The Rule of 72

July 26, 2021

If it were not for the pandemic, I would be in England right now, teaching our annual program Money & Responsibility at Cambridge University. Instead, this week I will share one of the basic mathematical principles that we teach our students: The Rule of 72. When I started my career as an accountant with Peat Marwick Mitchell & Co. in London, we had to learn to do math in our heads. We had to be numerate, able to spot financial trends or inconsistencies. To practice our computational skills, we would add telephone numbers from the directory in our spare time! The idea was to train the mind to understand the language of numbers. It was imperative to find ways to do math in your head with little tricks, and the Rule of 72 is one of them.

The rule in its most basic form allows you to estimate how long it will take to double your money, given a specified rate of return on an investment (also referred to as an IRR – internal rate of return). To calculate, you will divide the expected IRR into 72, which equals the time it will take to double. For example, if you want to double your money in ten years, you will need to compound your investment returns at 7.2%. If you desired to shorten the timeframe to 6 years, you would require an IRR of 12%. Similarly, if you know you can earn 8% on your investment, you will double your money in 9 years. Voila! So, now let us put this into practice.

I had the pleasure of spending an afternoon over tea with two bright young students last week. They are preparing to go to college and wanted to learn the basics of investing for the long term. Most encouraging! They had been given a graduation gift of $2,021. So, I first explained that the average long-range return of the U.S. stock market has been approximately 10% annualized. At that rate, ignoring taxes and inflation, their gift would be worth approx. $4,000 in 7.2 years, $8,000 in 14.4 years, $16,000 in 21.6 years, $32,000 in 28.8 years, $64,000 in 36 years, $128,000 in 43.2 years and $256,000 in 50 years when they are possibly retired.

But, what is the number if you adjust for inflation? Over the last 100 years, inflation has averaged around 3% annually. If we adjust the rate of return by 3%, we have a real rate of return (adjusted for inflation) of around 7%. Of course, these figures are just examples, but if you could double your money approximately every ten years, the Rule of 72 would turn $2,021 today into just over $64,000 in 50 years!

The $64,000 question is whether you can persuade your children or grandchildren to save $2,000 every year starting at age 18 and invest it wisely and for the long term in quality stocks or an index. Think how much additional income they could have in 50 years.

Nick Hoffman