The Rule of 70 is a mathematical formula used to estimate the years it takes for a quantity to double. It is a formula that divides the number 70 by the before-given fixed annual growth rate. 

This rule of 70 formula is commonly used in finance and economics to calculate the doubling time of investments, population growth, or inflation, among other things. 

This guide will dive deeper into the Rule of 70 and explain it with examples. So with all that said, let’s begin.

Rule of 70 Examples

The easiest way to explain the Rule of 70 is through examples. Here are a few financial, population, and inflation examples that explain the formula behind the rule. 

Rule of 70 for Investment Growth

As mentioned, The Rule of 70 is often used in finance to estimate the years it will take for an investment to double. For example, if an investment is expected to grow at 7% per year, the Rule of 70 tells us that it will double in approximately 70/7 = 10 years.

Rule of 70 for Population Growth

The Rule of 70 is also used to estimate the years it will take for a population to double, given a fixed annual growth rate. For example, if a population grows at a rate of 1% per year, the Rule of 70 tells us that it will double in approximately 70/1 = 70 years.

Rule of 70 for Inflation

We can also use the Rule of 70 formula to estimate the number of years it will take for the purchasing power of money to be halved, given a fixed annual inflation rate. For example, let’s say the inflation rate is 3% per year. In that case, the Rule of 70 formula tells us that the purchasing power of money will be halved in approximately 70/3 = 23 years.

Why 70 in the Rule of 70?

The number 70 is used in the Rule of 70 because of mathematics. Since the formula determines the years it takes for an investment to double, it looks at the number “2” to calculate.  

First, we need to calculate the natural logarithm of 2, which is 0.69. We can round up the number to 0.7. 

Then, we need to convert 0.7 to percentages, which is 70% or 70. This is why mathematicians use the number 70. Although it’s commonly accepted in finance to use the number 72 as they believe it is a “nicer” number to divide into.

How to Use It?

To use the Rule of 70, you simply need to remember the formula, which is 70 divided by the annual growth rate expressed as a percentage. 

For example, let’s say the annual growth rate is 7%. In that case, the doubling time will be approximately 70/7 = 10 years.

The rule is based on the exponential growth formula, which states that the quantity at any time can be calculated as the initial quantity multiplied by the exponential function of the growth rate. 

This rule of 70 formula shows that the growth of a quantity depends on both the size of the initial quantity and the annual growth rate. It’s also important to understand the exponential function, which has the property of compounding, which means that the growth rate multiplies the quantity over time.

The Rule of 70 isn’t accurate for very high or low growth rates or for quantities that grow at a variable or non-constant rate and is used to express a rough estimate.

However, it is a useful tool for making quick, rough estimates and comparing different quantities’ growth.

Conclusion

The Rule of 70 is a simple and useful formula for estimating the doubling time of a quantity given a fixed annual growth rate. It is widely used in finance and economics and can provide a rough estimate for various applications. However, it is important that the rule is an estimate and may not be accurate for all situations.

Alternatively, the Rule of 72 and the Rule of 69 can also be used for the same purpose. 

FAQs

How Does the Rule of 70 Work?

The rule of 70 is a mathematical formula calculating the years it takes for a quantity to double. It works by dividing 70 by the annual growth rate.

What is the Rule of 70 in Population?

The rule of 70 in population is a formula that helps governments and institutions calculate the years it takes for a population to double.

What is Rule of 70 In Inflation?

The rule of 70 in inflation helps calculate the years it takes for the purchasing power of money to be halved.