Compound interest: The crux of the exponential function

Updated October 23, 2023

You want to build up wealth? Then it helps to know the legend of the invention of chess. The story goes like this: The wise Brahmin Sissa invented a game - chess - and gave it to the tyrannical ruler Shihram. He was so impressed by it that he granted Sissa a wish. The Brahmin wished for grains of wheat: one on the first square of the chessboard, two on the second, four on the third and so on - on each square the number of grains was to be doubled.

Shihram was half amused, half annoyed at the modest-looking Sissa, but agreed. But he had made the calculation without the exponential function. The required amount of grain could not be found in his entire empire. For all 64 squares of the chessboard, the total would be more than 18 trillion grains - that's about a quadrillion kilos of wheat.

Shihram's error is human. Our brain simply has a hard time grasping an exponential increase correctly. The result is that this weakness often has a negative effect on investments as well. This is because almost everyone underestimates the compound interest effect, which also ensures exponential growth, since the income once earned generates new income again over many years when it is reinvested. The longer the investment, the more powerful the growth. Because hardly anyone is aware of this, most people start building up their wealth far too late. An example shows what this can lead to.