The Rule of 72: A Simple Way to Estimate Your Investment Growth
How long will it take my money to double? The rule of 72 is a simple yet powerful mathematical concept that can help you estimate the time it will take for your investments to double in value. The market generally gives no guaranteed return, but you can estimate how long it takes for your money to double at a given rate of return. This rule is used by investors and financial advisors as a quick and easy way to gauge the potential growth of their investments.
Here's how it works. All you have to do is take the number 72 and divide it by an estimated annual rate of return. The result is the approximate number of years it will take for your investment to double.
Example of the Rule of 72
Let's estimate how long an investment would take to double with an annual rate of return of 3%, 6%, and 9%.
72/3 = 24 It would take 24 years for the money to double at an annual rate of 3%.
72/6 = 12 It would take 12 years for the money to double at an annual rate of 6%.
72/9 = 8 It would take 8 years for the money to double at an annual rate of 9%
The More Precise Method
That was simple and relatively painless. Now, let's take a trip back to algebra class. You may remember or have tried to forget about natural logarithms. If you use a simple calculator or (my favorite) pull-up Microsoft Excel, you can better estimate the time it takes for money to double at a given rate of return. Here's the equation. Remember, t = time in years and r=rate of return. Of course, this assumes r is a stated rate with annual compounding.
t = (ln(2))/(ln(1+r))
How does this compare to our trip back to algebra class?
At a 3% rate of return (ln(2))/(ln(1 + 0.03)) = 23.45 Years
At a 6% rate of return (ln(2))/(ln(1 + 0.06)) = 11.90 Years
At a 9% rate of return (ln(2))/(ln(1 + 0.09)) = 8.04 Years
So how does our rule of 72 estimations compare to the more precise algebra?
Not perfect, but not bad. The rule of 72 may not be the solution you are looking for when planning out the nitty-gritty of your retirement. But it can help you get some quick estimations. Here are some other practical applications.
Other Applications
Debts
You can estimate how long your debts will take to double if you let them sit and don't pay anything off. This is essentially the same math problem, but someone else ultimately gets the money. This can be particularly useful when looking at things like student loans.
Inflation
Another practical application of these tools is estimating how long it will take for inflation to cut your purchasing power in half. If you decide to keep stacks of cash under your mattress or in an account earning essentially 0% in interest, this is helpful to know.
If we estimate the inflation rate to be 3% over time, we can use these two estimations to see how long purchasing power will take to cut in half.
At a 3% rate of return
72/3 = 24 years for the purchasing power to be cut in half
or
At a 3% rate of return
(ln*2)/(ln(1 + 0.03)) = 23.45 Years
Conclusion
The two equations we went through today have some practical applications. The rule of 72 makes it easy to get an approximation without all the algebra. The rule of 72 is a simple yet powerful tool that can help investors estimate the time it will take for their investments to double in value. While it is important to remember that the rule of 72 is an estimate and not a precise calculation, it can be a valuable tool.