Geometric Series and Gordon Growth Model

In 1991 letter to shareholders, Buffett explained his thought process in valuing a business. Given below is the excerpt from the letter. A few years ago the conventional wisdom held that a newspaper, television or magazine property would forever increase its earnings at 6% or so annually and would do so without the employment of additional…

The Rule of 72

The rule of 72 states that, if you want to find the number of years it would take to double your money at a given interest rate (r), you divide 72 by r. For example at 8% compound interest it would take 9 years (72 / 8) to double your money. I have been using this rule…

Working Backwards

I came across an interesting problem in the book How to Solve It by G.Polya. How can you bring up from the river exactly six quarts of water when you have only two containers, a four quart pail and a nine quart pail, to measure with? Given below are the containers. Notice that they are not…

Mathematical Induction

A team in Germany made over 270,000 dominos to fall and created a world record. It took a week for them to set this up. How do they know for sure that if the first domino falls all the dominos will fall? They came to that conclusion by knowing two facts The first dominos falls.…

Logarithms in real life

I came across logarithms in my 9th grade. For a long time I never really understood its use in real life. Logarithm of a number is simply the power to which 10 (or any other base) must be raised to equal the number in question. log10(100) is 2 because 102 = 100 log10(1000) is 3…

Power Law

Hundreds of balls are poured on top of a Galton board. Each ball has to randomly bounce off the pegs and drop into one of the bins placed at the bottom. The final pattern of the ball is very predictable and it forms a bell shaped pattern. In statistics this is called as a normal…

Proof by Contradiction

To disprove a theorem or a statement all you need is one counter example. Unfortunately, no number of examples supporting the theorem is sufficient to prove its correctness. You can never really prove the proposition that “All swans are white” even if you have only seen white swans in your entire life. But you can…