Rule of 72
What Is the Rule of 72?
The Rule of 72 is a simple way to determine how long it will take for an investment to double, given a fixed annual rate of return.
The rule states that the number of years required to double your money is approximately equal to 72 divided by the annual expected return, expressed as an integer (not a percentage).
So, if you expect your investments to grow at a rate of 8 percent per year, it will take approximately 9 years (72/8) for them to double.
Of course, this is just a rule of thumb and not an exact science. Nevertheless, it can be a helpful tool for quickly estimating how long it will take your money to grow. And, it can be especially useful when comparing different investment opportunities.
For example, let’s say you’re trying to decide between investing in a stock that you expect will return 10 percent per year and a bond that you expect will return 5 percent per year.
Using the Rule of 72, you can estimate that it would take approximately 7.2 years for your money to double with the stock investment (72/10) and 14.4 years for the bond investment (72/5).
So, in this case, the stock investment would be the better option taking return as the only criteria because it would take less time for your money to grow.
Of course, there are other factors to consider when making investment decisions.
But, the Rule of 72 can be a helpful tool for quickly estimating how long it will take your money to grow.
How Does the Rule of 72 Work?
The Rule of 72 works by taking the number 72 and dividing it by the expected annual return on your investment. The resulting number is approximately equal to the number of years it will take for your money to double.
For example, if you expect your investments to grow at a rate of 8 percent per year, it would take approximately 9 years (72/8) for them to double. Similarly, if you expect your investments to return 6 percent per year, it would take approximately 12 years (72/6) for them to double.
How Is the Rule of 72 Derived?
The Rule of 72 is based on the compounding interest formula:
A = P(1+r/n)^nt.
- P is the original investment (the principal).
- r is the annual interest rate.
- n is the number of compounding periods per year; for example, if you’re investing in a savings account that compounds interest monthly, n would be 12 (12 compounding periods per year).
- t is the number of years the investment is held.
- A is the final value of the investment after t years.
The Rule of 72 can be derived from this formula by solving for t when A = 2P (i.e., when the investment has doubled).
The more accurate number for the Rule of 72 would be 69 or 70 (hence why there exists a Rule of 69 and a Rule of 70), but 72 is commonly used because 72 is easily divisible by more numbers than 69 or 70.
Rule of 72 Formula
The formula for the Rule of 72 is:
T = 72 / r
Where T is the number of years it will take for an investment to double and r is the annual rate of return.
For example, if you expect your investments to return 10 percent per year, you would plug 10 into the formula like this:
T = 72 / 10
Which would give you a result of 7.2 (it would take approximately 7.2 years for your money to double at a 10 percent annual return).
Similarly, if you expect your investments to grow at a rate of 8 percent per year, you would plug 8 into the formula like this:
T = 72 / 8
Which would give you a result of 9 (it would take approximately 9 years for your money to double at an 8 percent annual return).
As you can see, the Rule of 72 is simply a shortcut for calculating the amount of time it will take for an investment to double.
And, it can be a helpful tool for quickly estimating how long it will take your money to grow.
How Accurate is the Rule of 72?
The Rule of 72 is only a quick rule of thumb and not as exact as what will be produced by accurately following the compound interest formula.
For example, if you wanted to know how long it would take for an 8 percent investment to double, the rule of 72 would predict 9 years.
To calculate the number of years it will take for an investment to double using the compound interest formula, we can rearrange the equation as follows:
n = ln(FV/PV) / ln(1+r)
substituting in the values from our example:
n = ln(2) / ln(1 + 0.08)
n = 9.006
The Rule of 72, in this case, is very accurate.
Let’s take a different number.
Let’s take the example of many central banks targeting an inflation rate of two percent.
Based on the Rule of 72, the price level of goods and services would double every 36 years.
Plugging into the compound interest formula:
n = ln(2) / ln(1.02)
n = 35.002
In this case we can see that the Rule of 72 is inaccurate by about one year, but is still less than three percent off.
This is why the Rule of 70 is considered more accurate, as it would have gotten it exactly. But the Rule of 72 generally enables easier mental calculations.
Should I use the Rule of 72 or the Rule of 70?
The Rule of 70 is usually more accurate, but the Rule of 72 enables easy division by 3, 4, 6, 8, 9, and 12, for example, while 70 does not.
In general, the Rule of 72 will give you an answer that is close enough for many purposes.
When Might the Rule of 72 Not Be Accurate?
The Rule of 72 makes some simplifying assumptions that might not always be realistic.
For example, it assumes that:
The investment will compound continuously
In reality, most investments don’t compound continuously, but rather on a yearly, monthly, or quarterly basis.
Nevertheless, the Rule of 72 can still be a helpful tool for estimating how long it will take your money to grow.
The interest rate stays constant
In reality, interest rates are often variable and can change over time.
Nevertheless, the Rule of 72 can still be a helpful tool for estimating how long it will take your money to grow.
Rule of 72 – FAQs
How Can I Use the Rule of 72?
The Rule of 72 can be a helpful tool for giving a rough estimate of how long it’ll take for your money to double given a certain return.
It can also be useful for comparing different investment opportunities.
For example, if you’re trying to decide between two investments, one with an 8 percent annual return and one with a 10 percent annual return, the rule of 72 can help you quickly estimate which one will grow your money faster.
Plugging 8 percent into the formula, we get:
T = 72 / 8 = 9 years
And plugging 10 percent into the formula, we get:
T = 72 / 10 = 7.2 years
As you can see, the investment with the higher annual return (10 percent) will grow your money faster (in 7.2 years vs. 9 years).
Keep in mind that the Rule of 72 is only an estimate.
Why Is the Rule of 72 Important?
The Rule of 72 is important because it can help you understand how compound interest works and how long it will take for your money to grow.
Compound interest is often called the “miracle of compounding” because it can cause your money to grow very quickly over time.
The rule of 72 can help you understand how quickly compound interest can work.
For example, if you invest $1,000 at an 8 percent annual return, your investment will be worth $2,000 in 9 years (72 / 8 = 9).
When Is the Rule of 72 Not Accurate?
The Rule of 72 becomes less accurate the greater the outlier.
For example, if an investment earns a one percent rate of return, it will double in a bit under 70 years, not in 72 years as the Rule of 72 would suggest, giving an estimation error of a bit over two years.
Summary – Rule of 72
The Rule of 72 is a quick and easy way to estimate how long it will take your money to double given a certain return.
You can perform the calculation by taking 72 and dividing it by the return percentage. So, for example, if your investment returned 4 percent per year, it would take 18 years to double according to the Rule of 72.
It can also be used for things like inflation (how long will it take for the price level to double at X percent inflation) or for determining population growth.
In trading, investing, and financial market contexts, it can be helpful for comparing different investment opportunities and for understanding how quickly compound interest can work.