How do seasoned investors know how to make lightning-quick decisions? What kind of magic tricks do they have up their sleeve?
A lot of this comes from experience, but there are some handy shortcuts that any burgeoning investor can consider. One of these shortcuts is the Rule of 72.
This rule is a reasonably accurate estimate of how long an investment is going to take to double with a fixed annual rate of interest. All you have to do is divide the number 72 by the annual rate of return to obtain a rough estimate of the number of years it will take for your initial investment to double.
Calculating Using The Rule of 72
For example, if an investment scheme that you’ve been eyeing promises around an annual growth rate of 6%, then 72/6 = 12. This means you’ll be getting double your original investment back in twelve years.
It’s a super useful shortcut you can use on the go to get a rough idea of how long you have to wait to see double the returns.
For clarity, you’ll be using the annual return as it is, and not in decimal form. This is so you get the result in years.
Other Ways To Use The Rule of 72
You can also work this rule backward to find different values. To demonstrate, say you’re hoping to double your money in 5 years. Divide 72 by 5 and the answer (14.4) is how much annual growth rate you’ll need to double your principal in five years.
If it grows, it goes. The Rule of 72 can be used to estimate inflation, interest, and even population.
For example, it’s been found that your country’s GDP grows at 3% a year. This means that the economy is expected to double in 24 years (72/3 = 24). If this percentage gets pushed up by even one percent, then the economy doubles in 18 years (72/4 = 18).
On a personal scale, this principle can also be used on credit card fees. If you sign up for a credit card with 12% interest, then the amount you owe the company will double in six years (so pay your card off in time!).
Where did this come from?
This rule is derived as follows. Assume the following:
t = Time to doubleln = natural log function d = compounded interest rate per period in decimal number w = 100d so interest rate in whole numbers
If d = 0.06 and t = 12, then (1+0.06)12 = 2.012
In other words, if you compound 6% interest twelve times, you arrive just above doubling the original principal, just like the Rule of 72 would suggest.
If we move things around a bit, we get the following (remember logarithmic rules?):
That's nice. If we then divide by t, later add d to numerator and denominator and move things around a little, we get:
This is quite helpful, since the ln (1+d)stays close to just d with small d values and thus, the right parenthesis stays close to 1.
If we take an appropriate example for d, e.g. 8%, we can simplify our calculations, while still keeping it quite precise.
The right parenthesis becomes an approximate constant:
We then use this approximation for the righter parenthesis. Multiplying with ln 2we get approximately 0.72.
We then multiply both the numerator and denominator by 100 to get to whole numbers.
Ta-da!There's the Rule of 72!
To find out how long it would take to double an investment with 8% returns annually, you would calculate it like this:
T = ln(2) / ln(1+0.08)) = 9.006 years
This value is close to the approximate value obtained by the Rule of 72 (72 / 8) = 9 years. Because logarithmic calculations can be a real chore and require the use of scientific calculators, this was eventually simplified to The Rule.
Limitations Of The Rule
As long as the interest rate is less than 20%, this tool is an incredibly accurate measure for returns. Any more than that and the likelihoods of error start to become significant. At 20% a more accurate number to use would be 76 and at just 2% the number would be 70.
But, 72 is both good in the right range, plus it can be divided with 2, 3, 4, 6, 8, 9, 12 and 18.
While it can be helpful for helping you gain a quick understanding of the value of an investment, it should not be used on its own. Remember to conduct additional research and consult any investment professionals to help you make better, more informed decisions.
Happy investing!
FAQs
The Rule of 72 is a calculation that estimates the number of years it takes to double your money at a specified rate of return. If, for example, your account earns 4 percent, divide 72 by 4 to get the number of years it will take for your money to double. In this case, 18 years.
What is the rule of 72 which amount will double faster? ›
How the Rule of 72 Works. For example, the Rule of 72 states that $1 invested at an annual fixed interest rate of 10% would take 7.2 years ((72 ÷ 10) = 7.2) to grow to $2. In reality, a 10% investment will take 7.3 years to double (1.107.3 = 2). The Rule of 72 is reasonably accurate for low rates of return.
Is the rule of 72 a reliable way to estimate doubling time? ›
Key Takeaways
The Rule of 72 is a simplified formula that calculates how long it'll take for an investment to double in value, based on its rate of return. The Rule of 72 applies to compounded interest rates and is reasonably accurate for interest rates that fall in the range of 6% and 10%.
How to double $2000 dollars in 24 hours? ›
Try Flipping Things
Another way to double your $2,000 in 24 hours is by flipping items. This method involves buying items at a lower price and selling them for a profit. You can start by looking for items that are in high demand or have a high resale value. One popular option is to start a retail arbitrage business.
What interest rate doubles in 20 years? ›
For example, at 5% annual interest, it would take 20 years to double your money (100 / 5 = 20).
What does the Rule of 72 calculate? ›
Do you know the Rule of 72? It's an easy way to calculate just how long it's going to take for your money to double. Just take the number 72 and divide it by the interest rate you hope to earn. That number gives you the approximate number of years it will take for your investment to double.
What is the Rule of 72 quizlet? ›
Rule of 72. The number of years it takes for a certain amount to double in value is equal to 72 divided by its annual rate of interest.
What are the flaws of Rule of 72? ›
Errors and Adjustments
The rule of 72 is only an approximation that is accurate for a range of interest rate (from 6% to 10%). Outside that range the error will vary from 2.4% to 14.0%. It turns out that for every three percentage points away from 8% the value 72 could be adjusted by 1.
What is the limitation of Rule 72? ›
It is not an exact value and can only provide a general estimate of the time required to double the investment. If the interest rate changes due to some factor, the Rule of 72 becomes null and void. The Rule of 72 does not apply to changing interest rate investments or basic interest investments.
What is the Rule of 72 assumptions? ›
The rule of 72 is a calculation that estimates how many years it will take an investment to double in value. The calculation is based on the interest rate of the investment and the assumption that the investment's growth remains consistent.
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- Invest in Real Estate.
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- Invest in real estate.
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- Make Money Blogging.
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- Consulting.
Final answer:
It will take approximately 15.27 years to increase the $2,200 investment to $10,000 at an annual interest rate of 6.5%.
How many years would it take money to grow from $5000 to $10000 if it could earn 6% interest? ›
Final answer:
It would take approximately 11.90 years for the money to grow from $5,000 to $10,000 with a 6% interest rate.
How long will it take to double $1000 at 6 interest? ›
So, if the interest rate is 6%, you would divide 72 by 6 to get 12. This means that the investment will take about 12 years to double with a 6% fixed annual interest rate. This calculator flips the 72 rule and shows what interest rate you would need to double your investment in a set number of years.
What is rule 72 and rule 69 of doubling period? ›
Rules of 72, 69.3, and 69
Rules of 69.3 and of 69 are also methods of estimating an investment's doubling time. The rule of 69.3 is considered more accurate than the Rule of 72, but can be much more troublesome to calculate. Therefore, investors typically prefer to use a rule of 69 or 72 rather than the rule of 69.3.
What is the rule of 70 and how is it related to doubling time? ›
The rule of 70 is used to determine the number of years it takes for a variable to double by dividing the number 70 by the variable's growth rate. The rule of 70 is generally used to determine how long it would take for an investment to double given the annual rate of return.
What is the 8 4 3 rule of compounding? ›
The rule of 8-4-3 for mutual funds states that if you invest Rs 30,000 monthly into an SIP with a return of 12% per annum, then your portfolio will add Rs 50 lacs in the first 8 years, Rs 50 lacs in the next 4 years to become Rs 1 cr in total value and adds further Rs 50 lacs in the next 3 yrs to reach Rs 1.5 cr.
What is the Rule of 72 114 and 144? ›
Rules 72, 114, and 144 can be used to determine the period your investment can take to double, triple, and quadruple respectively. Follow the Minimum 10% Rule to get started with investing. Also, if you are beginning your investment journey, you might want to consider the Emergency Fund Rule.
