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Magic of Compounding

Albert Einstein once famously said and I quote, “Compound interest is the eighth wonder of the world. He who understands it earns it … he who doesn’t … pays it”.

Some of you might have definitely heard about the famous chess board story ( It is in fact part of folk lore in multiple cultures in different forms). When an inventor of chessboard went to show the same to the king of his time. King was so impressed and asked him for a reward. The inventor, in turn, said my wish is simple. I only wish for one grain of rice for the first square of the chessboard, two grains for the second square, four grains for the third square, eight for the fourth square and so on for all 64 squares.

King surprised at the small ask promptly granted the gift not realising that this amount of grains will not be produced for hundreds of years.

You must do calculations how much grain will be required (hint: 2 to the power something). You can see the answer in post script.

So know let us understand compounding from an investment management perspective.

Here is a table which shows how your investments behave with time and returns. Let’s say if you have Rs 1 lac to invest

 Table 5% 10% 15% 10 Years 1,62,899 2,59,374 4,04,553 15 Years 2,65,328 6,72,748 16,36,640 20 Years 4,32,191 17,44,930 66,32,140

So at 15 % Return if you invest for 15 years versus if you invest for 20 years your corpus can be approximately 4 times.

Here is another simple analysis I did so that you understand power of compounding. Let us say you start saving Rs 5000 per month for your retirement when you are 25 year versus you start saving Rs 5000 per month when you are 30 and your plan to retire at 60. The below graphs shows your retirement corpus. Annual return assumed is 10%

So a 5 year head start can double your retirement corpus this is called magic of compounding.

Let’s take another example where we have an interest rate change. Let’s say two friends start investing monthly Rs 10000 for their retirement

Source : SIP Calculator

So a difference of 2 % Return can result in a 50 % bigger corpus over 30 years. The above to graphs have profound insights on how we should manage our personal finances. I am summarizing some of them below

1. Start early even if you start small
2. Let your money grow over long periods magic happens in long term
3. Even small investments can grow big over long periods
5. Choose your investment wisely even 2 % difference in returns can be big money in long term
6. Avoid keeping money in savings account , you can easily beat saving account returns without much risk
7. Teach compounding to your children.

Post Script: The Chess board puzzle. Let’s say he puts 1 grain in first , next square will have 2, next will have 4 (2^2) and so on. So number of grains in the last square will be 2^63. Use your calculators to calculate it. A grain of rice is approximately .2 inches long. Converting .2 inches to feet (divide by 12 inches to a foot) and then dividing that number by 5,280 feet in one mile, we get the length of the grains of rice, placed end-to-end, to be approximately 60,000,000,000,000 miles.

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