What is the Rule of 72?
The Rule of 72 is a fast way to estimate the time it will take an investment to double in value. This back-of-the napkin formula is a good way to compare two investment opportunities, identify the best place to put your money for optimal growth, examine the potential outcomes of fees or inflation, and more.
The Rule 72 Formula
The Rule of 72 formula is straightforward and easy to use.
Simply divide 72 by the interest rate or anticipated rate of return on an investment, and voila! The result is the number of years you can expect it to take for that investment, loan, or other number that grows at a steady, compounding rate to double.
Interest Rate = the rate of return on an investment
Let’s take a look at a brief example.
The Rule of 72 in Action
An investment in XYZ Corp. has historically (over the last decade) yielded a healthy 7 percent return. If we want to make an investment in it now, how long will it take for our money to double?
Plugging our numbers into the equation, we can see that if that 7 percent rate stays constant, we can expect to double our money in a little over a decade: 72/7 = 10.29.
Note that we enter the interest rate (rate of return) as a whole number larger than the number 1. If we entered 7 percent into the denominator as .07, the answer would be in excess of a thousand years—not the kind of time frame most investors have in mind.
Here are some benchmarks you can use to guestimate the amount of time it will take an investment to double, without having to do any calculations at all.
Armed with this quick and dirty estimate, we can easily compare any investments with a stable rate of return—but that’s not all.
Using the Rule of 72, we can also determine that a personal loan with a fixed interest rate of 8 percent and a principal of $4,000 will have grown to $8,000 in nine years if allowed to grow unchecked (72/8 = 9). It can tell us that an inflation rate of 3 percent will halve the value of our money in 24 years (72/3 = 24).
In fact, any numbers that will grow at a steady rate can halve the length of time it will take for them to double (or halve) in size. This applies to populations, macroeconomic conditions such as GDP (gross domestic product), and other interesting cases outside the world of investing.
What Does the Rule of 72 Mean for Investors?
Besides basic comparisons between investments, the Rule of 72 has some other interesting insights to offer investors. Though the simplified version we are talking about here is straightforward to use, the concept behind it originates from a more complicated logarithmic formula.
By opting to use the simplified version, we lose some precision and accuracy in calculation, but not so much that the calculation ceases to be useful. Additionally, it is outside the scope of many investors’ experience to use log tables or scientific calculators to determine the exact month, day, hour, and minute that their investment will double in size.
Nevertheless, the concept behind the Rule of 72 is an important factor in shaping the way we think about different money opportunities.
The Rule of 72 and Savings Accounts
It is often said that if you scrimp and save and sock away every extra penny into your savings account, you will be surprised to find that it hasn’t grown much at all, come year end. While savings accounts can be an important part of a personal money management plan, they are generally poor money-growth vehicles.
Many savings accounts offer interest rates lower than 1 percent. We intuitively know this is a small amount, but when put into perspective via the Rule of 72, we can see that it will take 72 years—roughly the average life span of most elephants—to double in value, assuming no other deposits were made.
Is the Rule of 72 Accurate?
Rule of 72 calculations are sufficiently accurate for most investments with a low rate of return. As with all quick and dirty calculations, it isn’t perfect and it shouldn’t be relied upon as the sole determining factor in deciding where to invest your money.
This is especially true for investments with high rates of return.
The accuracy of the Rule of 72 calculation starts to break down as the rates of return get larger than the 10 percent mark. A general rule of thumb is that investors should add 1 to 72 for every three percentage points past an 8 percent rate of return. This would mean that to determine the most precise amount of time it would take an investment with an 11 percent rate of return, the formula would divide 73 by 11 instead of using 72 in the numerator.
Bearing this pattern out, the amount of time an investment with a 14 percent rate of return would take to double would be determined by dividing 74 by 14. For most investors, however, the fast and simple Rule of 72 is a sufficiently accurate calculation.