25 September, 2017

# What is Rule of 72?

Albert Einstein is said to have told that ‘compound interest is the eighth wonder of the world.' It may not be his quote, but he’d certainly agree that the meaning and consequences of compound interested are very underrated.

For many, compound interest and exponential growth are terms that evoke bad memories from school math. They just sound too complicated.

But 'Rule of 72' doesn’t sound so tough, right? It sounds like a movie title (think a sports documentary or something). And it’s just a different way to illustrate the power of compound interest and the exponential function.

## How does it work?

You cannot talk about the Rule of 72 without talking about compound interest. Basically, it’s a function that helps you find out how much money you will earn if you invest it at a fixed rate for a certain amount of time.

If you put a \$1000 in a 5% per year deposit for 5 years, it means that every year that money will grow 5%. So in the first year, you’ll have \$1050, next year it will be \$1102 and in the final year, you’ll receive \$1276.

So.. what does ‘Rule of 72’ mean in this context?

It lets you find out when will your investment double given the rate at which it grows in compound interest function.

The calculation is really simple: you just take 72 and divide it by the percentage of your investment. Why 72? Because it’s a close approximation of natural logarithm of 2 times 100.

You can check it in this Rule of 72 Calculator.

Rule of 72 Calculator

## Why is it important?

Because it gives you perspective on how fast things can grow. If you see that cinema ticket prices go up 7% per year, you’ll probably not bat an eyelid. What’s 7%, after all?

But that means that in roughly 10 years you’ll have to pay twice as much to see a movie than now. And that’s is an entirely different story.

## The legend of Rule of 72

Remember the legend of how a king wanted to reward his mathematician for beating him at chess? ‘You can have anything you want,' the king said.

‘Alright, please put one grain of wheat on the first chess field and then twice as much on the second one. Then twice as much on the third and continue until the last field on the chessboard’, the mathematician replied.

The king thought it was foolish because the mathematician could have asked for much more and ordered his staff to fulfill that request. But soon he discovered that he wouldn't have enough grain. Because on every field, there would be twice as much grain as ever before combined.

It’s a general rule. If we double our oil consumption in a decade, we use more oil than in every decade before, combined. That’s the power of compound interest that Einstein spoke of. And the ‘Rule of 72’ helps us understand it better.