Exponential Growth ..... the Wonder of Compounding

The Power of Exponential Growth

1 + 1 is 2



2 + 2 is 4



4 + 4 is 8



8 + 8 is 16

This is how the dictionary explain the phrase "Exponential growth"

• (microbiology) The period of bacterial growth during which cells divide at a constant rate
• extremely fast growth. On a chart, the line curves up rather than being straight
• growth of a system in which the amount being added is proportional to already present; the bigger the system, the greater the increase
• in everyday speech, exponential growth means runaway expansion

The surprising characteristics of exponential growth have fascinated people through the ages. Lets see what the story of the chessboard, borrowed from a dictionary, can teach us.............

Rice on a chessboard

A courtier presented the Persian king with a beautiful, hand-made chessboard. 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. The king readily agreed and asked for the rice to be brought. All went well at first, but the requirement for 2^{n - 1} grains on the nth square demanded over a million grains on the 21st square, more than a million million on the 41st and there simply was not enough rice in the whole world for the final squares. (From Meadows et al. 1972, p.29 via Porritt 2005)

Second Half of the Chessboard is a phrase, coined by Ray Kurzweil, in reference to the point where an exponentially growing factor begins to have a significant economic impact on an organization's overall business strategy.

The total number of grains of rice on the first half of the chessboard is 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 ... + 2,147,483,648, for a total of exactly 2³² − 1 = 4,294,967,295 grains of rice, or about 100,000 kg of rice, with the mass of one grain of rice being roughly 25 mg.

The total number of grains of rice on the second half of the chessboard is 2³² + 2³³ + 2³⁴ ... + 2⁶³, for a total of 2⁶⁴ − 2³² grains of rice. This is about 460 billion tonnes, or 6 times the entire weight of the Earth biomass.

On the 64th square of the chessboard there would be exactly 2⁶³ = 9,223,372,036,854,775,808 grains of rice. In total, on the entire chessboard there would be exactly 2⁶⁴ − 1 = 18,446,744,073,709,551,615 grains of rice.

The Chessboard story, which is mind boggling, is to simply illustrate the power of compounding...... no wonder it is dubbed as "The 8th Wonder of the World". Now that we understand how powerful compounding is, lets us look for ways to make use of this principle to multiply whatever money we have..............if you are saying you don't have, relook at your expenses, read again Point No. 2 of my initial post...... get out of debts and start saving now, no matter how small, to start with. Put your plan into ACTION.