What Is Compound Interest? The Math That Builds Wealth — or Debt
Compound interest is interest earning interest. The formula, real examples of compounding on savings and credit cards, and why starting early beats saving more.
Sarah ChenEditor-in-ChiefCompound interest is interest earned on interest: each period, interest is calculated not just on your original principal but on everything it has grown to so far.
A = P × (1 + r/n)^(nt) — where P is principal, r the annual rate, n the compounding frequency per year, and t the years. The formula is less important than what it produces: growth that starts slow and bends sharply upward.
A worked example
$10,000 invested at 7% per year, compounded annually:
- Year 10: $19,672
- Year 20: $38,697
- Year 30: $76,123
- Year 40: $149,745
Notice the shape: the first decade adds ~$9,700; the last adds ~$73,600. That is compounding’s signature — time contributes more than money. Someone who invests $200/month from 25 to 35 and stops ends up roughly even with someone who invests $200/month from 35 to 65, because the early dollars compound for decades longer.
Compounding frequency, briefly
The same rate compounds into slightly different results depending on frequency: 5% compounded yearly yields exactly 5%; daily, about 5.13%. That effective number is the APY on savings products. When comparing accounts, compare APY to APY and the frequency question answers itself.
The dark side: compounding on debt
The identical math runs against borrowers. Credit cards compound daily at APRs that averaged well above 20% in recent Federal Reserve data. Carried balances grow on the same accelerating curve as investments:
- $5,000 at 24% APR, minimum payments only: roughly 17 years to pay off, ~$7,000 in interest.
- The mechanics are detailed in our APR explainer — daily compounding is exactly why APR understates the true cost.
The rule that follows
Compounding is indifferent — it amplifies whatever position you are in. Hold appreciating assets and time is your employee; hold revolving debt and time is the bank’s. The entire discipline of personal finance reduces, in large part, to moving your money from the second side of that equation to the first: kill high-rate debt, then let low-cost index funds compound for decades, as we cover in why index funds beat stock picking.
Frequently asked questions
What is compound interest in simple terms?
Compound interest is interest calculated on both your original money and on the interest that money has already earned. Each period, the base grows, so the next period's interest is larger. Over years the growth curves upward — which is why long-term savers and long-term debtors see such extreme outcomes.
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal: $1,000 at 5% simple earns a flat $50 every year forever. Compound interest adds each period's interest to the principal: that same $1,000 earns $50, then $52.50, then $55.13 — after 30 years, compounding has produced roughly 3.3x the simple-interest total.
How often does interest compound?
It depends on the product: savings accounts typically compound daily and credit monthly, credit cards compound daily, and mortgages compound monthly. More frequent compounding means slightly faster growth — a 5% rate compounded daily yields about 5.13% over a year, the APY.
Can compound interest work against me?
Yes — on debt. Credit cards compound daily at APRs above 20%, so a carried balance grows the same accelerating way a good investment does, in reverse. A $5,000 balance at 24% APR left to minimum payments can cost more in interest than the original debt.
Updated July 26, 2026.
Primary sources
Rates, rules and figures in this article are drawn from the primary sources below. We refresh money pages quarterly — always confirm current terms with the issuer or regulator before acting.
This article is for informational purposes only and does not constitute financial advice. Always do your own research.