# Exponential Growth, Double Time, and the Rule of 72

## What is Exponential Growth?

Exponential growth is a universal principle and can be used to describe any increase that is proportional to what is already there. In other words, even though the growth rate remains constant, each successive period of time the amount of growth is greater than the previous period.

The concept is very powerful because the results have great implications in finance and many other areas of study including science. Important studies in exponential growth are constantly being done in areas such as world population growth or the spread of bacteria.

## Is There a Difference Between Exponential and Compound Growth?

What is the difference between exponential growth and compound growth? The simple answer is: there is no difference. Compound growth is a term usually used in finance to describe exponential growth in interest or dividends. Compounding is not linear growth (i.e. 1,2,3,4,5,6,7) but geometric or exponential growth (i.e. 1,2,4,8,16,32,64).

### Example of Exponential Growth

Here is a simple example and how it is so powerful. What if someone offered you a choice between 5 million dollars today or 30 payments starting with 1 penny today and double the amount you receive each day for 30 days.

If you are like most people you would choose the 5 million if you had to choose quickly. That decisions would cost you millions of dollars. The first day you receive 1 cent, the next day 2 cents, then 4 cents, then 8 cents, and so forth. It doesn’t seem possible but by day 15 you would be receiving $164, by day 20 $5243, and by day 30 over 5.3 million dollars just for that day!

This example dramatically illustrates the power of compounding because the growth rate is 100% per time period. But the principle works at lower growth rates; it just takes more time periods.

Related Reading: Dividend Growth Compounding Versus Interest Compounding

The benefits of compound growth can be magnified with dividend growth compounding. As dividends increase over time the explosion of reinvested earnings is even more dramatic.

This makes time the most important aspect of reaping the benefits of exponential growth. This is why financial advisors exhort the advantages of starting your retirement plan early in life.

## Double Time

*Double Time* is the number of time periods it takes exponential or compound growth to double a given amount. Time periods may be any measurement such as seconds, hours, days, months, or years. The amount measured could be anything that is growing at a constant rate such as the population, bacteria in a lab, or money.

## Rule of 72

The *Rule of 72* is a helpful concept to estimate double time. In order to approximate the number of years it takes to double an investment, divide the growth rate into 72. For example, if an amount is growing by 10% per period, it will take approximately 7.2 periods (72 divided by 10 = 7.2) to double.

## Using Exponential Growth in Investment Planning

*Double Time* and the *Rule of 72 *are valuable tools in investment planning. If an investment is earning 8% per year it will take approximately 9 years to double (72 divided by 8 = 9 years). This means a $100,000 investment at age 20 (earning 8% annually) would grow to $3.2 million by age 65 without any additional capital. Forty-five years allows the $100,000 to double 5 times or every 9 years. This illustrates the power of exponential and compound growth as well as the importance of time.

*Exponential growth* is sometimes described as the “miracle of compounding” because of the extraordinary explosion that takes place over time. Investors can use *double time* and the *Rule of 72* to estimate the power of exponential growth to meet their retirement goals. Use this important financial concept to meet your investment goals!

Related Reading: 10 Investing Principles Fundamental To Successful Outcomes

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Disclaimer

While Arbor Investment Planner has used reasonable efforts to obtain information from reliable sources, we make no representations or warranties as to the accuracy, reliability, or completeness of third-party information presented herein. The sole purpose of this analysis is information. Nothing presented herein is, or is intended to constitute investment advice. Consult your financial advisor before making investment decisions.