Every investor wants to know how long they have to wait to see their investment double in value. Is there a formula to determine the exact number of years it would take, given a fixed rate of return?
Investors have had this question for centuries. The first answer to this problem was given 527 years ago by Italian mathematician Luca Pacioli. In his book, “The summary of arithmetic, geometry, proportion and proportionality,” Pacioli summarised all mathematics known at that time. Using a magic number, Pacioli stated that you could calculate (to a good approximation) how long you need to wait for your money to double at any compound interest rate. And the magic number was 72. This is now known as the Rule of 72.
How does the rule of 72 work?
When you divide 72 by the interest rate in percentage value, you get to know the number of years it would take for your investment to approximately double.
72/rate of return = number of years it takes to double your investment
Let us see a few examples of how the rule of 72 works
| Dividing factor | Interest rate as a percentage | Number of years it takes to double |
| 72 | 15 % | 4.8 |
| 72 | 8 % | 9.0 |
| 72 | 20 % | 3.6 |
| 72 | 4 % | 18.0 |
Using the rule of 72, you know that for an investment that offers you a rate of return of 2%, you will need 36 years to double your money. With an investment that gives you a rate of return of 15%, you need only 4.8 years to double your investment. Since you would not want to wait 36 years to double your investment, you will choose the investment that has a 15% rate of return.
We can also use this formula in reverse. Say you already know how many years you can invest for a particular goal. However, you need to know the ideal annual rate of return to be considered or which avenue can potentially generate this required rate of return. Well, here’s what you need to do:
Assume that you plan to spend ₹10,00,000 for your child’s education in ten years. You only have ₹5,00,000. If you want to know how to make this investment double in ten years. You divide 72/10 =7.2. You need to make an investment that offers you a rate of return of at least 7.2% to double your investment to have enough money to spend on your child’s education.
| Dividing factor | Years in which investment should double | Annual interest rate needed | Investment avenue to consider |
| 72 | 4.8 | 15% | Equity mutual funds or direct stocks |
| 72 | 9.0 | 8% | Hybrid mutual funds |
| 72 | 3.6 | 20 % | Equity mutual funds or direct stocks |
| 72 | 18.0 | 4 % | Debt or hybrid mutual funds |
This rule of 72 can also tell you the number of years it takes for your money to become half its current value. For example, suppose the inflation rate is 6%. Then 72/6 = 12 years. It takes 12 years for your money to reduce by half. If you have invested ₹200 now, it will take 12 years for your investment to become ₹100. If the inflation rate falls to 3%, it will take 72/3 =24 years for your investment of ₹200 to become ₹100.
Conclusion
Investing can be complex. Not everybody understands interest rates and returns. The investing rule of 72 is a tool that simplifies this process. With this, you can predict how much you can earn under various rates of return, and decide the most suitable investment avenue.
However, it is important to remember that the returns you earn on your investments depend on the performance of the market and the risks associated with it.