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.