Why is the rule of 72 the number 72?

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By Nick

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Want to know how long it will take for your investments to double in value? Use the rule of 72! This simple formula uses the value 72 as a numerator, which has many small divisors making it easy to calculate regardless of interest rate. Although not precise, it provides a good approximation for annual compounding and typical rates. So, invest wisely and watch your money grow!

The Rule of 72: Why 72?

Have you ever heard of the rule of 72? It’s a simple formula that can help you estimate how long it will take for your investments to double in value. All you have to do is divide 72 by the interest rate you expect to earn, and the result is the number of years it will take for your investment to double.

But why is the number 72 used in this formula? Why not 73 or 71?

The Convenience of 72

The value 72 is a convenient choice of numerator, since it has many small divisors: 1, 2, 3, 4, 6, 8, 9, and 12. This makes it easy to calculate the number of years it will take for your investment to double, regardless of the interest rate.

For example, if you expect to earn a 6% annual return on your investment, you can divide 72 by 6 to get 12. This means it will take approximately 12 years for your investment to double in value.

Similarly, if you expect to earn a 10% annual return on your investment, you can divide 72 by 10 to get 7.2. This means it will take approximately 7.2 years for your investment to double in value.

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The Accuracy of 72

While the rule of 72 is not a precise formula, it provides a good approximation for annual compounding, and for compounding at typical rates (from 6% to 10%).

For example, if you invest $10,000 at a 6% annual interest rate, it will take approximately 12 years for your investment to double to $20,000. If you invest the same amount at a 10% annual interest rate, it will take approximately 7.2 years for your investment to double to $20,000.

Of course, actual investment returns may vary, and the rule of 72 should only be used as a rough estimate.

The History of 72

The origin of the rule of 72 is unclear, but it has been used by investors for centuries. Some historians believe that the rule may have been developed by ancient mathematicians, while others attribute it to medieval bankers.

Regardless of its origins, the rule of 72 remains a useful tool for investors today.

In Conclusion

The rule of 72 is a simple formula that can help you estimate how long it will take for your investments to double in value. The value 72 is a convenient choice of numerator, since it has many small divisors, and it provides a good approximation for annual compounding and for compounding at typical rates. While the rule of 72 is not a precise formula, it remains a useful tool for investors today.

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