If you were to understand just one concept from all of financial mathematics, let it be compound interest. It is the mechanism that makes long-term investing something other than saving - and it explains why time plays a bigger role in investing than the amount. This article takes it apart step by step, with concrete calculations.
The mechanics: returns on returns
Imagine you invest CZK 100,000 and the investment earns 7% in a year. You have CZK 107,000. Nothing remarkable so far - that is an ordinary simple return.
What matters is what happens in the second year. The 7% return is no longer calculated on CZK 100,000 but on CZK 107,000 - including last year's return. You gain CZK 7,490 and have CZK 114,490. In the third year, CZK 114,490 earns interest and CZK 8,014 is added. Each year the increase is a little larger, even though the percentage stays the same. Returns earn returns of their own - and that is exactly what compound interest means.
The difference from simple interest seems negligible at first, but it widens with time. At a hypothetical return of 7% a year, CZK 100,000 would grow with simple interest to CZK 310,000 over 30 years (plus CZK 7,000 each year). With compound interest, to roughly CZK 761,000. Same amount, same percentage, same period - and more than double the result. The entire difference was created by returns on returns.
The Rule of 72: a quick mental estimate
You do not need a calculator to roughly gauge the power of compounding. The Rule of 72 says: divide 72 by the annual return in percent and you get the approximate number of years it takes for an investment to double.
- At a hypothetical return of 4% a year: 72 / 4 = doubling in roughly 18 years
- At a hypothetical return of 6% a year: 72 / 6 = roughly 12 years
- At a hypothetical return of 8% a year: 72 / 8 = roughly 9 years
The rule works in reverse too - it shows what inflation does to uninvested money. At 3% annual inflation (72 / 3 = 24), cash loses half its purchasing power in roughly 24 years. Compounding works in both directions: for those who own assets, and against those who hold nothing but cash.
What different horizons do: a worked example
The power of compound interest shows best on a single amount over different lengths of time. Take a one-off investment of CZK 100,000 at a hypothetical return of 7% a year - no additional purchases, just time:
- After 10 years: roughly CZK 197,000 - the returns amount to about half the deposit
- After 20 years: roughly CZK 387,000 - the returns are already nearly three times the deposit
- After 30 years: roughly CZK 761,000 - the deposit is only a fraction of the result
- After 40 years: roughly CZK 1,497,000 - the last ten years added more than the first thirty combined
Notice the last line. Between year 30 and year 40, about CZK 736,000 was added - almost as much as over the entire previous three decades. The compound interest curve is not a straight line; it is a curve that climbs ever more steeply with time. That is why each year of delay does not cost "just a year" - it costs the most profitable year at the end.
The same logic explains why starting early beats starting big. Someone who invests CZK 100,000 for 40 years ends up, at the same hypothetical return, about level with someone who invests twice as much ten years later for 30 years (roughly CZK 1,497,000 versus CZK 1,522,000 - double the amount only barely caught up with a ten-year head start). Missing money can be added later; missing years cannot. The article Why invest at all explores this topic in more detail.
Why the first years look boring
This is where most beginners stumble. The first years of compound interest do not look like a miracle - they look like nothing. A year after investing CZK 100,000, at a 7% return you are up CZK 7,000. After three years, about CZK 22,500. These are amounts that impress nobody, and on top of that the market fluctuates along the way, so some years are even negative.
But that is exactly what the boring phase is supposed to look like. Compounding needs a base - and in the first years it is still building one. Most of a long-term investor's total return arises only in the second half of the journey, once the percentages are working with large numbers. Anyone who quits during the boring phase because "nothing is happening" walks away just before the mechanism kicks into full gear.
In practical terms this means one thing: the results of the first years are not the measure of whether investing works. The measure is the discipline to stay.
Reinvestment: the condition without which nothing compounds
The whole effect described here rests on one assumption - the returns stay in the investment. As soon as you withdraw and spend them, compounding stops: next year, only the original amount earns again.
With rising stock prices, reinvestment happens by itself - the value grows inside the investment and flows nowhere else. But watch out for dividends, the profit shares some companies send to shareholders' accounts. A dividend paid out and spent is a pleasant bonus; a dividend used to buy more shares is fuel for compounding - it increases the number of shares that will earn and pay out a little more next time. The long-term difference between spent and reinvested dividends is vast. For an overview of when companies pay their dividends, see the dividend calendar.
Summary
Compound interest means your returns start earning on their own. The Rule of 72 tells you off the top of your head how quickly money doubles at a given return. The growth curve is flat at first and steepens with time - which is why the first years are boring, the last years decisive, and every year of delay expensive. And it all works only as long as the returns stay in the game. Patience is not an extra virtue here; it is the engine itself.