The compound interest formula
Four terms describe a compounding investment, and the calculator asks for nothing else. The future value of a capital on its own is capital × (1 + r/12) to the power of 12n, where r is the annual rate and n the number of years. Every monthly contribution follows the same rule over the time it has left, and the calculation adds the two parts together.
Simple interest only pays on the starting capital. €10,000 at 5% for 20 years earns €10,000 of simple interest, so €20,000 in total. With monthly compounding at the same rate, the same capital reaches €27,126. The €7,126 gap is the interest earned by the interest.
The rule of 72 gives a rough doubling time: 72 divided by the annual rate. At 6% it says 12 years, and the exact monthly calculation gives 11.6. The approximation is good enough for mental arithmetic, not for a plan.
- Starting capital: the amount already invested in the first month.
- Monthly contribution: what is added afterwards, counted at the end of each month.
- Annual return: the rate used, divided by twelve and compounded every month.
- Horizon: the number of years the calculation runs for.
How to use the calculator
The four visible fields are enough for a first answer. The three chips under the return fill the rate in at 3, 5 or 7% when no figure comes to mind. The headline number, the chart and the table recompute on every keystroke.
The advanced options add what the short version leaves out: annual fees taken out of the return, an inflation rate that restates the result in today’s money, and a yearly rise of the contribution for a budget that follows income.
The “Reach a target” toggle turns the question around. Instead of projecting a known contribution, it works out the monthly amount that reaches the target capital within the horizon. The contribution field disappears, because it has become the answer. When an inflation rate is set, the target is read in today’s money.
Every parameter lives in the page address. The “Copy link” button hands back a URL that reopens the same simulation, figures included.
Reading the result
The headline number is nominal: it is the amount in the euros of the final year, before tax. The legend splits what was paid in from what was earned, and the table repeats both, line by line.
With €1,000 to start, €150 a month and 5% a year, the balance reaches €129,307 after 30 years: €55,000 paid in and €74,307 of interest. Add 2% inflation and that €129,307 is worth €71,386 in today’s money. The amount does not move, the purchasing power does.
Fees are taken out of the return, so their cost grows with the capital. On the same plan over 20 years, the result falls from €64,368 with no fees to €57,239 with 1% of annual fees. The legend shows the cumulative fees as soon as they rise above zero.
What the calculation shows
Time weighs more than the amount. €300 a month for 20 years at 5% gives €123,310 for €72,000 paid in; €150 a month for 30 years, at the same rate, gives €124,839 for €54,000 paid in. Ten extra years beat twice the monthly effort here.
A point of fees costs more than it looks. On €1,000 to start and €150 a month at 5% for 20 years, 1% of annual fees removes €7,129 from the result, about 11% of the total reached without fees.
Inflation works the other way. €150 a month for 20 years at 5% gives €61,655. At 2% inflation a year, that €61,655 buys what €41,492 buys today.
Frequently asked questions
Is the calculation monthly or annual?
Compounding is monthly. Each month the balance grows by one twelfth of the annual return, then that month’s contribution is added. The table shows annual rows, but the figures come from that month-by-month calculation.
What is the compound interest formula?
For a capital on its own, the future value is capital × (1 + r/12) to the power of 12n, where r is the annual rate and n the number of years. Regular contributions are added as an annuity: each one compounds over the time it has left. The calculator adds the two parts together.
How does compounding work with stocks?
A portfolio pays no interest in the banking sense. Compounding comes from reinvested dividends and from price gains kept from one year to the next. The return typed here is a smoothed average, while a market rises and falls year to year. The result describes an average path, never one particular year.
What is a compound interest investment?
It is an investment whose gains stay invested instead of being withdrawn, so they earn in turn. A savings account that capitalises its interest every year works this way, as does an accumulating fund. A product that pays its income into a current account compounds nothing.
What is the difference between simple and compound interest?
Simple interest is always computed on the starting capital. Compound interest is computed on the capital plus the interest already earned. On €10,000 at 5% for 20 years, simple interest gives €20,000 while monthly compounding gives €27,126.
How does the rule of 72 work?
Divide 72 by the annual rate to estimate how many years a capital needs to double. At 6% it says 12 years; the exact monthly calculation gives 11.6. The gap stays small at ordinary rates, which makes it a useful mental shortcut.
Go further
FIRE calculator: target capital and independence age
Your independence date in one calculation, or a multi-phase path on your real balance.
Loan calculator
Estimate your monthly payment, total cost and effective rate (TAEG).
Rent vs Buy
Compare renting against buying and find your break-even year.