72: Easily Predicting Growth Rates

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Mathematics undeniably has countless applications that are both intriguing and vital to modern society. It’s of pivotal importance in broad areas such as research, innovation, engineering and human progress in general.

However, it often seems that maths other than basic arithmetics is of little importance in everyday life, doesn’t it?

Apart from the obvious, such as all the wondrous contraptions we use every day made possible by modern technology, which in turn by a large part is made possible through solid mathematical foundations, there are also quite a few – at first glimpse often seemingly magical – mathematical properties which have highly useful applications for almost everyone in everyday life.

One of these properties is The Rule of 72. This rule allows you to quickly estimate the effects of growth rates and compound interest. It goes like this:

Years to double = 72 / Interest Rate

So, if for example you have an investment portfolio with a projected growth rate of 6% per year you’ll have 72 / 6 = 12, meaning after 12 years your assets will have doubled. Pretty neat, isn’t it?

This article at BetterExplained does a fantastic job at explaining The Rule of 72 as well as providing a derivation (If you’ve been asking yourself all along why it’s exactly 72, in short the answer is: Natural logarithm).

If you want to delve a little deeper into this subject Albert Bartlett, professor emeritus of physics at the University of Colorado in Boulder once gave a terrific talk on this rule (admittedly, he uses 70 instead of 72 though) and how it’s connected to exponential growth – economic and population growth in particular:

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