The Rule of 72 for Compound Interest

0
A commonly asked question about investments and their annual rate of return is

“How long will it take to double my investment?”

The answer to that question could be complex with some pretty involved logarithmic math.

Most people would have to rely on a calculator to use the equation to get the number of years required for an investment to double.

Fortunately there is a simple division formula we can use that gives an accurate estimation of the complicated logarithmic equation.

In this article I’ll explain the shortcut that will help you determine how long it will take for your investment money to double.

The Rule of 72

The shortcut to calculate the years needed to double your investment is known as the Rule of 72.

The rule is as follows –

Years needed to double investment = 72 divided by the compound annual interest rate.

If you are unsure of what a compound interest rate is, I’ve written an article on it.

The Rule of 72 in action

Let’s take an example of the rule of 72 in action.

If we take an investment that returns 6% annually to calculate this we would use this equation

T = ln(2)/ln(1.06)=11.895 (where T is time)

Now you could do that with a scientific calculator but using the Rule of 72 you have a much simpler calculation that gives you nearly the same result.

T = 72/6 = 12

So as you can see an investment with a 6% annual interest rate doubles in twelve years.

The rule of 72 is much easier no?

Caveats to the Rule of 72

The Rule of 72 will tend to over-estimate with lower interest rates and under-estimate for higher ones.

Optimally the rule is mostly accurate for interest rates between 6% and 10%.

If an interest rate is lower than 6% you can adjust the rule by adding or subtracting 1 from 72 for every three points of divergence from 8%.

Here are a couple of examples

4% annual compounding interest – 71

11% annual compounding interest – 73

20% annual compounding interest – 76

Here is a more complete scenario

Let’s say you have a return rate of 15%. The rule of 72 without adjustment would say the investment would double in 4.8 years.

However 15 – 8 = 7 and 7 / 3 = 2.3333 . Therefore the adjusted rule would equal 72 +2 or 74. Using our adjusted rule we get –

74/15 = 4.9333

Comparing this to our logarithmic equation

T=ln(2)/ln(1.15) = 4.959

We see the adjusted rule gives us a more accurate result of around 5 years.

Continuous Compounding and the Rule of 72

If daily or continuously compounding is used in lieu of annual compounding you can use 69.3 to get a more accurate result.

You can also use 69 or 70 as well as 69.3 to simplify the calculation even more.

The Rule of 72 – Simplifying Return Calculations

You can see how the Rule of 72 simplifies the calculation to determine the amount of time needed to double an investment.

It takes the complicated logarithmic calculation needed to calculate the result and changes it into a simple division equation that most people can do in their head.

Find an excel template for this rule of thumb below. Plug some numbers in and play around.

Check out our other calculators

Savings Rate Calculator

Financial Freedom Calculator

Early Retirement Calculator

Mortgage Loan Payment Calculator

Fee Effect Calculator

Compound Interest

Leave a Reply