Exponential growth applied to your investments

What is Exponential Growth?

Most people can’t realize the effects of the exponential growth.

To do so, it’s necessary to understand correctly how it works.
Theoretically, it occurs when the growth rate of a mathematical function is proportional to the function's current value. Sometimes it is called geometric growth.

Some real examples are:

• The number of microorganisms in a culture broth will grow exponentially.
• A virus typically will spread exponentially at first.
• Human population, if the number of births and deaths per year were to remain at current levels.
• Compound interest at a constant interest rate provides exponential growth of the capital.

Regarding the compound interest, that is closely related to the exponential growth, Albert Einstein, fascinated with its mathematical implications, is quoted as saying: "It is the greatest mathematical discovery of all time." And if it’s used correctly could be the greatest discovery to your investments.

Let’s focus in a fictitious investment case.
If 100,000.00 of a monetary units were invested in a fund earning 12,68% a year (1% a month) - considering a nominal rate of return * - let’s say, by ten years, we’ll have the following growth.

* We had already learned about nominal and real return rates in How inflation erodes your investments

Nothing really impressive, isn’t it? The initial investment growth looks like a straight line (arithmetic growth) not an exponential.

The graph above shows an inexpressive progress on our investment. From this perspective, we aren't getting anywhere. But if we truly understand the potential of exponential growth, we could realize that the results were just beginning to show up.
Most of the time we can barely understand the exponential growth practical implications; its frequently is not completely understood by our common sense.

Exponential growth's implications

The following exponential story can illustrated it clearly:

A courtier presented the Persian king with a beautiful, hand-made chessboard (A chessboard have 64 squares, 32 black and 32 white).
The king asked what he would like in return for his gift and the courtier surprised the king by asking for one grain of rice on the first square, two grains on the second, four grains on the third etc. (an exponential growth). The king readily agreed and asked for the rice to be brought.
All went well at first, but the requirement demanded over a million grains on the 21st square, more than a trillion on the 41st and there simply was not enough rice in the whole world for the final squares.

On the entire chessboard there would be necessary a heap of rice larger than mount Everest!

The exponential growth is characterized by an accelerated upward curve like a population size graph below:

The real results of exponential growth applied to our investments can be noted if we analyze the results on a more wide period of time. Let’s see the evolution of our investment for a 30 years period with the same interest rate:

Pretty cool! If we invest 100,000,00 monetary units for 30 years with an interest rate of 12.68% a year, we’ll end up with almost 4 million.

In conclusion

For most people, the 30 years period of time to keep money invest it’s not practical at all.
But think about your kids, or in yourself if you are young enough. You could ensure a peaceful future for your children using the power of exponential growth.