# How does Rule of 72 work math? By Nick

### Quick Peek:

Want to know how long it will take for your money to double? The Rule of 72 can help. Simply divide 72 by the interest rate you hope to earn and you’ll get an estimate of how many years it will take for your investment to double. But remember, this is just an estimate and doesn’t account for inflation, taxes, and fees. So, use it as a guide, but don’t rely on it completely.

## Do you know the Rule of 72?

If you’re an investor, you’ve probably heard of the Rule of 72. It’s a simple way to estimate how long it will take for your money to double based on the interest rate you hope to earn. All you have to do is divide 72 by the interest rate, and the resulting number is the approximate number of years it will take for your investment to double.

For example, if you’re hoping to earn a 6% return on your investment, divide 72 by 6 and you get 12. This means that it will take approximately 12 years for your investment to double.

### How does the Rule of 72 work mathematically?

The Rule of 72 is based on the logarithmic function. The formula for calculating the number of years it takes for an investment to double is:

t = ln(2) / ln(1 + r)

Where t is the number of years, r is the interest rate, and ln is the natural logarithm. The natural logarithm of 2 is approximately 0.693. If we simplify the formula using this value, we get:

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t = 0.693 / r

This formula gives us the same result as the Rule of 72, but it requires a calculator or a spreadsheet to calculate.

### Why is the Rule of 72 useful?

The Rule of 72 is a useful tool for estimating the time it will take for your investment to double. It’s quick and easy to use, and it can give you a rough idea of how long you need to hold onto your investment to achieve your financial goals.

However, it’s important to remember that the Rule of 72 is just an estimate. It assumes that your investment will earn a consistent rate of return over time, which may not be the case. It also doesn’t take into account factors like inflation, taxes, and fees, which can all impact the growth of your investment.

### Conclusion

In conclusion, the Rule of 72 is a simple and useful tool for estimating how long it will take for your investment to double. It’s based on the logarithmic function and can be calculated using the formula t = 0.693 / r. While it’s a quick and easy way to estimate the growth of your investment, it’s important to remember that it’s just an estimate and doesn’t take into account other factors that can impact your investment’s growth.