The Rule of 72.

In our last post, we used our equations to calculate yield for a specific interest rate over a specific time.  Our last problem, we looked at a $10,000 principle at 8% for 9 years, and at 9% for 8 years.  They were pretty close in amounts – $20,495 and $20,489 respectively.  But they shared one special characteristic…they both doubled the principle at those rates over that specific time. 

Today we will look at a very simple rule that helps you approximate how long it will take to double your principle at a given rate.  It is called the Rule of 72.  The Rule of 72 states that if you divide 72 by an interest rate percentage, you will have a good approximation how many years it will take to double your initial principle.  This also works for if you want to find out what interest rate you need to invest at in order to double your principle over a determined time period. 

Let’s make this equation, its rather simple.  First let’s arrange our variables:

I = Interest Rate Percentage

T= Time (in years)  

Ok, there is only one tiny thing about this equation.  Lets say we are talking about percentages – 5% for instance.  Normally for equations we make 5% = .05, but for the purposes of this equation it must remain the whole number percentage (or else we would call it the rule of .72!) 

Our equation will look like this if we want to find out how long it will take to double the principle at a given interest rate: 

T = 72 / I  

Our equation will look like this if we want to find out what rate you would need to double the principle over a given time: 

I = 72 / T 

Let’s take this equation for a test drive.

How long will it take to double the principle at 3%, 6%, and 12%?

What interest rate would you need to double your investment in 5 years, 10 years, and 20 years? 

Ok, we will start with 3%. 

T = 72 / 3    Divide.

T = 24 years.   

Next, 6%.

T = 72 / 6    Divide.

T = 12 years. 

Finally, 12%

T = 72 / 12    Divide.

T = 6 years.  

For the next set of problems, we need to use the second form of the equation. 

Ok, we will start with 5 years.

I = 72 / 5    Divide.

I = 14.4%. 

Next, 10 years.

I = 72 / 10    Divide.

I = 7.2%.

Finally,  20 years.

I = 72 / 20    Divide.

I = 3.6%. 

The Rule of 72 is a pretty simple way to approximate these two things.  It is important to note that for higher interest rates, the equation has to be adjusted.  Wikipedia has a good explanation why this is and how to adjust: http://en.wikipedia.org/wiki/Rule_of_72 

They also go into other conclusions that can be derived from this formula.  It’s a good read.  CD