How long will it take to double your money?
The Rule of 72 is a mathematical shortcut, that estimates the time it will take for an investment to double in value, given that it’s compounding at a set interest rate.
The calculation is: Years to double = 72 / interest rate. For example, if the interest rate is 12%, then the years to double = 72 / 12 = 6 years.
The Rule of 72 dates back to 1494, when Italian mathematician and monk, Luca Pacioli referenced the rule in his book Summa de Arithmetica. As a side note, Pacioli was also known as the ‘father of accounting’, and in the same book he laid out the first clear description of double-entry accounting.
The beauty of the Rule of 72 is its simplicity. The maths is relatively easy, especially given 72 is divisible by a lot of numbers. On top of this the results are surprisingly accurate.
The Rule of 69.3 is even more accurate, but only when the interest rate is 3% or below.
An easy example
Just recently, Vanguard released its 2022 Index Chart, which shows the 30-year returns for a number of asset classes. These returns assume that all dividends received are reinvested.
The chart shows that Australian shares have returned on average 9.0% p.a. over the last 30 years, and US shares have returned 10.2% p.a.
Given these average returns, the Rule of 72 can be used to calculate the time it would have taken for people to double their money.
For Australian Shares the calculation is: Years to double = 72 / 9.0 = 8 years, and for US Shares: Years to double = 72 / 10.2 = 7.1 years.
Other uses
The formula can also be spun around to calculate the interest rate needed, if we are wanting to double our money in a set number of years.
This formula is: Interest rate = 72 / Years to double.
Let’s say we are wanting to double our money in 10 years, then the interest rate required to achieve this would be: 72 / 10 = 7.2%.
The Rule of 72 can be used for any growth rate where compounding is involved.
For example, if the economy is growing each year at 3%, we can calculate that the economy will double in size in 72 / 3 = 24 years.
The Rule of 72 can also be used for non-financial exponential growth. For example, if a particular country has a human population growth rate of 2% p.a., we can calculate that the country’s population will double in size in 72 / 2 = 36 years.
Comparing returns
The Rule of 72 can also help us to compare investments. For example, if we have an investment opportunity that guarantees a 3% return, and another opportunity that guarantees a 4% return, we can work out the timeframe difference between the two, for doubling our money.
The 3% return will take 72 / 3 = 24 years, and the 4% return will take 72 / 4 = 18 years.
Given that 6 years is quite a long time, the comparison helps us in our decision making. It also highlights the difference that 1% can make when compounding returns.
The Rule of 72 is a powerful formula, because it’s quick and easy to use, but it can also help us work out realistic timeframes for achieving our financial goals.
Frequently Asked Questions about this Article…
The Rule of 72 is a simple mathematical formula that estimates how long it will take for an investment to double in value at a given interest rate. It's a handy tool for investors to quickly assess the potential growth of their investments.
To calculate the time it takes to double your money using the Rule of 72, divide 72 by the annual interest rate. For example, if your investment grows at 12% per year, it will take approximately 6 years to double.
Yes, the Rule of 72 can be applied to any scenario involving exponential growth, such as population growth. For instance, if a population grows at 2% annually, it will double in about 36 years.
The Rule of 72 is surprisingly accurate for most interest rates. However, for rates below 3%, the Rule of 69.3 is more precise. Despite this, the Rule of 72 remains popular due to its simplicity.
The Rule of 72 allows investors to compare the timeframes for doubling their money across different investments. For example, a 3% return takes 24 years to double, while a 4% return takes 18 years, highlighting the impact of even a 1% difference.
Yes, you can rearrange the Rule of 72 to find the required interest rate by dividing 72 by the desired number of years to double your money. For example, to double your money in 10 years, you need a 7.2% interest rate.
The Rule of 72 dates back to 1494, when it was referenced by Luca Pacioli, known as the 'father of accounting,' in his book Summa de Arithmetica. It has been a valuable tool for centuries in financial calculations.
Using historical data, such as Vanguard's 2022 Index Chart, the Rule of 72 can estimate how long it would take for investments in Australian or US shares to double, based on average annual returns of 9.0% and 10.2%, respectively.
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