Compound Interest Calculator — Growth & APY
Project compound growth on a lump sum plus monthly additions. Compare APY, compounding frequencies and compound versus simple interest year by year, free.
A clear path from inputs to results.
Project how a lump sum grows when interest earns interest — with or without regular monthly additions. The tool reports the future value and the effective annual yield (APY), and plots a year-by-year comparison of compound growth against simple interest so you can watch compounding widen the gap.
How to use
- Enter the starting principal — the amount you deposit today.
- Set the annual rate and the number of years to project.
- Choose the compounding frequency (monthly by default; other periods and a continuous option are available). The APY readout shows the effective annual rate for that frequency.
- Optionally add a monthly contribution; deposits are credited at the start of each month and compound from that same month.
- Read the future value, then scan the year-by-year table, which tracks total invested, simple-interest earnings, compound-interest earnings and the running balance.
The formula
Reference: Standard compound-interest future value and effective annual yield (Broverman, Mathematics of Investment and Credit; any algebra-of-finance text). Continuous mode uses A = Pe^{rt}, evaluated in daily steps. Contributions are added monthly before that month's compounding.
Worked example
$10,000 lump sum at 8% for 10 years, monthly compounding
- Principal $10,000; APR 8%; 10 years; compounding monthly (12 periods per year); no additions.
- 1
Each month the balance grows by 8% ÷ 12 = 0.6667%, so the effective annual yield is (1 + 0.08/12)^12 − 1 ≈ 8.30%. After 120 monthly compounding periods the $10,000 grows to $22,196.40, of which $12,196.40 is compound interest. Simple interest on the same principal would earn only 8% × $10,000 × 10 = $8,000.00, so compounding adds $4,196.40 over the decade — and the chart shows that gap widening every year.
Future value $22,196.40; compound interest $12,196.40 versus $8,000.00 simple (a $4,196.40 advantage); APY 8.30%.
Interpreting the result
The future value is what the account holds; the APY is the honest annual rate to compare across banks because it folds the compounding frequency in. The compound-versus-simple table shows why time matters more than rate at long horizons: the simple-interest line is straight while the compound line bends upward. If you plan to add money monthly, the contribution feature shows those deposits compounding immediately rather than sitting idle.
Assumptions & limitations
- The rate is constant for the whole projection; no taxes, fees or inflation are applied, so results are gross.
- Monthly contributions are credited at the start of each month and earn interest from that same month.
- Compounding runs on a monthly engine: frequencies above monthly compound monthly at the equivalent effective rate; lower frequencies compound at the end of each period.
- Continuous compounding is approximated with daily (365-step) accrual.
- Projections illustrate the arithmetic of a fixed rate; they are not forecasts of any actual account or market.
Frequently asked questions
What is the difference between APR and APY here?
The 8% you enter is the nominal annual rate; APY is what you actually earn per year once compounding is included. Monthly compounding at 8% produces an APY of about 8.30% — over ten years on $10,000 that is the difference between $8,000 and $12,196.40 of interest.
Does compounding frequency matter much?
Some, but far less than time or rate: annual compounding at 8% ends the example at $21,589.25 versus $22,196.40 with monthly compounding — about $607 over ten years. Use the APY readout to compare offers directly instead of guessing from nominal rates.
Are taxes or inflation included?
No — the projection is gross. Interest in a taxable account is usually taxed annually, which lowers the net rate, and inflation lowers what the future balance buys. Treat the output as the pre-tax, pre-inflation arithmetic of compounding.
How much do monthly additions really add?
Adding $100 a month to the worked example lifts the ten-year balance from $22,196.40 to $40,612.97. You contribute $12,000 extra out of pocket, but the balance grows by $18,416.57 because every deposit starts compounding the month it lands.
Why compare against simple interest?
Simple interest (principal × rate × years) is the straight-line baseline: $8,000 on the example. The $4,196.40 gap after ten years is entirely the effect of interest earning interest. Stretch the same inputs to 20 years and the compound balance reaches $49,268.03 while simple interest only doubles to $16,000.
Can I model continuous compounding?
Yes — the frequency selector includes a continuous option, evaluated as A = Pe^(rt) via daily steps. It yields an APY of e^0.08 − 1 ≈ 8.33% on the example rate, only marginally above monthly compounding.
Methodology last reviewed 2026-10-06. Results are informational and not financial or engineering advice — see our disclaimer.