Compound Interest Calculator

Last reviewed: June 16, 2026

What is compound interest?

Compound interest earns interest on your principal and on every dollar of interest you've already accumulated. Each period, a little more growth lands in the account — and next period, you earn interest on that growth too. Simple interest, by contrast, earns only on the original deposit: the same dollar amount every year, no matter how long you hold.

The gap between the two looks small in year one and enormous over decades. A $1,000 deposit at 5% yields $50 in simple interest after year one — the same every year. At 5% compounded monthly, year one produces $51.16. That extra $1.16 goes to work next year. After 10 years, simple interest totals $500; compound interest (monthly) produces $647. After 30 years: $1,500 simple against $3,467 compounded. The difference is entirely the compounding effect — interest earning interest, year after year.

This is why time is the most powerful variable in the formula. Doubling the rate roughly doubles the outcome. Doubling the time more than doubles it — because every additional year compounds the whole prior stack of growth, not just the original principal.

The formula

The standard compound interest formula is:

• A — future value (what you end up with)
• P — principal (initial deposit)
• r — annual rate as a decimal (0.05 for 5%)
• n — compounding periods per year (12 for monthly)
• t — time in years

The term (1 + r/n) is the periodic growth factor — how much one dollar grows each compounding period. Raising it to the power n×t (total periods) chains those growth factors together over time.

When you add regular contributions, the total future value is the lump-sum term plus the future value of an annuity:

Where i = r/n is the periodic rate and N = n×t is total periods. If contributions are made at the beginning of each period (annuity due), multiply by (1+i) for one extra period of compounding.

The combined total is the sum of both terms — the lump sum grows independently of the annuity stream, so they add linearly.

Worked example

Using the calculator's defaults — P = $10,000, r = 7% nominal, monthly compounding, 30 years, $500/month end of period:

• Periodic rate: 7% ÷ 12 = 0.5833% per month
• Total periods: 12 × 30 = 360 months
• Lump-sum term: $10,000 × (1.005833)^360 ≈ $81,165
• Annuity term: $500 × [(1.005833)^360 − 1] / 0.005833 ≈ $609,985
• Total future value: ≈ $691,150

You deposited $10,000 upfront plus $500 × 360 months = $190,000 total. The remaining ~$501,000 is interest — more than 2.6× your contributions, produced entirely by thirty years of compounding. Adjust the rate or time in the calculator and watch how dramatically those proportions shift. Cutting the rate to 5% drops the total to roughly $416,000. Extending to 40 years at the same 7% nearly doubles it again.

Nominal vs. effective rate — why it matters

The same number means different things depending on how it's quoted. A 7% nominal rate compounded monthly means you earn 7%/12 each month. Over a full year that compounds to: (1 + 0.07/12)^12 − 1 ≈ 7.229% — your effective annual rate (EAR). The nominal rate understates what you actually earn.

A 7% effective annual rate means you realize exactly 7% over the year regardless of compounding frequency. The periodic rate is derived backward: (1 + 0.07)^(1/12) − 1 ≈ 0.565% per month — slightly less than 7%/12. This framing is more honest when the stated rate is an annual return assumption rather than a quoted APR.

In practice: savings accounts and CDs quote nominal APR — use “nominal.” Portfolio return projections (“I expect 7% annual growth”) are more naturally modeled as effective rates, since the 7% already accounts for the compounding. The FIRE calculators on this site use effective rates by default for that reason. The calculator above labels which rate type is active and shows the EAR for any nominal input, so the distinction is always visible.

What this calculator assumes

Every projection has assumptions. These are labeled rather than buried:

• Contributions fire at the compounding cadence. If you select monthly compounding, contributions are monthly. Modeling monthly deposits with annual compounding is not supported in the current version — the two are locked together. This matches the investor.gov reference calculator.
• Nominal dollars only. All figures are in nominal terms — the actual dollars you'll hold, not their future purchasing power. A “today's dollars” view (deflating by an assumed inflation rate) is a planned extension.
• Daily compounding uses a 365-day year. Leap years are not modeled.
• Contributions are constant. The same amount every period. An escalating-contribution option (e.g., +3%/year) is a future addition.
• Pre-tax results. Taxes on gains — capital gains, income tax on interest — are not modeled.

Frequently asked questions

How often should I compound for maximum growth?

More frequent compounding adds marginally more interest, but the practical difference between monthly and daily is small for most balances. At 5%, the EAR for monthly compounding is 5.116%; for daily, it's 5.127% — an 11-basis-point difference. The rate and time matter far more than the compounding cadence. That said, daily compounding is common in high-yield savings accounts, so it's worth entering the exact terms of your account.

Does this account for inflation?

No. All outputs are in nominal dollars — the actual dollars you'll hold in the future, not their equivalent purchasing power today. At 3% annual inflation, a dollar in 30 years has about $0.41 of today's purchasing power. Expressing results in “real dollars” by deflating by an assumed inflation rate is a planned extension. For now: when comparing projections, keep in mind that the future dollar figures overstate real purchasing power by roughly the cumulative inflation rate over the term.

What's the difference between APR and APY?

APR (Annual Percentage Rate) is a nominal rate — it does not account for within-year compounding, so it understates the true annual return. APY (Annual Percentage Yield) is an effective rate — it does account for compounding and reflects what you actually earn. Banks are required to disclose both for deposit accounts. For mortgages, APR includes origination fees and typically exceeds the stated interest rate; that's a different calculation from what this tool covers.

Can I model monthly contributions with annual compounding?

Not in the current version. Contributions fire at the same cadence as compounding, so monthly contributions require monthly (or finer) compounding. This is labeled in the calculator. If your scenario genuinely involves a mismatch — for example, payroll deposits every two weeks into an annually-compounded account — the most conservative approach is to use the compounding frequency that matches the contribution cadence and note the simplification.

Related calculators

Compounding appears throughout personal finance. These tools apply the same engine to more specific scenarios — links will be live as they ship:

• DRIP Calculator — compound interest applied to dividend income; models the reinvestment of quarterly payouts
• Investment Fee Drag Calculator — fees compound against your returns just as returns compound for you; shows the exact cost over time
• Coast FIRE Calculator — compound growth to a target retirement number; at what balance can you stop contributing and coast to your goal?