The 30-second version
- Compound interest is interest earned on your interest.
- Formula: A = P(1 + r/n)^(nt).
- Time matters more than the amount — start early.
- Rule of 72: 72 ÷ interest rate = years to double your money.
What is compound interest?
Compound interest is the interest you earn on both your original money *and* the interest it has already earned. Simple interest only ever pays on your original deposit; compound interest pays on a balance that keeps getting bigger, so growth accelerates over time.
Albert Einstein reportedly called it the eighth wonder of the world: "He who understands it, earns it; he who doesn't, pays it."
The compound interest formula
The future value of a lump sum is: A = P(1 + r/n)^(nt), where:
- A = final amount
- P = principal (your starting amount)
- r = annual interest rate (as a decimal, so 7% = 0.07)
- n = number of times interest compounds per year
- t = number of years
Worked example
Invest $10,000 at 7% compounded monthly for 20 years: A = 10,000 × (1 + 0.07/12)^(12 × 20) ≈ $40,275. You quadrupled your money without adding a cent.
$10,000 at 7%, monthly compounding
Notice how the balance roughly doubles each decade — that is compounding at work.
Adding monthly contributions
Most people invest a bit every month, not one lump sum. That is where compounding really shines. Adding $500/month to that same $10,000 at 7% for 20 years grows to about $271,000 — and roughly half of it is interest you never deposited.
Why starting early beats investing more
A 25-year-old who invests $300/month until age 65 ends up with more than a 35-year-old investing $600/month — despite contributing half as much each month. The extra decade of compounding does the heavy lifting.
The Rule of 72
Want a quick estimate without a calculator? Divide 72 by your interest rate to get the years it takes to double your money. At 8%, money doubles in 72 ÷ 8 = 9 years. At 6%, it takes 12 years.
How often should interest compound?
More frequent compounding means slightly more growth. Daily beats monthly beats annually — but the difference is small compared to your rate and time horizon. Focus first on a good return and a long runway.
See your own numbers grow
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Frequently Asked Questions
What is the difference between simple and compound interest?
Simple interest is always calculated on your original deposit. Compound interest is calculated on your deposit plus all previously earned interest, so it grows faster and faster over time.
How do I calculate compound interest by hand?
Use A = P(1 + r/n)^(nt). For $5,000 at 6% compounded monthly for 5 years: 5,000 × (1 + 0.06/12)^(12×5) ≈ $6,744. Or just use our free compound interest calculator.
Does compound interest work against me with debt?
Yes. Credit cards compound interest on your balance, so unpaid debt grows the same way investments do — just in the wrong direction. Paying it off is a guaranteed return equal to the card's rate.