How long will it take my money to double? That is a great question. 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. There are two ways to do this.
The Simple Method
The first way to estimate it is a simple estimation method called the rule of 72. Here's how it works. All you have to do is take the number 72 and divide it by the rate of return estimate you will receive. This is assuming the rate of return is compounded annually.
For example:
At a 3% rate of return
72/3 = 24 years for the money to double
At a 6% rate of return
72/6 = 12 years for the money to double
At a 9% rate of return
72/9 = 8 years for the money to double
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 get a better estimation of 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. This is assuming 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?
For example:
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 estimation compare to the more precise algebra?
| Rule of 72 | t = (ln(2))/(ln(1+r)) |
3% rate of return | 24 years | 23.45 Years |
6% rate of return | 12 years | 11.90 Years |
9% rate of return | 8 years | 8.04 Years |
Not perfect, but not bad. The rule of 72 may not be the solution you are looking for when you are planning out the nitty-gritty of your retirement. But, it can be useful in helping you get some quick estimations.
Debts
You can estimate how long it will take your debts to double if you let them sit and don't pay anything off. This is essentially the same math problem, but someone else gets the money in the end. This can be particularly useful if you are looking at things like student loans.
Inflation
Another useful 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.
For example
If we estimate the rate of inflation to be 3% over time then we can use these two estimations to see how long it will take for purchasing power to be 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 helpful applications. The rule of 72 makes it easy to get an approximation without all the algebra.