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Heard on the Street Blog

Understanding the "Rule of 72" in Investing

Albert Einstein is known as the greatest mind to ever walk the Earth. Known for his Theory of Relativity and his equation E=MC2 which still acts as the basis of our understanding of the entire universe. However, Albert Einstein didn’t consider that his greatest discovery, in fact, his greatest discovery didn’t have anything to do with space, time, gravity, etc., it had to do with compound interest. Albert Einstein’s greatest discovery, in his own eyes, was the “Rule of 72” which is actually a mathematical equation that showcases the power of compound interest.

Before we get into the Rule of 72, you need to understand what compound interest is – Compound interest is the addition of interest to the principal sum, or in other words, it is interest on interest. Compound interest doesn’t grow linearly, it grows exponentially – meaning while your interest earned from your principal remains constant, the interest earned from your past interest grows exponentially. Basically a way to simplify it is let’s say you have $10,000 and you earn a 10% return, after year one you would have $11,000 ($10,000 + .10(10,000)) but in year two you start to notice a difference because assuming you earn a 10% return, you are earning that return on $11,000, not just on the original principal of $10,000 ($10,000 in principal and $1,000 in interest) so after year two you have $12,100 ($11,000 +.10(11,000)). This process continues over and over, and each time the amount of interest from interest gets larger and larger. Albert Einstein once stated that “Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn’t, pays it.”

Now that you have a basic understanding of compound interest, we can get back to Albert Einstein’s famous “Rule of 72”. Basically, the “Rule of 72” is a very easy (and quite accurate) way to determine how long it will take for your money to doublefrom compound interest. How the rule works: determine the annual return you plan to earn (aka the interest rate, yield, etc). Now that you have that number, divide 72 by that number and that is how many years it will take for your money to double. Yes, it is that simple. Let’s do a quick example: let’s say you earn a 12% annualized return, take 72 and divide it by 12 and you get 6 – meaning it will take 6 years for your initial amount of money to double. (Mathematically, you can use this in rule with returns between 2.25% and 20% and have it be pretty darn accurate). Let’s do another example but this time let’s use dollars. Say you start with $25,000 and you want to know how long it will take you to turn that into $50,000 and you know you can earn a 10% annual return. Well take 72 and divide it by 10, it will take you 7.2 years for you to get $50,000. How long will it take you to get $100,000? Well, this is where we start to notice the power of compound interest because conventional wisdom would tell you that it would take you another 7.2 years to get to $75,000 and another 7.2 years to reach $100,000. However, you would be forgetting that you would be earning interest on $50,000 now ($25,000 initial principal and $25,000 interest earned). So, it would only take you an additional 7.2 years to reach $100,000. Following this same trend, in another 7.2 years you would have $200,000; 7.2 years after that you would have $400,000; 7.2 years after that you would have $800,000 and 7.2 years after that you would have $1,600,000and so on. So let’s say your distant Aunt Beatrice died and bequeathed you with $25,000 when you turned 18 years old and you invested it, earned a 10% annual return, and didn’t touch the money for 43 years, you would have turned that $25,000 into $1.6 million dollars without even doing anything.

By staying alive and not touching your money, you have let the unstoppable force that is compound interest do what it does best. The “Rule of 72” is a nifty way to easily calculate how many years it will take for your money to double. But more importantly, what the “Rule of 72” really does is reveal just what a powerful force compound interest is — That is why Einstein claimed that “the most powerful force in the universe is compound interest.”

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