The Rule of 72

 The Rule of 72 is a simple mathematical shortcut used to estimate the time it takes for an investment to double in value, given a fixed annual rate of return. It's a handy tool for quick mental calculations in finance and investment planning.

Here's how it works:

Divide 72 by the annual rate of return (expressed as a percentage) to get an estimate of the number of years it will take for an investment to double.

Mathematically, the formula can be represented as:

$\text{Years to Double}=\frac{72}{\text{Annual Rate of Return}}$

For example, if you have an investment with an annual rate of return of 8%, you can estimate that it will take approximately $\frac{72}{8}=9$ years for the investment to double in value.

Similarly, if the annual rate of return is 10%, it would take approximately $\frac{72}{10}=7.2$ years for the investment to double.

The Rule of 72 provides a quick approximation and works well for interest rates between 6% and 10%. However, it becomes less accurate for significantly higher or lower interest rates. For more precise calculations, especially with variable rates or compounding, it's better to use more sophisticated financial formulas or calculators.