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Compound interest calculator
Geschrieben von
Janine El-Saghir
Finanzanalystin & Wirtschaftsredakteurin
Dr. Janine El-Saghir ist eine erfahrene Finanzanalystin und Wirtschaftsredakteurin, die sich darauf spezialisiert hat, komplexe Finanzthemen für Anleger verständlich aufzubereiten. Mit über 16 Jahren Erfahrung...
- Compound interest means the interest stays invested and earns interest itself the following year. €10,000 at 3% grows to €13,439.16 in ten years instead of €13,000.00 – the €439.16 are the compounding effect.
- The effect grows faster than the capital: after ten years it makes up 12.8% of the interest earned, after 30 years 36.9%, after 40 years almost half.
- Time works like rate: €10,000 at 3% for 40 years gives €32,620.38, at 6% for 20 years €32,071.35.
- Doubling takes 23.45 years at 3% and 11.90 years at 6%. Rule of thumb: 72 divided by the interest rate.
- The calculator starts with compound interest switched on, credits interest once a year and has no field for regular contributions.
What the compounding effect is
Invest €10,000 at 3% and you receive €300 of interest after one year. Leave it in the account and the bank pays interest on €10,300 in the second year – that is €309, so €9 more. In the third year it is €318.27 on €10,609, and after three years the account holds €10,927.27 instead of €10,900. Those €27.27 are interest on interest: the compounding effect.
The formula behind it: future value = principal × (1 + interest rate)years. Without compounding, interest is calculated on the principal alone every year and the balance grows in a straight line: principal × (1 + interest rate × years). The compounding effect is the difference between the two results.
The calculator shows the future value and the interest earned. To isolate the effect itself – the part of the interest that comes from interest on interest – run it twice, once with compound interest set to “Yes” and once with “No”; the difference between the two future values is the compounding effect. For the common cases it is already worked out in the tables below. If you are looking for one of the other quantities – the principal, rate or term you would need – switch the “Solve for” selector at the top; three inputs stay, the fourth is calculated.
How big the effect gets
In the first years the compounding effect is small, because little interest has accumulated that could earn interest of its own. Over time the ratio turns around:
| Term | without compounding | with compounding | compounding effect | share of interest earned |
|---|---|---|---|---|
| 5 years | €11,500.00 | €11,592.74 | €92.74 | 5.8% |
| 10 years | €13,000.00 | €13,439.16 | €439.16 | 12.8% |
| 20 years | €16,000.00 | €18,061.11 | €2,061.11 | 25.6% |
| 30 years | €19,000.00 | €24,272.62 | €5,272.62 | 36.9% |
| 40 years | €22,000.00 | €32,620.38 | €10,620.38 | 47.0% |
| Own calculation following the calculator’s logic, as at 2 September 2026. “Share of interest earned”: compounding effect divided by total interest with compounding. | ||||
After 40 years almost every second euro of interest comes not from the principal but from interest that has itself earned interest. The interest rate amplifies this once more:
| Interest rate | without compounding | with compounding | compounding effect |
|---|---|---|---|
| 1% | €12,000.00 | €12,201.90 | €201.90 |
| 2% | €14,000.00 | €14,859.47 | €859.47 |
| 3% | €16,000.00 | €18,061.11 | €2,061.11 |
| 5% | €20,000.00 | €26,532.98 | €6,532.98 |
| 7% | €24,000.00 | €38,696.84 | €14,696.84 |
| Own calculation following the calculator’s logic, as at 2 September 2026. | |||
At 7% the effect after 20 years is larger than the principal itself. Rates like that do not exist for savings accounts – they are here because compounding matters most exactly where returns are high and terms are long: in long-term equity investments with reinvested income.
Time or rate: which matters more
The rule of 72 condenses both into one number: 72 divided by the interest rate gives roughly the number of years until an amount has doubled.
| Interest rate | exact | rule of 72 |
|---|---|---|
| 1% | 69.66 years | 72.0 years |
| 2% | 35.00 years | 36.0 years |
| 3% | 23.45 years | 24.0 years |
| 4% | 17.67 years | 18.0 years |
| 6% | 11.90 years | 12.0 years |
| 8% | 9.01 years | 9.0 years |
| Exact: ln 2 : ln(1 + rate). Own calculation, as at 2 September 2026. Between 4% and 10% the rule is accurate to within half a year; at 1% it is off by more than two years. | ||
Doubling the interest rate works almost exactly like doubling the time: €10,000 at 3% for 40 years gives €32,620.38, at 6% for 20 years €32,071.35. The difference is that you choose the term and not the rate. Whoever starts early can make do with a lower rate – which is the whole reason compound interest appears in every guide to building wealth.
Once a year, partial years pro rata
The calculator adds the interest to the capital at the end of each full year. If the term is entered in months, it compounds the full years and treats the remainder pro rata: 18 months are one year plus a half, so €10,000 at 3% becomes €10,454.50 – €300 for the first year and €154.50 for the half year on €10,300.
Some banks credit interest quarterly or monthly. Compounding then kicks in more often and the future value ends up slightly higher: €10,000 at 3% over ten years gives €13,439.16 with annual crediting, €13,483.49 with quarterly and €13,493.54 with monthly crediting. The calculator models annual crediting only; at usual rates the deviation stays below half a percent of the future value.
Tax slows compounding down
The taxation section lets you switch on German capital gains tax. The defaults are 26.375% – the 25% flat rate under section 32d (1) of the Income Tax Act (Einkommensteuergesetz, EStG) plus the 5.5% solidarity surcharge on it – and a saver’s allowance of €1,000 per year (section 20 (9) EStG). Each year the calculator deducts tax from the interest above the allowance and reinvests only the net interest.
That is exactly what makes tax more expensive under compounding than the rate suggests: whatever is withheld is missing as capital in every following year. €100,000 at 3% over ten years gives €134,391.64 before tax and €127,333.00 after tax. The deduction of €6,209.28 corresponds to a net rate of 2.45% instead of 3%. With the preset €10,000, however, the switch changes nothing, because €300 of annual interest stays below the allowance – at 3% that holds up to an investment of roughly €33,300.
The allowance only works at the bank once you have filed an exemption order (Freistellungsauftrag). Without it the bank withholds tax from the first euro, and compounding works with correspondingly less until you reclaim the tax through your tax return. How the flat rate, surcharge and church tax add up, and what applies if your broker is abroad, is explained next to the capital gains tax calculator.
A lump sum only
The calculator applies interest to an amount invested once at the start. It has no field for later deposits or monthly contributions. If you save regularly, use the savings calculator, which compounds the principal and the contributions together – it also offers the choice between reinvesting and paying out, which here is handled by the “Compound interest” switch.
Nor does the calculator model an interest rate that changes during the term. Calculate such phases one after another and enter the future value of the first as the principal of the second. All amounts are nominal – how much purchasing power they will have is a question for the inflation calculator – and are shown to the cent; the precision applies to the arithmetic, not to the assumption about the rate.
The calculator is a computing tool and does not replace investment or tax advice.
Sources
- German Income Tax Act: section 32d EStG (25% rate), section 20 EStG (saver’s allowance), section 4 SolzG 1995 (5.5% solidarity surcharge) – German only, retrieved 2 September 2026
- German Income Tax Act: section 44a EStG (exemption order) – German only, retrieved 2 September 2026
- Worked examples and tables: own calculation following the logic of the embedded calculator (annual crediting, pro-rata partial year, allowance per year) and the compound interest formula, as at 2 September 2026
Frequently asked questions
It applies the annual interest rate to the principal, adds the interest to the capital at the end of each year and applies the rate to the new balance in the following year. From three of the four quantities – principal, rate, term and future value – it works out the fourth; the “Solve for” selector decides which. With the presets, €10,000 at 3% for ten years, it shows a future value of €13,439.16.
Interest earned on interest that has already been credited. If €10,000 earn 3%, the first year yields €300; in the second year the bank pays 3% on €10,300, which is €309. The extra €9 are compound interest. Over ten years the difference to simple interest adds up to €439.16, over 30 years to €5,272.62.
Yes: future value = principal × (1 + rate) to the power of the years. €10,000 × 1.03¹⁰ = €13,439.16. Without compounding the balance grows in a straight line: principal × (1 + rate × years) = €13,000.00. The difference between the two is the compounding effect. The calculator applies the same arithmetic year by year, which is why it can also handle tax deductions and terms entered in months.
No. The calculator works with a single lump sum and credits interest once a year; partial years are calculated pro rata. Regular contributions are handled by the savings calculator, which also offers monthly to yearly intervals. Monthly crediting, which some banks offer, would give slightly more: €13,493.54 instead of €13,439.16 for €10,000 at 3% over ten years.
Because the effect grows faster than the capital. After ten years at 3% it makes up 12.8% of the interest earned, after 30 years 36.9%, after 40 years 47.0%. And doubling the time works almost like doubling the rate: €10,000 at 3% for 40 years gives €32,620.38, at 6% for 20 years €32,071.35. Time is the one factor you control.
Yes. Set “Solve for” to “Interest rate” and enter principal, future value and term. To double €10,000 in ten years you need 7.18% per year with compounding and 10.00% without. The result is shown to two decimal places.
Yes. Set “Solve for” to “Term” and enter principal, future value and rate. Doubling takes 23.45 years at 3% and 11.90 years at 6%. The rule of 72 – 72 divided by the rate – gives a quick estimate: 24 and 12 years.
Optionally. Switch on the tax option and the calculator deducts, every year, the rate you enter – the default is 26.375%, the 25% flat tax plus the 5.5% solidarity surcharge – from the interest above the saver’s allowance of €1,000, and reinvests only the net interest. €100,000 at 3% over ten years gives €134,391.64 before tax and €127,333.00 after tax. Church tax is not added automatically; enter 27.8186% (8%) or 27.9951% (9%) yourself.