Compounding is the essence of why investing works. The human brain is notoriously poor at grasping exponential growth, and that might explain why so few people invest their savings. But understanding its power will set you apart from the rest and make you a better investor. It will give you confidence knowing that your monthly saving contributions will build up to a much greater value after 20 or 30 years.

The king who didn’t understand compounding

Let’s start with an ancient Indian legend about the origin of chess. According to the legend, the Indian god Krishna once disguised himself as a sage, and challenged a local king to a game of chess in his own court. The king, being a chess enthusiast himself, gladly accepted the invitation. He asked the sage to choose the winning prize. The sage explained he was a man of few material needs, so he only wished for a few grains of rice. The amount of rice itself would be determined using the chess-board in the following manner: one grain of rice would be placed in the first square, two grains in the second square, four in the third square, eight in the fourth square, sixteen in fifth square and so on. Every square would then have double the number of grains of its predecessor.

Krishna and the king playing chess (from Wikipedia)

The king lost the game and the sage demanded the agreed-upon prize. As he started adding grains of rice to the chess board, the stunned king soon realised the true nature of the sage’s demands. The royal granary soon ran out of grains of rice. As the number of grains increased exponentially, the king became certain he would never be able to fulfill the promised reward. The total amount of rice required for a 64-squared chess board is 18,446,744,073,709,551,615 translating to trillions of tons of rice!

We cannot blame the king for not having understood the severity of the bet he was getting into. After all, the human brain is not good at intuitively understanding exponential growth. However, investors must understand it because, as we said earlier, it is the foundation of investing.

Even on the first row of the chessboard, it gets crowded with grains of rice very quickly! (by Eden Henricks)

Compounding accelerates the growth of your investment

In investing, we don’t compound grains of rice. Instead, we compound money. Also, to our misfortune, our investments (usually) don’t double yearly! Still, as we will see in the next example, even a modest initial investment with a realistic yearly return rate will grow to a considerable amount over time.

Imagine you invest €1,000 today in something that yields an 8% average yearly return. Passive investing through index funds can achieve such returns. For instance, we computed in a previous article “Why you should passively invest your savings” that the MSCI World index has an average yearly return of 8.7%.

The following table shows how your investment will grow over time:

AFTER X YEARS VALUE OF YOUR INVESTMENT
0 €1000
1 €1,080
2 €1,166
3 €1,260
4 €1,360
5 €1,469
10 €2,159
20 €4,661
30 €10,063
40 €21,725

If you look closely, you see that every year, your return increases. After the first year, you have earned €80. Then at the end of the second year, your return was €88. The following year you earned €94, then €100, and so on. In fact, growth is accelerating, and this is exactly why compounding is so effective.

The explanation behind the accelerated growth is that you earn returns on your returns. During the second year, you do not only get a return on your initial €1,000 but also on the €80 gain from the first year. During the third year, you again earn a return on this €80. This goes on, year after year. The returns are compounding.

The image below shows the previous table as a graph. If you remember your mathematics classes from school, you can likely recognize the typical accelerated shape of the exponential curve. The exponential curve is the mathematical basis for the compounding effect in investing.

The exponential curve is the foundation of the compounding effect in investing.

The law of 72

Finally, there exists a useful technique that helps investors quickly calculate the amount of time it takes to double an investment.. It’s a simple calculation: you divide 72 by the yearly growth rate. The result is approximately the number of years it takes to double the investment. Going back to our previous example, an investment at an 8% growth rate doubles roughly every 9 years (72 divided by 8).

The table below shows how the number of years to double an investment evolves for different return rates. As you can see, an increase of 1% in the return rate makes a big difference in the number of years needed to double your investment!

RETURN RATE NUMBER OF YEARS TO DOUBLE THE INVESTMENT
0.5% (savings account) 144
1% 72
2% 36
3% 24
4% 18
5% 14.4
6% 12
7% 10.3
8% (MSCI World index) 9
10% 7.2

To summarize

Like the story of the Indian king illustrates, most people have trouble with grasping compounding. After all, the human brain is simply not great at predicting the outcomes of exponential growth. But understanding compounding can put you ahead of the curve, and will give you the peace of mind that your investment will grow substantially over time. You won’t even need to play the guessing game in when you’ll begin to see results! Thanks to the nifty law of 72, you won’t even need a calculator to figure out just how long it will take to double in on your investments.