What Is Compound Interest? Formula, Examples, and How It Works

What Is Compound Interest?

Compound interest is the interest you earn on both your original money and on the interest you've already earned. Simply put, it's "interest on interest" — and it's the most powerful force in personal finance.

Albert Einstein reportedly called compound interest "the eighth wonder of the world." Whether he actually said that or not, the sentiment is correct: compound interest can turn modest savings into substantial wealth over time.

Simple Interest vs. Compound Interest

Simple interest is calculated only on the principal amount. If you invest $10,000 at 5% simple interest, you earn $500 every year — no more, no less. After 30 years: $10,000 + ($500 × 30) = $25,000.

Compound interest is calculated on the principal plus accumulated interest. Year 1: $500. Year 2: 5% on $10,500 = $525. Year 3: 5% on $11,025 = $551. After 30 years: $10,000 × (1.05)^30 = $43,219.

The difference: $18,219 more with compound interest — earned without adding a single extra dollar.

The Compound Interest Formula

A = P (1 + r/n)^(nt)

Where: A = Final amount, P = Principal, r = Annual rate (decimal), n = Compounds per year, t = Years

With monthly contributions, the formula extends — but you don't need to do it manually. Use our Compound Interest Calculator for instant results.

The Rule of 72

The Rule of 72 is a quick way to estimate how long it takes your money to double: divide 72 by your annual interest rate.

• At 6%: 72 ÷ 6 = 12 years to double
• At 8%: 72 ÷ 8 = 9 years to double
• At 10%: 72 ÷ 10 = 7.2 years to double
• At 15%: 72 ÷ 15 = 4.8 years to double

Why Time Is Your Greatest Asset

The most important factor in compound interest is time. Consider two investors:

• Alice invests $5,000/year from age 25 to 35 (total: $55,000), then stops. At 8%, her money grows to ~$700,000 by age 65.
• Bob starts at 35 and invests $5,000/year until 65 (total: $155,000). At 8%, he ends with ~$612,000.

Alice contributed $100,000 less but ended with $88,000 more — just by starting 10 years earlier. That's compound interest at work.

How to Harness Compound Interest

1. Start early — The sooner you start, the more time compounding works for you
2. Be consistent — Regular contributions, even small ones, add up significantly
3. Reinvest dividends — Let your earnings compound rather than taking them out
4. Be patient — Compounding requires time; don't interrupt the process
5. Increase contributions — As your income grows, increase your savings rate

Compound Interest Can Work Against You

Compound interest is a double-edged sword. It works against you on debt. A $5,000 credit card balance at 22% APR with minimum payments ($200/month) takes over 3 years and costs over $800 in interest. That's the negative side of compounding — and why paying off high-interest debt should be your first priority.

Use Our Free Calculator

Our Compound Interest Calculator shows you exactly how your money grows with monthly contributions and a visual growth chart. Plan your future with our Retirement Calculator or project returns with our Investment Return Calculator.