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If you’re struggling to wrap your head around complicated exponential growth, the rule of 70 is here to help. This popular formula in finance breaks down growth equations into a simple equation using the number 70 and the rate of return. By dividing 70 by the rate of return, you can estimate how long it will take for the quantity to double. This rule is based on logarithms, which convert exponential growth into a linear equation, making it easier to manage and understand. Whether you’re investing or tracking population growth, the rule of 70 can be a useful tool.
The Reason Why the Rule of 70 is Popular in Finance
Finance can be a complicated field, with many different formulas and calculations to keep track of. One of the most popular formulas is the rule of 70, which is used to manage exponential growth. The reason why this rule is so popular is because it offers a simple way to manage complicated growth formulas. By using the number 70 alongside the rate of return, the rule of 70 can break down growth formulas into a simple equation.
Understanding Exponential Growth
Before we dive into the rule of 70, it’s important to understand exponential growth. This type of growth occurs when a quantity increases at a fixed percentage rate over a fixed period of time. This means that the growth rate is not constant, but instead increases over time.
Exponential growth can be difficult to manage because it can quickly become overwhelming. When growth rates are high, it can be difficult to keep up with the changes and make adjustments accordingly. This is where the rule of 70 comes in.
The Rule of 70
The rule of 70 is a simple formula that can be used to manage exponential growth. It works by dividing the number 70 by the rate of return. The resulting number is the approximate number of years it will take for the quantity to double.
For example, if you have an investment that is growing at a rate of 7%, you can use the rule of 70 to determine how long it will take for the investment to double in value. Simply divide 70 by 7, which gives you a result of 10. This means that it will take approximately 10 years for the investment to double in value.
The rule of 70 can be used in a variety of different situations, including investments, population growth, and more. It’s a versatile formula that can help you manage exponential growth in a simple and effective way.
Why is the Rule of 70 True?
Now that we understand what the rule of 70 is and how it works, the question remains: why is it true? The answer lies in the mathematical concept of logarithms.
Logarithms are a way to express exponential growth in a more manageable way. They allow us to convert exponential growth into a linear equation, which is much easier to work with. The rule of 70 is based on the natural logarithm, which is a specific type of logarithm that is commonly used in finance and economics.
Without getting too deep into the math, the rule of 70 is true because it is based on the properties of logarithms. By using the natural logarithm, we can convert exponential growth into a linear equation, which makes it much easier to manage and understand.
In Conclusion
The rule of 70 is a popular formula in finance because it offers a simple way to manage complicated exponential growth. By using the number 70 alongside the rate of return, the rule of 70 can break down growth formulas into a simple equation. It’s a versatile formula that can be used in a variety of different situations, and it’s based on the mathematical concept of logarithms. So, the next time you need to manage exponential growth, remember the rule of 70.
References for Why is Rule of 70 True?

Book: The Rule of 70 by Donald A. Redfoot
Redfoot explains the history and mathematics behind the rule of 70, as well as its applications in various fields.

Web article: Understanding the Rule of 70 and Compound Interest by Investopedia
This article provides a detailed explanation of the rule of 70 and how it relates to compound interest.

Book: Principles of Economics by N. Gregory Mankiw
Mankiw discusses the rule of 70 in the context of economic growth and its limitations.

Web article: The Rule of 70: How to Double Your Money in Seven Years by The Balance
This article explains how the rule of 70 can be used to calculate investment growth and doubling time.

Book: The Mathematics of Investment by William L.Hart
Hart explores the rule of 70 in relation to investment and financial planning.
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