What compound interest is
Compound interest is, in one sentence, earning interest on your interest. Instead of withdrawing what you earn each year, you leave it in so it also produces a return. Year after year the snowball grows on its own, faster and faster.
The key is the intuition: the money you don't withdraw works for you.
Simple interest vs. compound interest
Imagine you invest €1,000 at 7 % a year.
- With simple interest, you earn €70 every year, always on the original €1,000. After 10 years: €700 of interest.
- With compound interest, in the second year you earn 7 % of €1,070, not of €1,000. And so on. After 10 years: €967 of interest.
The gap looks small over a decade, but it explodes with time.
A step-by-step numerical example
Starting from €1,000 at 7 % a year, with no new contributions:
| Year | Starting balance | Interest (7 %) | Ending balance |
|---|---|---|---|
| 1 | €1,000.00 | €70.00 | €1,070.00 |
| 2 | €1,070.00 | €74.90 | €1,144.90 |
| 3 | €1,144.90 | €80.14 | €1,225.04 |
| 4 | €1,225.04 | €85.75 | €1,310.80 |
| 5 | €1,310.80 | €91.76 | €1,402.55 |
Look at the interest column: it keeps growing even though the percentage is always the same. That is the compounding effect.
The formula
Final value = C × (1 + r) ^ n
Where C is the initial capital, r the annual return (0.07 for 7 %) and n the number of years. With €1,000, 7 % and 30 years:
1,000 × (1.07)³⁰ ≈ €7,612
Without adding a single euro, the money multiplies by more than 7 in 30 years.
The two ingredients that matter most
- Time. It is the most powerful factor, because the exponent n rules. Ten years of head start are worth more than one extra point of return.
- Consistency. If you also contribute every month, each contribution starts its own snowball. Starting early and never stopping is almost the whole secret.
What slows the snowball down
- Inflation erodes purchasing power: a 7 % return with 3 % inflation is equivalent to a 4 % real return.
- Fees are subtracted every year from the capital that compounds, so a 1 % fee does far more damage over the long run than it seems.
- Withdrawing the interest breaks the very mechanism you wanted to exploit.
The rule of 72: quick mental maths
To know how long your money takes to double, divide 72 by the annual return. At 7 %, you double in about 72 ÷ 7 ≈ 10 years; at 3 %, in 24. It gives you instant intuition with no calculator and makes clear why a couple of points of return —or of fees— change the outcome so much.
The mistake that costs the most
Starting late. Someone investing €200/month from age 25 reaches 65 with far more than someone who starts at 35 contributing twice as much, because those first euros get an extra 10 years of compounding, and they compound the most. Lost time can't be bought back by adding money later. Start with whatever you can, today, and don't interrupt the process: that is almost the whole secret.