Compound Interest Formula Explained (With Examples)

Compound interest is the reason a modest savings habit can quietly become a large number — and the reason unpaid debt grows faster than most people expect. The compound interest formula looks intimidating at first glance, but it only has four moving parts. This guide breaks each one down, walks through a real example, and shows why the compounding frequency matters less than most people think.

The formula

The standard compound interest formula is:

A = P (1 + r/n)^(n·t)

Where:

• A — the final amount (principal + interest)
• P — the principal, your starting amount
• r — the annual interest rate as a decimal (5% = 0.05)
• n — the number of compounding periods per year (12 for monthly, 365 for daily)
• t — the time in years

The key idea: interest is calculated on the running balance, not the original deposit. Each period, the interest earned joins the principal, so the next period's interest is calculated on a slightly larger base. That feedback loop is what people mean by "interest on interest."

A worked example

Say you deposit $10,000 at 5% annual interest, compounded monthly, for 10 years:

• P = 10,000
• r = 0.05
• n = 12
• t = 10

A = 10,000 × (1 + 0.05/12)^(12×10) = 10,000 × (1.004167)^120 ≈ $16,470

With simple interest, the same deposit would earn 10,000 × 0.05 × 10 = $5,000, ending at $15,000. Compounding added roughly $1,470 more — for doing nothing differently.

How much does compounding frequency matter?

Less than the marketing suggests. Here is $10,000 at 5% for 10 years across frequencies:

Going from annual to monthly compounding earns about $181 extra over a decade; monthly to daily adds only $17. The rate and the time horizon dominate. A 0.25% higher rate beats daily compounding every time.

The variable that actually matters: time

Because growth is exponential, the later years do most of the work. In the example above, the account earns about $512 in year one — and about $783 in year ten, at the same rate. Double the horizon to 20 years and the balance reaches $27,126: the second decade earns more than the first two combined would suggest.

This is also why compound interest cuts both ways. Credit card balances compound too, usually daily and at far higher rates. The same math that builds savings inflates debt.

Adding regular contributions

Most people don't invest once and walk away — they contribute monthly. Regular contributions use a separate future-value formula, and the results compound on top of each deposit's own timeline. Rather than computing that by hand, run your numbers through the Compound Interest Calculator, which projects growth with recurring contributions and shows the year-by-year breakdown. If you're comparing debt payoff instead, the Loan Calculator applies the same logic in reverse.

Common mistakes

1. Using the percentage instead of the decimal. 5% is 0.05 in the formula, not 5.
2. Mismatching n and t. If you compound monthly, the exponent is n×t total periods — 120 for ten years, not 10.
3. Ignoring fees and tax. A 1% annual fee on a 5% return removes roughly a third of your compound growth over 30 years.

FAQ

What is the difference between simple and compound interest? Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus all previously earned interest, so it grows faster over time.

How often is compound interest usually calculated? Savings accounts typically compound daily or monthly. Credit cards usually compound daily. Bonds often compound semi-annually. Check the account's terms — the advertised APY already reflects the compounding frequency.

What is the Rule of 72? A quick estimate for doubling time: divide 72 by the annual rate. At 6%, money doubles in roughly 72 ÷ 6 = 12 years. It's an approximation, but accurate within a few months for rates between 4% and 10%.

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*Ready to see your own numbers? Try the free Compound Interest Calculator — no sign-up, runs entirely in your browser.*

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