It works powerfully in your favor when saving, and powerfully against you when borrowing at high rates.

How Compound Interest Is Calculated

A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years. For example, $10,000 at 6% compounded monthly for 10 years: A = 10,000 x (1.005)^120 = $18,194.

Compounding Frequency

Interest can compound annually, quarterly, monthly, or daily. More frequent compounding produces a higher effective annual rate. A 6% nominal rate compounded daily produces an effective annual rate of approximately 6.18%. Most installment loans use monthly compounding; most savings accounts use daily compounding.

Compound Interest on Credit Card Debt

If you carry a $5,000 balance on a card with 22% APR compounded daily and make only minimum payments, it can take over 15 years to pay off and cost more than $8,000 in total interest. This is the mathematical argument for paying credit card balances in full each month.

Common Compound Interest Mistakes

Comparing accounts by nominal rate alone. A 6% rate compounded daily earns more than 6% compounded annually -- compare effective annual yield (APY), not just the stated rate.

Assuming a "small" minimum payment stops a balance from growing. On a card with daily compounding, a minimum payment close to the monthly interest charge means the balance can still creep up even with on-time payments.