Compound interest is interest calculated on both the initial principal and the accumulated interest from prior periods. On savings and investments, compounding grows wealth exponentially. On debt, compounding accelerates the balance owed — making early repayment especially valuable.
The compound interest formula is: A = P(1 + r/n)^(nt), where P is principal, r is annual interest rate, n is compounding periods per year, and t is years. The more frequently interest compounds (daily vs. monthly vs. annually), the higher the effective yield or cost. On savings accounts and high-yield savings, the [[apy]] (Annual Percentage Yield) reflects the effective return after compounding — always compare APY, not just the stated rate, when evaluating deposit products. Daily compounding on $10,000 at 5% produces a slightly higher return than annual compounding at the same stated rate. On credit card debt, compounding works against the borrower. Most cards compound daily: your [[statement-balance]] unpaid from last month has interest added each day, and that added interest itself earns more interest. The CFPB's Truth in Lending Act disclosures (Regulation Z) require issuers to disclose the APR in a way that reflects this compounding burden. Albert Einstein is often (likely apocryphally) attributed with calling compound interest 'the eighth wonder of the world' — whether on a savings account or a debt balance, the math is consistently dramatic over time.
Simple interest is calculated only on the original principal. Compound interest is calculated on principal plus accumulated interest. Most financial products — savings, investments, loans, credit cards — use compound interest.
Depends on the product. Savings accounts and credit cards typically compound daily. CD interest often compounds daily but pays at maturity or monthly. Bonds typically pay simple interest semi-annually. Always check the APY/APR for the effective cost or return after compounding.