Compound interest formula: the four terms behind the number
Say €150 is paid in every month for 20 years, with an assumed 6% a year. The monthly rate r is 6% divided by 12, so 0.5%. The number of months n is 20 × 12, so 240. The formula gives 150 × ((1.005)^240 − 1) / 0.005, which comes to €69,306.
Of that €69,306, you paid in €36,000 from your own pocket. The rest, €33,306, is interest. This split between capital paid in and interest earned is the one that matters: the first is your effort, the second is the work of time.
| Term | What it stands for | In the example |
|---|---|---|
| M | The deposit made each month | €150 |
| r | The monthly rate, so the annual rate divided by 12 | 6% / 12 = 0.5% |
| n | The number of months | 20 years × 12 = 240 |
| FV | The final value, capital and interest together | €69,306 |
For a single starting sum with no monthly deposit, the formula is shorter: FV = C × (1 + r)^n. A €10,000 deposit at 4% a year, compounded once a year, is worth 10,000 × 1.04^10 after ten years, which is €14,802. The two formulas combine when you have both a starting sum and regular deposits.
The 6% or 4% rate is an assumption made for the calculation, nothing more. The formula works the same way with 1% or 8%.
Compound interest is interest worked out on capital that already contains interest.
Compound interest calculator: €150 a month over ten, twenty and thirty years
The calculator below applies the formula from the first section, compounding monthly with a fixed assumption of 6% a year. The two sliders give the result for your own amounts and your own time spans. It is an estimate for teaching purposes, not a projection of what any product will pay.
The full calculator in the app adds annual fees, inflation shown in today's euros, a yearly increase to the deposit and a reverse mode that targets a capital goal. Its link can be shared as it stands, with your own settings.
The table that follows uses the same formula, worked out for €150 a month at two assumed rates, 4% and 6%. The figures are rounded to the euro. They come from the same calculation as the calculator, not from an outside source.
| Duration | Paid in | Final value at 4% | Of which interest | Final value at 6% | Of which interest |
|---|---|---|---|---|---|
| 10 years | €18,000 | €22,087 | €4,087 (19%) | €24,582 | €6,582 (27%) |
| 20 years | €36,000 | €55,016 | €19,016 (35%) | €69,306 | €33,306 (48%) |
| 30 years | €54,000 | €104,107 | €50,107 (48%) | €150,677 | €96,677 (64%) |
Two ways to read the table. The first: at 6%, the share of interest goes from 27% after ten years to 64% after thirty. Past a certain point, the interest weighs more than what you paid in. The second: the third decade earns more than the first two put together. Between 20 and 30 years, the value at 6% goes from €69,306 to €150,677, though you only added €18,000.
This lopsidedness is why duration matters more than amount in the formula. Doubling the deposit doubles the result. Doubling the duration does far more than double it.
For the same monthly deposit, at 6%, the last decade of a thirty-year plan earns more than the first twenty years.
Simple and compound interest: the same deposit, two curves
Simple interest is worked out on the starting capital alone. Each year pays the same sum, whatever happens. With €10,000 at 4%, that is €400 a year, every year, for thirty years: €12,000 of interest in total.
Compound interest is worked out on the starting capital plus the interest already earned. The first year also pays €400. The second pays 4% of €10,400, so €416. The thirtieth pays 4% of €31,187, so €1,247.
| After | Simple interest | Compound interest | Gap |
|---|---|---|---|
| 1 year | €10,400 | €10,400 | €0 |
| 5 years | €12,000 | €12,167 | €167 |
| 10 years | €14,000 | €14,802 | €802 |
| 20 years | €18,000 | €21,911 | €3,911 |
| 30 years | €22,000 | €32,434 | €10,434 |
The table takes €10,000 at 4% a year, compounded once a year, under both methods. Over five years, the gap is small change. Over thirty, compound interest has produced almost twice what simple interest has.
Simple interest still exists, mostly on short loans and on term accounts that pay the interest out somewhere else. As soon as the interest stays in the account that produced it, the calculation becomes compound, whether or not anyone uses the word.
Simple interest moves in a straight line, compound interest in a curve, and the gap between them widens with the years.
Monthly compound interest: how often it compounds changes little
"Compounding" means adding the interest to the capital. It can happen once a year, every quarter, every month or every day. The more often it happens, the sooner interest starts earning interest, and the higher the final value. But the effect is small.
| Compounding | €10,000 at 4% after 10 years | Effective annual rate |
|---|---|---|
| Yearly | €14,802 | 4.000% |
| Quarterly | €14,889 | 4.060% |
| Monthly | €14,908 | 4.074% |
| Daily | €14,918 | 4.081% |
Between yearly and daily compounding, the gap over ten years is €116 on €10,000 invested. The effective annual rate, the one that compares two offers with different frequencies, rises from 4.000% to 4.081%. That is real, and it is marginal next to the effect of the rate itself or of the duration.
The calculator on this page compounds every month, because the deposits in it are monthly. A calculator that compounds once a year will show a slightly lower figure for the same nominal rate. Neither is wrong: they describe two conventions, and a contract always states which one it uses.
The rule of 72 gives an order of magnitude without any calculator: 72 divided by the annual rate gives roughly the number of years it takes to double a sum. At 4%, that gives 18 years; the exact formula says 17.7. At 6%, the rule gives 12 years; the formula says 11.9.
Going from yearly to daily compounding is worth less than a tenth of a point of interest rate.
What inflation takes out of the calculation
The €150,677 in the table at 6% over thirty years are 2056 euros. They will not buy what €150,677 buys today, and the formula does not say so.
According to the flash estimate published by the European Central Bank on 1 September 2026, annual inflation in the euro area stands at 3.3% for August 2026, after 2.9% in July. The full series is series HICP.M.U2.N.000000.4D0.ANR on the ECB data portal. These are one month's figures, not a thirty-year average: they date the order of magnitude without fixing it.
The ECB, in its monetary policy strategy, aims for 2% inflation over the medium term. Nobody knows what the real average will be over the next thirty years.
The real return is worked out by dividing, not subtracting: (1 + 6%) / (1 + 3.3%) − 1 gives 2.61%, not 2.7%. With 2% inflation, the same 6% nominal comes to 3.92% real. Applied to the €150,677 in the table, that gives the equivalent of €83,185 in today's money if average inflation is 2%, and €56,890 if it is 3.3% every year for thirty years.
Another way to see it: at 3.3% a year, a basket that costs €100 today costs €138 in ten years and €191 in twenty. Compound interest applies to inflation exactly as it does to savings, in the other direction.
Two other things are missing from the bare formula: fees, which come off the nominal rate before any calculation, and tax on the interest, which depends on the country of residence and on the type of account. For a cross-border worker paid in Luxembourg, those rules are the ones of the country of residence, and they do not fit inside a calculator.
The formula counts euros, inflation counts what they buy, and in thirty years' time only the second figure will matter to you.
Frequently asked questions
How do you calculate compound interest?
For a single sum C invested for n periods at a rate r per period, the final value is C × (1 + r)^n. For a regular deposit M, it is M × ((1 + r)^n − 1) / r. The rate r and the number n refer to the same period: if the rate is monthly, n is counted in months. €10,000 at 4% a year is worth €14,802 after ten years with yearly compounding.
What is the difference between simple and compound interest?
Simple interest is worked out each year on the starting capital alone, so it always pays the same sum. Compound interest is worked out on the starting capital plus the interest already earned, so it pays a little more each year. On €10,000 at 4%, the gap is €167 after five years and €10,434 after thirty.
How much does €100 a month make over 20 years?
It depends entirely on the rate, which is an assumption. With the formula on this page and monthly compounding, €100 a month for 20 years gives €36,677 at 4% and €46,204 at 6%, for €24,000 paid in. Interest therefore comes to €12,677 in the first case and €22,204 in the second. These amounts are in end-of-period euros, before fees, before tax and before inflation.
How often is interest compounded?
It depends on the contract, which always states its convention. Regulated savings accounts in France often compound once a year; calculators built around monthly deposits compound every month. The gap between the two conventions is small: on €10,000 at 4% over ten years, daily compounding pays €116 more than yearly compounding.
Key points
- The compound interest formula for a monthly deposit is M × ((1 + r)^n − 1) / r, with r the monthly rate and n the number of months.
- With €150 a month and an assumed 6% a year, the share of interest in the final value goes from 27% at ten years to 64% at thirty.
- Simple interest applies to the starting capital alone, compound interest to the capital plus the interest already earned; the gap widens with time.
- Compounding frequency matters little: between yearly and daily, less than a tenth of a point of effective rate.
- Inflation, at 3.3% in the euro area for August 2026 according to the ECB flash estimate, comes off the nominal return by division, and the formula's result is in future euros.