Compound interest, made concrete

Compound interest is often called the most powerful force in personal finance — and yet it's a plain idea: returns start to earn returns of their own. The magic isn't in any single year, but in a run of them. This article shows the principle through illustrative examples; the numbers are there to make the mechanics clear, not as a promise of returns.

What it is: returns on returns

With a one-off deposit, the interest (or return) in the first year is simply added on. The difference shows up in year two: now it's not only the original deposit that earns, but also last year's return. And in year three, even the return on that return earns. The base the calculation runs on grows every year — and so does the amount added.

Simple interest grows in a straight line. Compound interest grows along a curve that keeps rising more steeply over time.

Simple vs. compound interest

Picture a deposit of €4,000 and an annual return of 7% (purely illustrative).

With simple interest the same €280 is added each year, always from the original sum. With compounding, 7% is added to a growing base, so the yearly increase rises year after year. After the first year the two numbers are identical — after thirty years the compound result is more than double. That widening gap is called exponential growth.

The power of time: two investors

Nothing shows the power of time better than comparing two people (again illustrative, 7% a year):

• Early starts at 25, sets aside €80 a month for ten years, and stops at 35. She puts in €9,600 in total, then just lets the money grow.
• Late starts only at 35 and sets aside €80 a month until 65 — thirty years without a break, €28,800 of contributions in all.

At 65, Early often ends up with more, even though she put in three times less money and last contributed thirty years earlier. How? Her first ten years of contributions also had thirty years to compound — and those thirty years do the heaviest lifting. Late's extra money never fully closes that head start.

The lesson isn't “contribute little”, but: time is a stronger lever than the size of your contributions. Every year of delay removes exactly the most valuable, longest-compounding years.

Reinvested dividends as compounding

Compounding doesn't have to come from price growth alone. With stocks and funds that pay dividends, a second engine appears: if you don't spend the dividends you receive but buy more shares with them, those new shares start paying dividends of their own. Return breeds return — precisely the compounding principle.

That's why long-term charts distinguish “price” from “total return”: the latter assumes dividends are reinvested and, over time, pulls sharply away from price alone. Accumulating funds do the same automatically — they reinvest the dividends inside the fund.

What slows compounding down

The very mechanics that work for you can work against you too, because every drag also compounds:

• Fees. One extra percentage point of annual fees doesn't vanish over decades — it cuts the final amount by far more than “one percent”, because it nibbles at a base that would otherwise keep compounding.
• Taxes. Being taxed along the way (rather than deferring to the end) shrinks the amount that goes on earning.
• Inflation. Nominal growth is one thing, purchasing power another. The real return is the one left after subtracting inflation — and only that tells you about actual wealth.
• Early withdrawals. Taking part of the portfolio out early removes the base from exactly the most valuable later years of compounding. Interrupting is costlier than it looks.

Where Invest Control helps

For compounding to work, you need to see the total return — the growth in value and reinvested dividends together, not just the current price. Invest Control tracks the historical value of your portfolio across currencies as well as dividends, so you can see the compounding effect on real data. Where the accumulated capital is headed is the subject of the intro to FIRE; and how to draw from it safely later is covered by the 4% rule.