Compound interest = P × (1 + r/n)^(nt). With €10,000 + €200/month at 7% APR, you reach €239,326 in 30 years (€187,726 of it interest).
Higher rates compound dramatically: doubling APR from 4% to 8% over 30 years grows the final balance ~2.6×, not 2×. The earlier you start, the more time compounding has to work — every year delayed costs years of growth at the back.
| Year | Deposits | Interest | Balance |
|---|---|---|---|
| Year 1 | $16,000 | $1,055 | $17,055 |
| Year 2 | $22,000 | $2,695 | $24,695 |
| Year 3 | $28,000 | $4,970 | $32,970 |
| Year 4 | $34,000 | $7,932 | $41,932 |
| Year 5 | $40,000 | $11,637 | $51,637 |
| Year 6 | $46,000 | $16,148 | $62,148 |
| Year 7 | $52,000 | $21,531 | $73,531 |
| Year 8 | $58,000 | $27,859 | $85,859 |
| Year 9 | $64,000 | $35,210 | $99,210 |
| Year 10 | $70,000 | $43,669 | $113,669 |
| Year 11 | $76,000 | $53,329 | $129,329 |
| Year 12 | $82,000 | $64,288 | $146,288 |
| Year 13 | $88,000 | $76,655 | $164,655 |
| Year 14 | $94,000 | $90,546 | $184,546 |
| Year 15 | $100,000 | $106,088 | $206,088 |
| Year 16 | $106,000 | $123,419 | $229,419 |
| Year 17 | $112,000 | $142,685 | $254,685 |
| Year 18 | $118,000 | $164,049 | $282,049 |
| Year 19 | $124,000 | $187,684 | $311,684 |
| Year 20 | $130,000 | $213,778 | $343,778 |
Educational tool. Not financial advice. Doesn't model taxes, fees, or inflation regime changes — real returns are usually 1–3% lower than nominal.
Compound growth at 7% APR (€10k + €200/mo)
| Time horizon | Final balance | Of which interest |
|---|---|---|
| Year 1 | €12,889 | €489 interest |
| Year 2 | €15,909 | €1,409 interest |
| Year 3 | €19,067 | €2,667 interest |
| Year 5 | €25,815 | €6,015 interest |
| Year 10 | €45,962 | €19,562 interest |
| Year 15 | €73,840 | €41,440 interest |
| Year 20 | €112,387 | €73,987 interest |
| Year 25 | €165,663 | €121,263 interest |
| Year 30 | €239,326 | €187,726 interest |
| Year 35 | €341,167 | €275,567 interest |
| Year 40 | €481,769 | €392,169 interest |
| At 4% APR (30y) | €144,929 | €95,329 interest |
History & origin
Compound interest investigations date back to Jakob Bernoulli's 1683 letter on continuous compounding, where he discovered the constant e ≈ 2.71828 while solving the problem of an account compounded infinitely often per year. The faster 'Rule of 72' for doubling time was published earlier by Luca Pacioli in 1494 (Summa de Arithmetica). Modern retirement applications include the Trinity Study (1998), which built on William Bengen's 1994 4% safe-withdrawal research.
Compound Interest — Calculator, Formula & Investment Growth
Visualize how your money grows with compound interest. Enter your initial investment, monthly contribution, interest rate, and time horizon to see a detailed growth chart. Compare two different rates side by side. Export your results as PNG or CSV.
How to use the compound interest calculator
- Enter your initial principal — the lump sum you're starting with.
- Set the annual interest rate, expected return, or APY of your investment vehicle.
- Optionally add a monthly contribution to model regular savings on top of the initial amount.
- Pick a time horizon in years and a compounding frequency (annual, monthly, or daily) to see year-by-year growth.
Common use cases
- Projecting how much an emergency fund grows over 20 years at a money-market rate.
- Comparing two index funds with similar expense ratios but different historical returns.
- Estimating the cost of waiting one year before starting to invest.
- Showing the gap between a savings account at 2% and a diversified portfolio at 7%.
About compound interest
Compound interest is the interest earned on both your initial investment and previously earned interest. It's often called 'interest on interest' and is the key driver of long-term wealth building.
- Interactive chart with gradient area fill
- Real-time updates as you adjust sliders
- Compare two interest rates side by side
- Yearly breakdown table with deposits, interest, and balance
- Export chart as PNG or data as CSV
- All calculations run in your browser
Free. No signup. Inputs stay in your browser. Ads via AdSense (consent required).
Sources (2)
- Bernoulli, J. (1690). Quaestiones nonnullae de usuris, cum solutione problematis de sorte alearum. Acta Eruditorum, May 1690, pp. 219–223 — published treatment of continuous compounding (problem investigated c. 1683).
- Fisher, I. (1930). The Theory of Interest, as Determined by Impatience to Spend Income and Opportunity to Invest It. Macmillan, New York — chapters 1–3 develop discrete and continuous compounding.
These are the original publications and regulations the formulas in this calculator are based on. Locate them by author and year on Google Scholar, SSRN, or the U.S. Government Publishing Office.
By Marco B. ·