Compound Interest Calculator

See how your savings or investment grows over time with compound interest.

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Interest earned
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Compound interest is interest that earns interest. Unlike simple interest, which is calculated only on the original principal, compound interest accumulates on the principal plus any interest already earned. Over long horizons, the difference is dramatic: $10,000 at 7% over 30 years grows to about $76,000 with annual compounding - roughly 7× the original. Most savings accounts, investments, and loans in the real world use compound interest.

How compound interest works

Compound interest follows this formula:

A = P × (1 + r/n)nt
  • A - final amount after compounding
  • P - principal (initial amount)
  • r - annual interest rate as a decimal (5% = 0.05)
  • n - number of compounding periods per year (1 = annually, 12 = monthly, 365 = daily)
  • t - number of years

The interesting feature: the exponent is nt, not just t. Doubling the time horizon doesn't double your money - it more than doubles it, because each year's interest earns its own interest in subsequent years. This is why long time horizons matter much more than high rates.

Worked example. $5,000 at 6% compounded monthly for 20 years. r/n = 0.06/12 = 0.005, nt = 12 × 20 = 240. A = 5000 × 1.005240 ≈ $16,556. Total interest earned: $11,556 - more than double the original.

The Rule of 72 is a fast mental shortcut: divide 72 by the rate to estimate the doubling time. At 6%, money doubles every 12 years. At 9%, every 8 years. At 3%, every 24 years. Useful for sanity-checking back-of-the-envelope projections.

What different scenarios look like
Saving early vs. saving more

$2,000/year for 10 years starting at age 25, then nothing more - at 7% growth that's about $237,000 by age 65. Same $2,000/year starting at age 35 for 30 years (3× the contributions): about $202,000. Time on the table beats more contributions.

Compounding frequency, briefly

$10,000 at 5% for 10 years: annual compounding = $16,289; monthly = $16,470; daily = $16,486. The jump from annual to monthly matters a little; from monthly to daily, almost nothing. APY (effective rate) captures this.

Long-term retirement savings

$50,000 at 7% (rough historical real return on stocks) over 30 years compounded annually: roughly $381,000. The same $50,000 over 40 years: $749,000. The extra decade nearly doubles the result.

Inflation eats compound returns too

If your investment grows at 7% but inflation runs at 3%, your real return is closer to 4%. $100,000 at 4% real over 30 years buys about $324,000 of today's dollars - meaningful, but not the headline 7% growth would suggest.

Frequently asked questions
What is compound interest?
Interest calculated on the principal plus all previously accumulated interest. Each period's interest earns its own interest in future periods, so the balance grows exponentially rather than linearly. It's how almost all real-world investments and savings work.
What is the compound interest formula?
A = P × (1 + r/n)nt, where A is the final amount, P is the principal, r is the annual rate as a decimal, n is the number of compounding periods per year, and t is years.
How much does $1,000 grow at 7% for 30 years?
Compounded monthly: about $8,116. Compounded annually: about $7,612. The difference between monthly and annual compounding is small relative to the size of the gain - time and rate matter much more.
What is the Rule of 72?
A shortcut for doubling time: divide 72 by the annual rate. At 6%, money doubles every ~12 years. At 8%, every ~9 years. At 10%, every ~7.2 years. It's an approximation but good enough for mental math.
What is the difference between annual and monthly compounding?
Monthly applies interest 12 times per year vs once. The effective annual yield is slightly higher. For $1,000 at 5% for 10 years: annual = $1,628.89, monthly = $1,647.01 - about 1% more.
What's the difference between APR and APY?
APR (Annual Percentage Rate) is the simple annual rate. APY (Annual Percentage Yield) accounts for compounding frequency - it's the effective rate you actually earn over a year. A 5% APR with monthly compounding has an APY of 5.116%. For comparing savings accounts, APY is the honest number.
Does this calculator account for taxes?
No. It shows pre-tax growth. In a taxable account, dividends, interest, or realized gains are taxed each year, which compounds against you. In tax-advantaged accounts (Roth IRA, 401k), the pre-tax growth shown here is closer to reality.
Does it model regular contributions?
No, this version assumes a single lump sum. To approximate regular contributions, run the calculator multiple times for each contribution (each with its own time horizon) and sum the results - or use a future-value-of-an-annuity calculator.
Why does inflation matter?
Because purchasing power is what matters, not nominal dollars. A $100,000 nest egg in 30 years buys far less than $100,000 today. Always think in real (inflation-adjusted) terms for long-horizon planning. A common rule of thumb: subtract 2–3% from your assumed nominal return to get a real return.

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