Selurio · Blog
Compound Interest — Why It Is Called the Eighth Wonder of the World
"Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn't, pays it." The quote is usually attributed to Albert Einstein. There is no solid evidence that he ever actually said it — but the idea behind it is entirely true and well worth understanding.
Compound interest is the reason the same money can work dramatically differently for two different people: the one who starts early and stays patient, and the one who keeps putting it off. This article explains exactly how the mechanism works — with no promises of returns and no "buy/sell" signals. Just the formula and its assumptions.
Simple vs. compound interest
With simple interest you earn a percentage only on the original amount. Put in €1,000 at 10% and you receive €100 every year, forever.
With compound interest you earn a percentage on the amount plus the interest already accrued. In the second year the 10% is charged on €1,100, in the third on €1,210, and so on. The gains start generating gains of their own. That "rolling up" — compounding — is the difference between linear and exponential growth.
The formula
Selurio's compound interest calculator uses the standard future-value formula with monthly compounding and regular contributions:
FV = P × (1 + r/12)^(12·t) + PMT × ( (1 + r/12)^(12·t) − 1 ) / (r/12)
Where:
- P — starting capital (the amount you begin with)
- PMT — monthly contribution (how much you add each month)
- r — annual return as a decimal (e.g. 7% → 0.07)
- t — period in years
The first part of the formula compounds the starting capital, while the second sums up every monthly contribution together with the interest it accrues by the end of the period.
The rule of 72
A quick way to feel the power of compounding without a calculator is the rule of 72: divide 72 by the annual return to get roughly how many years it takes for the money to double.
- At a 7% return: 72 / 7 ≈ 10 years to double.
- At 9%: about 8 years.
- At 3% (a typical deposit): a full 24 years.
That is why the same amount at 7% instead of 3% is not "a little better" — it doubles more than twice as often.
Example: the power of time
Take €1,000 of starting capital and a €500 monthly contribution at a 7% average annual return:
- Over 20 years you contribute a total of €121,000, while the final value exceeds €260,000. More than half of that is accrued interest.
- If you extend by just 10 more years (30 in total), the final value more than doubles — because the last years are the ones in which the interest already accrued works hardest.
See the exact numbers and change the assumptions in the compound interest calculator. Try changing only the period from 20 to 30 years — you will see why an early start matters more than the size of the contribution.
The three levers you control
| Lever | Effect | Who controls it |
|---|---|---|
| Time | The strongest — because of the exponent | You (start early) |
| Monthly contribution | Linear, but reliable | You (budget and discipline) |
| Return | Powerful, but riskier and out of your hands | The market, not you |
The takeaway: the only lever that is entirely in your hands and worth the most is time. You cannot guarantee the return, but you can start today.
Assumptions and caveats
Every compound interest calculator makes simplifying assumptions. It is important to know them:
- Constant return. Real markets do not grow by a steady 7% every year — there are ups and downs. The formula assumes an averaged figure.
- No inflation. €260,000 in 20 years will not have the same purchasing power as today. Inflation quietly eats part of the return — see real return to understand why.
- No taxes or fees. Commissions and capital-gains tax reduce the final result.
Continue reading
- Real return: what is your money really worth? — why inflation eats part of the interest.
- DCA: why regular investing beats market timing — how to deploy your contributions in practice.
- Retiring at 40 in Bulgaria — compounding is the engine of financial independence.
- Investing for beginners 2026 — if you are just starting out.
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