Compound interest is the most important financial concept most people never formally learn. Einstein supposedly called it the eighth wonder of the world. He probably didn't, but the line stuck because the idea is genuinely strange: a number can grow at a rate that itself grows, and the long-run effect is non-linear in a way human intuition is bad at picturing.
What the calculator does
One starting amount, one annual rate, one time horizon. Under the hood the math compounds daily, which is how real savings accounts and real credit cards work. You enter the rate the way it's quoted in the world (annual, e.g. "18% APR" or "5% return") and the calculator does the daily-compounding math in the background. The number you see is what you'd actually have or owe, not a simplified annual approximation.
The chart shows two lines: what your money does with compounding (solid line, green for savings, red for debt) and what it would do without (dashed line, the principal sitting flat). The gap between them is the compounding effect. At low rates and short horizons, the gap is barely visible. At higher rates or longer horizons, the gap dominates the chart.
Why both directions matter
The same math that makes savings grow makes debt grow. A €10,000 credit card balance at 18% interest, left to compound, becomes €27,000 after six years and €71,000 after 12. Most people who carry credit card debt do not realise this is happening; the monthly minimum payment hides the slope of the curve.
The savings direction is more familiar but no less surprising. €10,000 invested at 7% returns over 30 years becomes €76,000, and three quarters of that is interest, not contributions. The first decade looks slow. The last decade looks dramatic. That's compounding doing what it does: starting quietly, finishing loudly.
What this calculator deliberately leaves out
No monthly contributions, no tax, no inflation adjustment, no compounding frequency choice. Each of those is a real factor in real financial planning, but adding any one of them turns this from a teaching tool into a forecasting tool, and the lesson gets lost in the inputs.
For real planning, use a calculator that handles those things. For understanding what compounding fundamentally is, ignore everything except the starting amount, the rate, and the time. That's why this calculator only asks for those three.