What Is Compound Interest?
The formula, worked examples, and why Albert Einstein allegedly called it the "eighth wonder of the world."
Try the Free Calculator →Compound Interest, Defined
Compound interest is interest calculated on both the principal and the accumulated interest from previous periods. Each period's interest gets added to the balance, and the next period's interest is calculated on that larger number.
This creates a feedback loop: a growing balance earns more interest, which grows the balance faster, which earns even more interest. Over long time horizons, the acceleration is remarkable.
The Compound Interest Formula
- A — final amount (principal + interest)
- P — principal (starting amount)
- r — annual interest rate, as a decimal (e.g. 7% → 0.07)
- n — compounding periods per year (1 = annual, 12 = monthly, 365 = daily)
- t — time in years
Worked example
You invest $10,000 at 7% per year, compounded annually, for 30 years:
A = 10,000 × (1 + 0.07/1)1×30 = 10,000 × (1.07)30 ≈ $76,123
Your $10,000 grew to $76,123 — a gain of $66,123, all from interest alone.
Simple vs. Compound Interest
Simple interest applies only to the original principal each period. Compound interest applies to the running total. The gap widens dramatically over time.
| Year | Simple (7%) | Compound (7%) | Difference |
|---|---|---|---|
| 5 | $13,500 | $14,026 | +$526 |
| 10 | $17,000 | $19,672 | +$2,672 |
| 20 | $24,000 | $38,697 | +$14,697 |
| 30 | $31,000 | $76,123 | +$45,123 |
Based on $10,000 principal at 7% annual interest.
How Compounding Frequency Affects Growth
The more often interest compounds, the more you earn. In practice the differences at normal savings rates are small, but at high rates (like credit card debt) they add up.
| Frequency | Formula (n) | $10,000 at 7% / 30 yr |
|---|---|---|
| Annually | n = 1 | $76,123 |
| Monthly | n = 12 | $81,165 |
| Daily | n = 365 | $81,645 |
Monthly vs. annual compounding adds about $5,000 over 30 years at 7%. At 24% (credit card rates), the difference is far more punishing.
The Rule of 72 — A Quick Mental Shortcut
Divide 72 by the annual interest rate to estimate how long it takes to double your money. No calculator required.
Real-World Examples
📈 S&P 500 Index Fund
The US stock market has returned roughly 10% annually before inflation, ~7% after. Investing early and holding is the primary way ordinary people build wealth.
Try this in the calculator →💳 Credit Card Debt
A $5,000 balance left unpaid for 5 years at a typical credit card rate almost triples. Every month of delay adds interest on top of interest.
Try this in the calculator →How to Calculate Compound Interest (Step by Step)
- Identify your inputs: principal (P), annual rate (r), compounding periods per year (n), and time in years (t).
- Convert the rate to a decimal: divide by 100. 7% → 0.07.
- Apply the formula: A = P × (1 + r/n)n×t
- Subtract the principal to find the interest earned: Interest = A − P
Or skip the arithmetic and use the calculator — it handles any compounding frequency and lets you add a yearly contribution.
Frequently Asked Questions
What is compound interest?
Compound interest is interest calculated on both the original principal and the accumulated interest from previous periods. Unlike simple interest (which applies only to the principal), compound interest creates a snowball effect: a growing balance earns more interest each period, which grows the balance faster, and so on.
What's the difference between simple and compound interest?
Simple interest is always calculated on the original principal. If you borrow $1,000 at 10% simple interest, you owe $100 in interest each year regardless of how much has accumulated.
Compound interest is calculated on the running total. After year one you owe $1,100; in year two interest applies to $1,100, not $1,000 — so you owe $110 instead of $100. The difference compounds every period.
How does compounding frequency affect the result?
More frequent compounding means interest is added to the balance sooner, so subsequent interest calculations use a larger base. Daily compounding produces slightly more than monthly, which produces slightly more than annual.
At moderate savings rates (4–8%) the effect is modest over typical time horizons. But at high rates — credit cards, payday loans — more frequent compounding meaningfully increases what you owe.
What is the Rule of 72?
Divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 6%, 72 ÷ 6 = 12 years. At 9%, 72 ÷ 9 = 8 years. It's a rough approximation that works well for rates between 2% and 20%.
Does compound interest work against you with debt?
Yes — the same mechanism that grows savings also compounds debt. A $5,000 credit card balance at 24% APR, left unpaid for 5 years, grows to nearly $15,000. This is why financial advice consistently emphasises paying off high-interest debt before investing.
How much do I need to invest to reach a specific goal?
That depends on your target amount, timeline, expected rate of return, and any amount you already have saved. The Goal mode in our calculator solves for this automatically — enter your target and it tells you either the lump sum to invest today or the annual contribution needed.