How Compound Interest Works

The mechanism

With simple interest, a 5% rate on $10,000 pays the same $500 every year. With annual compounding, year one pays $500, but year two pays 5% of $10,500 = $525, year three pays 5% of $11,025, and so on.

Each year's interest is added to the base before the next year's interest is computed. The growth curve bends upward instead of staying flat.

The formula

A = P(1 + r/n)^(nt), where P is the starting amount, r the annual rate as a decimal, n the number of compounding periods per year, and t the years.

• Annual compounding: n = 1
• Quarterly: n = 4
• Monthly: n = 12
• Daily: n = 365

Rate beats frequency

Moving from annual to monthly compounding at 5% turns $10,000 into $16,470 instead of $16,289 over ten years — a difference of about $181.

Moving the rate from 5% to 6% with the same monthly compounding produces $18,194 — a difference of over $1,700. When comparing accounts, the rate (APY) matters far more than how often it compounds.

Working for you and against you

For savers, compounding is why starting early matters more than depositing more: money invested at 25 compounds for a decade longer than money invested at 35.

For borrowers, the same math runs in reverse — credit card balances compound at high rates, which is why minimum payments barely dent them.

APY vs APR

APY (annual percentage yield) folds compounding into a single comparable number and is the honest figure for savings. APR (annual percentage rate) ignores within-year compounding and is used for loans. A savings account advertising 4.9% APR compounded daily and one advertising 5.0% APY are effectively the same product.