Albert Einstein reportedly called it "the eighth wonder of the world." Whether or not the anecdote is true, compound interest is probably the most underrated financial concept for the average saver, and understanding it well can make a huge difference in how you plan your long-term finances.
Simple interest vs. compound interest
Simple interest is always calculated on the initial principal. If you deposit €10,000 at 5% annual simple interest, you earn €500 every year, always on that original €10,000.
Compound interest, on the other hand, is calculated on the principal plus the interest already earned. Each period, the base used to calculate interest grows, because previous interest becomes part of the principal. It's literally "interest on interest."
An example with real numbers
Imagine €10,000 invested at 5% annual return over 20 years, with no additional contributions:
| Year | With simple interest | With compound interest |
|---|---|---|
| 5 | €12,500 | €12,763 |
| 10 | €15,000 | €16,289 |
| 20 | €20,000 | €26,533 |
The difference looks small at first, but it accelerates over time. By year 20, compound interest generates 33% more than simple interest on the same principal and the same rate.
The compound interest formula
For a principal that compounds monthly:
Final capital = Initial capital × (1 + monthly interest rate)^number of months
If you also add a fixed periodic contribution, the calculation gets more complex, because each contribution earns interest for a different number of periods. That's why it's worth using a calculator instead of doing it by hand once monthly contributions are involved.
Why time matters more than the amount
The variable that most influences the final result isn't how much you contribute each month, but how long you let the capital compound. Starting to save 5 years earlier, even with modest contributions, usually builds more final wealth than starting later with larger contributions, precisely because compound interest needs time to accelerate.
Compounding frequency matters too
The same annual interest rate produces slightly different results depending on whether it compounds annually, quarterly, or monthly. The more frequent the compounding, the sooner previous interest starts earning interest of its own, and the higher the final result — though the difference tends to be modest except over very long horizons.
An important caveat
Everything above is pure mathematics: it describes how compound interest behaves, but it doesn't guarantee the return of any specific financial product. No savings or investment product guarantees a constant interest rate indefinitely, and past performance never guarantees future returns. Before investing, it's worth understanding the real risk of the chosen product, not just the mathematical projection.
Simulate your own scenario
With our compound interest calculator you can enter your initial capital, your monthly contribution, and your intended time frame, and see your projected savings grow year by year.