Investing Math - Compounding

Mathematics is an integral part of investing. Some of this math is intuitive and some not so intuitive. This is the first in a series of articles that helps demystify investment math.

"Money makes money. And the money that money makes, makes money."

- Benjamin Franklin

As per the Merriam-Webster dictionary, the definition of compound interest is as follows: to pay interest on both an amount of money and the interest it has already earned.

"The greatest shortcoming of the human race is our inability to understand the exponential function"

- Al Barlett

Compounding is a simple but a very powerful concept. However, it involves exponential math while most human beings are conditioned to think in linear terms. Let's test this with a simple trivia question:

Lily pads on a pond double every day. If the pond is completely covered on day 30, on what day was the pond half full? (The answer is at the end of this article).

Here is how compounding works its magic with capital:

The above chart shows that $100,000 invested at 10%, 15% and 20%, after-tax, over 25 years, will produce an ending amount of $1.08 mn, $3.29 mn and $9.54 mn, respectively.

Some of the very best investors, such as Warren Buffett or George Soros, have compounded capital at 20%+ for a very long period of time. However, they are the exceptions. Other notable and admired investors of our time have been able to compound at a respectable 15-18% over long periods of time. In contrast, from 1960 to 2020, the S&P 500 and the TSX indices, have been able to compound at 10.1% and 9.3%, respectively. As we see above, compounding produces dramatically different outcomes over time for only a 5% difference in annual returns!

Interestingly, Warren Buffett earned 99% of his wealth after he turned 50 as that is when his exponential compounding curve started going parabolic! Famously, he knew from a young age that he was going to be very wealthy as he was adept at performing compound interest calculations in his mind. He just knew that he had to, (a) earn reasonable rates of return, (b) not lose capital by taking a lot of risk, and (c) be patient and let compounding work.

White Falcon's mission and objective is to do just that - compound capital over a long period of time on a risk adjusted basis.

(Answer: Day 29)