Compound interest: The crux of the exponential function
October 23, 2023 |
The strongest factor when investing money is the compound interest.
However, because exponential growth is so difficult to imagine, it is almost always underestimated.
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.
Compound interest: the longer, the more powerful
Development of assets 1) (in euros) with an investment sum of 2,500 euros, a term of 40 years and an annual average return of 6.44 percent per year 2)
1) before taxes; 2) corresponds to the average return of the iShares STOXX Europe 600 UCITS ETF from 13.02.2004 - 31.08.2023; Note: Neither past performance nor forecasts are a reliable indicator of future performance.
If you invest 2,500 euros over 40 years and earn an average annual return of 6.44 percent, you will end up with more than 30,000 euros in savings. If, on the other hand, you only have ten years to invest, you have to be content with about 4,700 euros. Or calculated differently: If you want to achieve the same final sum of 30,000 euros in only ten years with an identical return, you have to invest almost 16,000 euros. So if you assume that you still have time until next year or the year after, it might be worth thinking about Shihram and Sissa.
This article was initially published on 13.07.2018 and has been updated.
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