Rule of 72

The rule of 72 is a formula that is used to assess how long it will take a venture to double its initial investment amount based on a certain interest rate. The results of this formula are expressed with years as the set period of time. 

The potential to double your money is an attractive thought for many investors. And it can help to put many different forms of investments on an equal footing. The rule of 72 gives a rough estimation that works great for calculating on the fly. 

Essentially, it helps you to compare the effect that interest rates have on your invested cash. It also gives you a reference for the time period it will take to see quality benefits from your investment. For example, if an investor places their money into an account with interest, how many years would it take them to double the value of the cash they had put in.  

Rule of 72 Formula

$$Years\: to\: Double = \dfrac{72}{Interest\: Rate}$$

It is important to enter the interest rate as a whole number, not a decimal point. While this may seem counter-intuitive, it makes for a much more exact result. For instance, a 12% interest rate would be entered into the equation as the number 12. 

This formula relies on the fact that the interest rate is equal to the return on investment (ROI). It assumes that no other payments will be made. The interest rate will be fixed and it will be annually compounded. 

Originally, the rule of 72 was derived from a formula that looks at the logarithms of numbers. However, the old formula is extremely complex and requires the use of a table to solve it. This makes it difficult to work quickly. The rule of 72 was created to give a faster option for estimating the timeline. As long as the investment has an interest rate of 20% or less, the formula is actually quite accurate. Beyond that, however, there is a greater margin of error to be aware of. 

You can also use the principle of this formula in reverse to identify the required interest rate needed to double your investment in a desired amount of time. That formula would look like this:

$$Interest\: Rate = \dfrac{72}{Years\: to\: Double}$$

So, if you knew you wanted to double your money in 5 years, you could use this formula to figure out what interest rate you would need to make that happen. 

Rule of 72 Example

David has invested $7,000 in a bond with an interest rate of 5%. How long will it take for David to double his initial investment?

Let’s break it down to identify the meaning and value of the different variables in this problem. 

  • Interest Rate: 5%

We can apply the interest rate to the formula and calculate the rule of 72.

$$Years\: to\: Double = \dfrac{72}{5} = 14.4\: Years$$

In this case, the rule of 72, or the years needed to double David’s investment would be 14.4 years. 

Let’s take a look at an example using the reverse formula.

Sarah has saved up $20,000 to invest with. She wants to double her money in 10 years. What kind of interest rate will she need in order to double her money in that time?

We can use the number of years (10) to calculate using the reverse of the rule of 72. 

$$Interest\: Rate = \dfrac{72}{10} = 7.2\%$$

In this case, Sarah would need to find an investment with an interest rate of 7.2% to double her money in 10 years. 

For both David and Sarah, they can now have a better understanding of the potential of their investments. They can use these calculations to help them meet financial goals. 

Rule of 72 Analysis 

Interestingly enough, the rule of 72 has uses outside of the financial realm. Instead of an interest rate, you could use that variable to plug-in growth rates or inflation rates

A small business could use it to know how long it would take them to double sales goals if their prices increase by a fixed percentage each year. A university could use it to predict how long it would take to double their student population if they are increasing the number of students they accept at a fixed rate over time. 

The rule of 72 is a great formula to have in your tool belt for quick projections on the growth of your money. You can use the information it provides to think about the time frame it would take to double your cash using one type of investment and compare it to other investment options during that same period of time. 

For example, if one venture would double your money in 12 years, What other investments could you make that would provide that kind of return at a faster rate? You should also consider the risk of the investment in this decision-making process. And even if your goal is not necessarily to double your money, doing a rule of 72 calculation can still give you a foundation of understanding of your investment’s potential.  

Rule of 72 Conclusion

  • The rule of 72 is a tool to determine how long it will take a venture to double its initial investment, based on an accompanying interest rate. 
  • The rule of 72 relies on only 1 variable: the interest rate. 
  • The formula can be applied in reverse, with the variables staying the same. 
  • The formula relies on a fixed interest rate that must equal to the return on investment rate. 

Rule of 72 Calculator

You can use the rule of 72 calculator below to quickly estimate how long it will take an investment to double its financing by entering the required numbers.

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