What is compound interest?
Compound interest is interest calculated not just on the original amount of money put in or borrowed, but also on the interest that amount has already earned or accrued. Each time interest is added to a balance, the next round of interest is calculated on the new, larger total, so growth accelerates the longer money sits and compounds. The 
Securities and Exchange Commission's Investor.gov provides an official calculator for estimating how a balance grows under compounding, letting users test different rates and compounding schedules. The same mechanic works in reverse on money owed: unpaid interest on a credit card or loan gets added to the balance, and future interest is charged on that larger amount too. Compounding shows up throughout the products the federal government regulates, insures, or lets people buy directly, from Treasury savings bonds to bank certificates of deposit.
How compounding actually works
The core idea is that interest earned in one period becomes part of the principal for the next period. Investor.gov's compound interest tool asks for four basic inputs to model this: the initial amount invested, an optional regular contribution (or withdrawal), the number of years the money grows, and an estimated annual interest rate, along with how often interest compounds — annually, semiannually, quarterly, monthly, or daily, options the calculator itself lists. The more frequently interest compounds within a year, holding the stated annual rate constant, the faster a balance grows, because each compounding period folds a bit more accumulated interest back into the base being charged or credited next. A related Savings Goal Calculator uses the same compounding-frequency inputs to work the problem backward, estimating the monthly contribution needed to reach a target amount by a given date at an assumed rate.
Compounding when saving or investing
Compounding rewards time as much as it rewards the rate itself, which is why the SEC's investor-education materials treat starting early as one of the most consequential decisions a saver makes. Tax-advantaged accounts are built around letting compounding run undisturbed for years: contributions to a traditional or Roth IRA grow either tax-deferred or tax-free until withdrawal, and 401(k), 403(b), and 457(b) employer plans work the same way, so none of the year-to-year growth is reduced by an annual tax bill along the way. U.S. Treasury savings bonds compound as well: electronic Series EE bonds are sold at face value and credit interest electronically over the life of the bond, while Series I bonds pay a fixed rate adjusted for inflation, and both defer federal tax on that accumulated interest until the bond is redeemed or matures, as described on Investor.gov's savings bonds page. A certificate of deposit works on the same principle over its fixed term — six months, one year, five years — with the depositor receiving principal plus accumulated interest at redemption, per Investor.gov's CD overview. Money held in these accounts at a federally insured bank benefits from FDIC coverage up to $250,000 per depositor per institution, and credit union deposits carry the same $250,000 limit through the NCUA's share insurance fund, protections summarized on Investor.gov's page on investment risk.
Compounding when money is owed
The same math cuts against a borrower when interest is not paid off. On a credit card or similar high-interest debt, unpaid interest is added to the balance, and the next billing period's interest is then charged on that larger total — which is why balances that aren't paid in full can grow quickly. Investor.gov's guidance on debt notes that credit cards may charge 18% or more when balances carry over, and recommends paying off high-interest debt — generally anything charging around 8% or more with no tax advantage — before directing money toward investing, since eliminating that compounding cost typically produces a better, lower-risk outcome than most investment returns would offset.
Estimating compound growth
Because the effect of compounding depends heavily on the rate, the time horizon, and how often interest compounds, small changes in any one of those inputs can produce very different results over long periods. Anyone trying to project how a specific savings goal, deposit, or loan balance will grow can use the SEC's Compound Interest Calculator directly, entering their own principal, contribution schedule, time frame, and assumed rate to see the results rather than relying on rough estimates. That tool, along with the related Savings Goal Calculator, is free and does not require an account to use.