It's impossible to predict how your investment is going to go, when it will pay off or if it will at all. But that's never stopped anyone from trying.
How do you possibly predict how much money you could make from an investment? One potential way is to look at the interest rates on possible investments. The problem is that calculating compound interest can get a little complicated, especially if you don't have a calculator handy.
That's why the "rule of 72" exists. So you can get a sense of how interest can play out on an investment over time in a pinch. It's a helpful shortcut that has been used for years.
Here's what you need to know about it.
What Is the Rule of 72?
The rule of 72 is a formula that lets you get a close approximation of how long it would take for an investment to double considering its set rate of return, an estimation that factors compound interest in without requiring you to do the more complex math required in calculating compound interest.
Using the rule of 72 allows you to have a solid idea of when your investment would double just from the investment rate. Very conveniently, the number 72 divides cleanly into 1, 2, 3, 4, 6, 8, 9 and 12, allowing for a quick and simple division problem instead of your usual compound interest problem.
Formula and Example
Because fixed interest rates are most often done in annual increments, we will use the following formula to explain the rule of 72:
Years it would take to double your investment = 72 / Compound annual interest rate
Pretty simple, right? If the annual interest rate on the investment is 8%, just plug it in. 72 / 8 = 9. Per the rule of 72, this investment would take approximately 9 years to double in value at this rate. The exact number is 9.006 years.
8% as an interest rate gets you the closest to exact via rule of 72, but other percentages get close as well. If it was an interest rate of 6%, the approximation would be 12 years, while the exact number is 11.896. A 10% interest rate through the rule of 72 would be 7.2; the exact number of years is 7.273.
This rule can potentially help you get a sense of how long an investment would take to double in value based on the interest rate you're being offered. It can also help you figure out the interest rate you'll want if you're looking to double your investment in a certain amount of time. Let's say you want your investment doubled within five years. The equation is now 5 = 72/x, and you need to solve for x. The interest rate on this investment would, per this rule, need to be around 14.4%. In this regard, another effective rule of 72 is: Compound annual interest rate = 72 / Years it would take to double your investment.
Variations on the Rule of 72
Some variations on the rule of 72 are the rules of 70, 69 and 69.3. On its face, these may seem like fairly negligible differences, but they can make a difference. Some prefer to use the rule of 69.3 when interest compounds daily instead of yearly.
Variations on the rule also tend to get used because the rule of 72's accuracy is best limited to a small number of low rates of return. It's most accurate at an 8% interest rate, with 6-10% being its most accurate window.
The general rule of thumb to help make the estimate more accurate is to adjust the rule by 1 for every 3 percentage points the interest rate differs from 8%. This is in either direction; if it is a 5% rate, you should use a rule of 71, and if it is 11% you use a rule of 73.
Let's use 14% as an example: 14% is 6 points higher than 8%, so the recommendation for a more accurate approximation would be the rule of 74. The rule of 74 puts it at about 5.285 years, as opposed to the rule of 72 which would say 5.14 years. The exact amount of time for this one to double would be 5.29 years, making the rule of 74 much closer.
How Can You Calculate the Exact Amount?
I've mentioned several times now what the "exact" number of years it would take for an investment to double. Where does that number come from?
The actual number of years comes from a logarithmic calculation, one you can't really determine without having a calculator with logarithmic capabilities. That's why the rule of 72 exists; it lets you basically figure out how long it will take to double without requiring an actual physical calculator on your person.
The exact equation for figuring out how many years it would take for your investment to double based on compound interest is: ln(2) / ln(1 + (interest rate/100)). In this case, "ln" means natural log value as it would on a calculator.
If you have the capabilities to determine the number of years it would take with natural logs while looking at return rates, this is how you would go about finding out exactly how long it would take for, as an example, your $100 to turn into $200. If you don't have that calculator on you, the rule of 72 and its variations are a great shortcut.
Why Does Rule of 72 Work?
It may not be apparent at first glance how this exact equation is able to bring us to the rule of 72. For it to become clearer, input ln(2) into a calculator. It's an irrational number, but when you put it into the calculator by itself it will give you a number that it equals: 0.69314718056.
Or, phrased in another way, 69.3%.
That's how you get the rule of 69.3, but unless you're a math whiz who somehow memorized multiples of 69.3 it's still pretty difficult to do the equation. Thus, 70 and 72, which have more numbers that divide cleanly into them while still giving close approximations, became popular.
Rule of 72 Applications
The gross domestic product (GDP) of a country is something that increases at a compounded rate, for example. Let's say a company's GDP grows at a rate of 5% annually. You can use the rate of 72 here - or, because 5% is 3 points below 8%, the rule of 71. With this rule, that country's GDP would be estimated to double in 14.2 years.
Money isn't the only thing that can increase at a compounded rate. Say there is a city whose population increases by 6% a year. With the rule of 72, you can estimate that that city will double its population in 12 years. Conversely, if the population is decreasing by 6% a year, you could use the rule to estimate that in 12 years, the population will be halved.
Using the rule of 72 to determine when something is halved instead of doubled also comes in handy if you're using it regarding increasing inflation. If a currency has a yearly inflation rate of 9%, we can ascertain by dividing by 72 that at this rate the currency would be worth half its value in approximately eight years.