Compounding calculator
How much can a starting amount and a fixed monthly amount grow to when the return is also earned on the returns of earlier years? Enter your own amounts and your own return: the result appears straight away.
A worked example
With €1,000 to start, €100 a month and 6% a year for 20 years, the balance reaches €49,514. Of that, €25,000 is what you put in and €24,514 is growth. The 6% is an illustrative assumption, not a forecast.
| After | Put in | Balance | Growth |
|---|---|---|---|
| 5 years | €7,000 | €8,326 | €1,326 |
| 10 years | €13,000 | €18,207 | €5,207 |
| 15 years | €19,000 | €31,536 | €12,536 |
| 20 years | €25,000 | €49,514 | €24,514 |
A second example with no monthly amount: €10,000 invested once and left alone at 6% a year ends at €18,194 after 10 years and at €33,102 after 20 years. Of the €33,102, €10,000 is what you put in and €23,102 is growth, more than twice the amount you started with. The first 10 years add €8,194; the next 10 add €14,908.
How it calculates. The tool works month by month. Each month the balance grows by one twelfth of the yearly return, and your contribution is added at the end of the month: new balance = old balance × (1 + return ÷ 12) + monthly amount. 6% a year is applied as 0.5% per month, which compounds to about 6.17% a year. Amounts are rounded to whole cents every month.
How to read the result. What you put in rises by the same €6,000 every five years, but the growth does not: in the first five years it adds €1,326, in the last five years €11,978. That acceleration is compounding. If you shorten the horizon, the growth part shrinks much faster than the amount you put in.
What is not included. Fund costs (TER), inflation, tax and transaction costs are left out, and the return is the same every month, while real returns fluctuate and can be negative. To see what ongoing fund costs do, use the ETF Calculator or Compare ETF costs.
Where it comes from. The tool uses the same calculation engine as the ETF Calculator, with fund costs set to zero. The return is your own input: the tool knows no prices, fetches nothing and stores nothing.
Questions about compounding
Why does the growth speed up over time?
Because the return is also earned on the growth of earlier years. In the first example the first five years add €1,326 and the last five years add €11,978, although the monthly amount is the same throughout. The balance is larger at the end, so the same percentage is applied to more money.
Which return should I enter?
That is your own choice: the tool does not know what any investment will return. The default of 6% a year is an illustrative assumption, not a forecast. Try several figures, including a low one and 0%. At 0% the balance is simply what you put in (€25,000 in the first example), so the whole difference with the other results is what the return adds.
Are costs, tax and inflation included?
No. Fund costs, tax, transaction costs and inflation are left out, so the result is a gross illustration. To see what ongoing fund costs do over the years, use the ETF Calculator or Compare ETF costs.
How the calculation works
The tool takes the yearly return you enter and divides it by 12. Every month it does two things in order: it multiplies the balance by one plus that monthly rate, and then it adds your monthly amount. In words: new balance = old balance × (1 + yearly return ÷ 12) + monthly amount. The result is rounded to whole cents each month, and the step repeats for every month of the horizon, so 20 years means 240 steps.
One line of arithmetic with the default settings: in month 1, €1,000 × (1 + 0.06 ÷ 12) + €100 = €1,000 × 1.005 + €100 = €1,105.00. Month 2 starts from €1,105.00 and applies the same step. At a return of 0% the multiplication changes nothing, so the balance is simply the start amount plus all monthly amounts.
Two other situations
Both situations below use the tool’s own calculation. The returns are assumptions chosen to show the mechanics, not forecasts: real returns fluctuate, can be negative in any year, and past performance guarantees nothing.
Saving from zero. Someone starts with nothing and puts away €200 a month for 15 years at an assumed 6% a year. The balance reaches €58,164: €36,000 is put in and €22,164 is growth. After 5 years the balance is €13,954, of which €1,954 is growth; over the last five years alone the growth is €13,388, although the monthly amount never changed. At 0% the balance would be exactly the €36,000 put in.
Starting with a lump sum. Someone starts with €20,000 and adds €300 a month for 10 years at an assumed 3% a year. The balance reaches €68,909: €56,000 is put in and €12,909 is growth. After 5 years the balance is €42,626 (growth €4,626); the last five years add €8,283. Here the start amount is large compared with the monthly amounts, so more of the balance is what was put in. At 0% the balance would be the €56,000 put in.
| Situation | Put in | Balance | Growth |
|---|---|---|---|
| €0 start, €200 a month, 15 years, 6% | €36,000 | €58,164 | €22,164 |
| €20,000 start, €300 a month, 10 years, 3% | €56,000 | €68,909 | €12,909 |
Common mistakes when reading the result
- Reading the return as a promise. It is an assumption that shows how the maths works; real returns differ from year to year and can be negative.
- Entering a yearly amount in the monthly field, which overstates the result twelve times.
- Judging a long horizon by a short one. The growth in the last years is far larger than in the first, so stopping early hides most of the effect.
What the calculation leaves out
The result is a gross illustration with a fixed return. Several things that matter in practice are not in it:
Costs. Fund costs and transaction costs are not deducted, so a real balance would be lower. Inflation. The amounts are in euros of the day they are reached; the same euros will buy less later. Tax. Tax is not calculated; Box 3 may apply to your assets, but this tool does not take it into account. Fluctuation. A real investment does not earn the same percentage every month. A year with a loss changes the end result, and the order in which good and bad years arrive matters when you keep adding money. Your own plans. The tool assumes the monthly amount stays the same and that you leave everything untouched until the end.
The figures on this page illustrate how compounding works. They are not advice and not a prediction of what any investment will return.
Further reading: