# The Rule of 72: What Is It, and How You Can Use It In Your Investing? Thom Benny June 20, 2022

## Using the Rule of 72 is a simple method for getting an approximate idea of how long it takes for your money to double. So how can you use it in tracking your investments?

In a perfect world, investors would like to know, in advance, how long it will take to double their money in the stock market. Knowing exactly how long this will take is helpful in planning out portfolio diversification, and eventually achieving financial freedom.

But, how does one go about working out how long it might take to double the value of a portfolio?. Investors can easily become confused. Especially when it comes to accounts that receive annual interest. Then, they may reach for complex formulae, and spreadsheets.

But, there’s a simpler, better way of calculating the period it will take to double one’s investment. One of the best ways is to use the Rule of 72 — one of the simplest methods of calculating when one’s portfolio will double in value.

# What is the Rule of 72?

The Rule of 72 refers to the mathematical concept that shows how long it will take an investment to double in value (in theory). It’s a simple formula that anyone can use to determine the approximate time when an investment will double at a given annualized rate of return.

However, the Rule of 72 only works for calculating compounding growth. Investors can use the Rule of 72 only for an account that earns compound interest, not simple interest. Additionally, the Rule of 72 works better with an interest rate ranging from 6% to 10%.

Besides being used to show exponential growth of a portfolio, the Rule of 72 is also used to show exponential decay. For example, the loss of purchasing power caused by inflation, or the drop in the population numbers.

### Compound Growth vs. Simple Growth

Interest helps the portfolio growth, and allocating a certain amount of money to an account that earns interest is a smart move investors make. There are two types of growth, or interest — simple and compound, and these are crucial for using the Rule of 72.

Compound interest is added to the already existing interest, plus the principal amount of the loan or deposit.

This type of interest is calculated with the following formula:

A = P (1 + r) (n)

On the other hand, simple interest is added only to the original investment. The formula for simple interest is:

A = P (1 + Rt)

Compound interest is better, as it can reduce the time required to double the money in an account, and grows the investments exponentially.

In other words, compounding interest grows an investment more and more every year, since the interest gets calculated on progressively larger amounts. Whereas simple interest doesn’t compound on itself over time.

## Origins of the Rule of 72

While it may sound surprising, the Rule of 72, and the concept of interest aren’t new ideas. Even ancient civilizations, such as the Mesopotamian, Greek, and Roman, used them in transactions, and basic money management.

While it may not have been called the Rule of 72, it was always around. For example, lenders always wanted to know how to manage their investments, and the rate of return.

## Who Came up With the Rule of 72?

The first person to ever take note of the Rule of 72 was Luca Pacioli. Pacioli was an Italian mathematician. He mentioned the Rule of 72 in his book Summa de Arithmetica, Geometria, Proportioni et Proportionalita (Summary of Arithmetic, Geometry, Proportions, and Proportionality), published in 1494.

Pacioli stated that people who wish to know how many years it will take to double their investment should always ‘keep the number 72 in mind.’

Pacioli never went deeper into defining or explaining the reasoning behind 72.

With that in mind, it could have happened that someone else invented the number to improve their calculation of the interest rate, and portfolio growth. Some even say that Albert Einstein was the one to invent the Rule of 72, but that was never confirmed.

### Why Is It Called the Rule of 72?

There’s no specific reason this rule is called the Rule of 72. Still, it serves to replace the complex logarithmic calculation that most investors are having trouble dealing with. The exact formula for determining how many years it takes to double your money based on compounding interest, or growth, is:

ln(2) / ln(1 + (interest rate/100))

where “In” represents the natural log value.

Good mathematicians could use this formula to get accurate results by observing return rates, and natural logs. The actual number that’s derived from the formula is 69.3. However, since this number is not easy to work with, people usually replace it with 72, since it’s equally good in showing the approximate number of years necessary to double the investment.

Navexa’s portfolio tracker is even easier to use. Our portfolio tracker automatically calculates every aspect of portfolio performance for shares, cryptocurrency, cash accounts and more.

## How to Use the Formula?

To calculate how long it would take for the investment to double in value, one can use the following formula:

Years to double = 72 / expected rate of return

This method can also be used to calculate the expected rate of return.

Investors should divide 72 with the years to double to get the rate of return on their investment (expected rate of return = 72 / years to double).

This principle handles fractions, or portions of the year. Plus, the resulting rate of return includes compounding interest on the investment.

However, there are a few things to pay attention to:

• the interest rate should not be a decimal
• this formula should be applied to an investment that receives annual interest (compounding)
• the farther the interest rates are from 8%, the less accurate the results would be
• to calculate lower interest rates, one can drop the number to 71
• this formula is easily divisible, but not perfectly accurate

## Rule of 72 — Variations

Since this principle provides an approximate result, sometimes investors use slight variations, like the Rule of 69, Rule of 70, or Rule of 73.

These numbers are used in the same way, and serve to calculate the years required for the investment to double in value.

### Rule of 72 — Examples

Here’s a simple example of using the method to calculate how long it takes for the investment to double:

Let’s say an account earns 4% of annual interest.

dividing 72 by 4 would give the years it takes for the money to double – 18.

When used to show inflation, and other deprecating numbers, the formula is the same.

However, the final result will show the years it will take for the amount to be cut in half. Since this principle provides an approximate result, sometimes investors use slight variations, like the Rule of 69, Rule of 70, or Rule of 73.

Both novice, and experienced investors could use the Rule of 72 to estimate the doubling time of their holdings. Since the Rule of 72 is easy to use, almost anyone can estimate how long it will take for a certain number to double in value.

# Who Uses The Rule of 72?

Since this rule can be used outside of personal finance and investing, it’s also used by other experts who need to estimate how many years it will take for a value to double.

## What Is the Rule of 72 Good For?

The Rule of 72 is a good method that can be applied to anything that grows (or decays) exponentially. For example:

• GDP
• Inflation
• Investment compounding interest rate
• Credit card debt
• House mortgage
• Car loan refinancing

## How Does the Rule of 72 Work?

By using the Rule of 72, investors can get an approximation of the years it will take for their assets to double in value.

This makes the Rule of 72 one of the key personal finance formulae to understand for investingt. Plus, this rule gives a general idea of how many “doubles” an investor might get during their lifetime, or for a certain period.

### Does It Show Accurate Results?

When it comes to the accuracy of this rule, the Rule of 72 provides approximate information about the desired time period.

This formula is a simplification of the more complex logarithmic equation. Investors who wish to get an accurate result would have to do the entire calculation, or use an electronic spreadsheet calculator.

Navexa’s smart portfolio tracker replaces the spreadsheet. It automatically shows portfolio growth, and helps investors get a clear insight into the years it takes to grow their wealth.

### What Are the Things the Rule of 72 Can Determine?

As we previously mentioned, this rule is usually used to determine the rate of return on the investment. However, experts in various industries can also apply this principle to anything that is compounding, and this doesn’t necessarily involve money.

For example, a city’s population that grows/decreases by a certain percentage per year can also use the rule to check how long it would take for the population to double, or halve.

### Limitations of This Principle

Besides not being completely accurate in showing data, this formula is also mainly applied to compounding interest accounts, not simple interest ones. What’s more, the Rule of 72 works better for lower interest rates, and is less precise as the interest rate increases.

Additionally, this calculation can’t be used to forecast how long it might take to get a double return with decentralized finance and cryptocurrency, due to high market volatility, and sudden changes in prices. In fact, no calculation can give anyone a 100% accurate prediction of what their investments may or may not do in the future.

## Speculating Future Returns With The Rule Of 72

When people invest, they often want to know how long it will take to double their money. However, predicting the exact number of years can be tricky.

This is why the Rule of 72 exists. When used correctly, with an investment that involves compound interest,this formula is generally fairly accurate — provided, of course, the annualized rate of return remains consistent.

here are certain limitations investors should be aware of. This mathematical concept works only with accounts that receive compounding annual interest at lower rates.

The higher the rates go, the less accurate the results will be.

This principle doesn’t work with simple interest.

On the other hand, investors can slightly change the number, based on their annual interest rate. For example, some may use 69.3, or 73, depending on the percentage of their rate.

The Navexa portfolio tracker and reporting platform is a fast, accurate way to determine your annualized rate of return across shares, ETFs, cryptos, cash accounts and more. We handle all portfolio performance calculations behind the scenes so you can focus on better understanding your portfolio and returns. Thom Benny

Thom Benny has worked in financial research & communications since 2013. He pursues his fascination with financial literacy, investing and economics as Communications Director at Navexa, a portfolio tracking platform for shares & crypto.