Compound interest
Compound interest is interest calculated on the starting capital plus the interest already accumulated: each period starts from the larger capital the previous one left, which is why growth accelerates over time. It is the mechanism behind any long-term investment, dividend reinvestment and the terminal value of a DCF.
How it is calculated
With €10,000 at 5% a year for ten years: the first year earns €500 and the capital becomes €10,500; the second, €525 on €10,500; the tenth, €776. At the end there is €16,289, which is 10,000 × 1.05¹⁰. With simple interest, always €500 a year, there would be €15,000. The difference, €1,289, is the interest earned by the interest. Over twenty years the gap widens: €26,533 compounded against €20,000 simple. With regular deposits the arithmetic runs month by month, and that is what the calculator is for.
The figures in the example are invented and rounded so the arithmetic can be redone by hand. They are not data from any real company.
What it is NOT
It is not a guaranteed return nor a promise that money "works on its own": the formula multiplies by whatever the asset actually returns, and if that is zero or negative, it compounds in that direction. Nor is compounding yearly the same as monthly, although the difference is small next to the one years make. And the rule of 72 (72 ÷ return = years to double) is a back-of-the-envelope approximation, not the formula.
Formula
Final capital = Starting capital × (1 + r)ⁿ On real data
Starting capital, monthly deposit, return and years, with the year-by-year table: compound interest calculator. And the annual rate between two values: CAGR calculator.
See it on real data
Celsmar computes this from the accounts companies file with their regulator, and shows which line every figure comes from. Free to start, no card.
Definition for informational purposes. It is not financial advice nor a recommendation to buy or sell.