What "compound interest" means
Interest is simple when it is computed each year on the starting sum and then withdrawn. It is compound when it stays put: the following year, the calculation applies to the capital plus the interest already earned. That is all. The whole difference comes from that one sentence.
"Interest" is meant broadly here: it also covers a reinvested dividend, or the unrealised gain on a holding you keep.
The same money, two ways of counting
€10,000 at 6% a year. On the left the interest is withdrawn every year; on the right it stays.
| After | Interest withdrawn | Interest reinvested | Gap |
|---|---|---|---|
| 5 years | €13,000 | €13,382 | €382 |
| 10 years | €16,000 | €17,908 | €1,908 |
| 20 years | €22,000 | €32,071 | €10,071 |
| 30 years | €28,000 | €57,435 | €29,435 |
At five years the gap is €382: negligible, which is exactly why the mechanism looks anecdotal when you start. At thirty years it exceeds the sum originally invested.
Why the curve steepens
The dashed line rises by €600 every year, indefinitely. The solid curve rises by €600 in the first year, €900 in the tenth, €3,250 in the thirtieth: what you earn depends on what has already been earned.
The snowball effect, in figures
The common case is not a single sum but a regular contribution. €200 a month for 30 years, with an assumed return of 5% a year:
| After | You have paid in | Value | Share coming from interest |
|---|---|---|---|
| 5 years | €12,000 | €13,601 | 12% |
| 10 years | €24,000 | €31,056 | 23% |
| 20 years | €48,000 | €82,207 | 42% |
| 30 years | €72,000 | €166,452 | 57% |
After thirty years, most of the sum was not paid in by the saver. That tipping point, around year twenty in this example, is what people call the snowball effect.
Half the result arrives in the final third
The same example, split by decade. The monthly effort is identical in all three:
| Period | What the value gains |
|---|---|
| Years 1 to 10 | +€31,056 |
| Years 11 to 20 | +€51,150 |
| Years 21 to 30 | +€84,245 |
The figure worth keeping
The last decade brings 51% of the final total, for exactly the same monthly contribution as the first. Put differently: starting ten years later, with the same effort, does not cost a tenth of the result but half of it.
Capital and return do not play the same part
The rate gets discussed a lot, the sum much less. Over twenty years the two do not offset each other the way one imagines:
| Starting sum | Assumed return | After 20 years |
|---|---|---|
| €10,000 | 7% a year | €38,697 |
| €20,000 | 5% a year | €53,066 |
| €50,000 | 3% a year | €90,306 |
Here the highest rate gives the lowest result. Over a given horizon the base matters more than the percentage, and the base is the only one of the two that depends on you.
What these calculations do not say
These are multiplications, not forecasts. Four reservations to keep in mind:
- No return is guaranteed. The 5% and 6% used above are calculation assumptions, chosen to keep the arithmetic readable. They are neither a promise nor an average to expect.
- A market does not rise at a constant rate. It alternates gains and falls; two paths with the same average do not produce the same final result, depending on the order of the years.
- Inflation eats into the result. The €166,452 in the example, with 2% inflation a year, represent the purchasing power of €91,893 today. At 5% nominal with 2% inflation, the real return is 2.94% a year, not 3%.
- Tax and fees apply. They depend on the wrapper and the product, and they are subtracted from the return every year, so they compound too, in the opposite direction.
And the Einstein quote?
You will often read that Albert Einstein called compound interest "the eighth wonder of the world", or humanity's greatest invention. That attribution is not sourced. It appears in no verifiable writing or statement of his; it has circulated in financial advertising for decades, which does not make it a quotation.
We mention it because it keeps coming back, and because a mechanism this solid needs no invented endorsement. The multiplication table above can be checked with a calculator, which is a better guarantee than a famous name.
Doing it with your own figures
The examples above are deliberately round. To project your actual situation, with your contributions and your horizon, the page Projection: what Monte Carlo does and does not tell you explains how to read a simulation, and why a range is more honest than a single number.
PulseMyPortfolio is a tracking and analysis tool. It describes mechanisms and computes on your data; it does not steer any investment decision, and we are not a financial investment adviser.