Effect of Compounding

Compounding is the fact that money grows faster purely because more time has elapsed since it started to grow.

ChessboardLet me start with an anecdote close to my heart: Chess is a board game played on 64 squares. In an ancient epic, an arrogant king was humbled by the mathematical agility of the inventor of Chess. The king asked the inventor for any reward.

To teach the king a lesson, the inventor asked – put one grain of rice on first square (1), double that on the second square (2), double that on third square (4)… and so on and so forth. And when you reach 64 square, just collect all these rice grains and give it to me (1+2+4+8+…. till 64th square).

The king laughed thinking that the inventor is foolish asking for a ‘few’ grains of rice BUT soon realized what compounding is.

Box 11 on the chess boardThe total number of grains equals 18,446,744,073,709,551,615, weighing 461,168 million metric tons – which is 50,000 times more rice than produced in United States every year, and if put together would be a heap of rice larger than Mount Everest. (Picture on the left shows the heap on square 10, this bunch becomes larger than Mount Event till square 64.)

In investing, your biggest friend is ‘compounding’. Start saving early enough and you will amass fortunes. By my own analysis posted here, with other things unchanged you will have $4.6 Million accumulated at retirement viz-a-viz a meager $877,000 just because you started to save at the age of 20 instead of 40.

Let us take some financial examples – on the chess square 4, you are at the minimum wage per hour. It will take you up to square 15 to reach the median income of United States but guess what? You are in the top 1% earners of the country at square 20…. notice how long did it take to go from bottom to median …. and from median upwards. At square 15, there were 50% Americans making more than you but at square 20, not even 1%.

Let us keep going, at square 35, we are talking about the total personal income of all the 300 Million Americans. Beyond square 35, I am finding it hard to think of financial examples (because I do not want to introduce the term GDP, but for those who understand it – GDP of United States is at square 45).

Now that money examples are exhausted, let us talk Niagara falls. At square 51, we are talking about a number that is a million billion – it would take Niagara Falls over 210 years to drop so many Albert_Einstein_Compound_Interestgallons of water. At square 61, Niagara falls would need 210,000 years.

Abert Einstein is believed to have said once “The most powerful force in the universe is compound interest” and I agree.

$1,000 invested at 10% annual in 1950 would equal more than $5 Million today. Don’t you wish your grandfather had invested just a thousand dollars for you back then?

Your personal compounding calculator

Last piece of Advice

Do not get disheartened even if you do not see huge changes overnight, start small but keep improving and you will reach a point when the exponential growth will have an overwhelming impact on your personal wealth. In strategy, this is called “second half of the chessboard“.

Why is it called second half of the chessboard?

Because even though the number of grains on the first half were itself large, they still accounted for only 0.00000002% of the rice grains that are there on the chessboard. No prizes for guessing which half of the chessboard do you want to be playing on?

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6 thoughts on “Effect of Compounding

    • Capital gains tax happens only on the gains….. so may be you will gain a little less but you still gain by long term compounding. Most commonly applied tax rate for long term capital gains is only 15%.

      In the last 10 years, inflation has ranged from 0% to 4%. But inflation exists whether you invest (and let your money grow) or you let it sit idle.

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