One of the most promising paths to wealth is through investment vehicles.
Depending on one’s risk tolerance, there are many different investment options, namely, short-term and long-term. Generally speaking, long-term investments serve many purposes, but it also attracts the risk-averse as there tends to be far less risk involved.
Whichever type of investment is chosen, most people care about how they can double their initial investment as soon as possible.
When it comes to calculating the estimated growth of your investment, that’s where things get tricky for most people.
The good news is that many online tools will do the calculations for you and give you an idea of how long it will take to double your money.
However, if you’re looking for something quick and straightforward, you should consider applying the “Rule of 72.” It’s a simple equation that requires you to plug in just two numbers.
Let’s get right on it.
- What Is the Rule Of 72? (aka Einstein’s Rule Of 72)
- How to calculate returns using the rule of 72?
- When should you use the Rule of 72?
- What Einstein Has to Say About Compounding Interest
- The Power of Compounding: A Story of the King and a Peasant
- Examples of How the Rule of 72 Work
- When does the rule of 72 not work?
- Bottom Line
What Is the Rule Of 72? (aka Einstein’s Rule Of 72)
The Rule of 72, otherwise known as Einstein’s Rule of 72, is a straightforward way to calculate the time it will take for a total amount of invested money to double in value based on its fixed annual rate of interest.
Although there is no proof that Einstein ever coined the phrase Rule of 72, Einstein did say that, “compound interest is the eighth wonder of the world. He who understands it, earn it… he who doesn’t…pays it.” If Einstein believes in it that much, we should definitely take the time to learn it.
How to calculate returns using the rule of 72?
To make this calculation, all you have to do is:
- Divide 72 by your estimated annual rate of return
The total value given will be the estimated amount of years it will take for your initial investment to double its value.
It’s that simple.
However, keep in mind that this is only an estimate, and if your interest rate changes over time, it will invalidate your initial calculation. To account for this, you could always give an estimated average rate of return over multiple years.
For a detailed example, keep reading!
When should you use the Rule of 72?
We recommend using the Rule of 72 if you’re a beginner investor with a small portfolio and dealing with only a few interest rates.
The larger your portfolio gets, the more important it is to incorporate a more sophisticated tool to give you an accurate projection.
You can use the Rule of 72 at any point in your investment journey; however, it provides the most accurate results with lower interest rates as well. The greater the interest rate, the greater the margin of error.
In cases where you have multiple investment portfolios with various interest rates, the best way to calculate the timeframe in which your initial investment will double is by hiring a personal or Robo investment advisor.
Or you can always reach for an investment calculator. Many online investment platforms come with built-in calculators to aid you in such calculations. If you need some particular suggestions to help you get started, feel free to reach out to us.
What Einstein Has to Say About Compounding Interest
Some people look at compound interest as the “8th Wonder of The World,” a saying coined by the great Albert Einstein. And it certainly makes sense when you consider how compound interest is designed to make money off money, a phenomenon that we’re fortunate to have access to.
While there’s no way to know for sure, it has been recorded in the past that Einstein was once asked what mankind’s greatest invention was. To that, he allegedly responded: “compound interest.”
Even more, it has been documented that he said, “Compound interest is the eighth wonder of the world. He who understands it earns [money]; he who doesn’t, pays [money].”
The bottom line is that compound interest is considered the 8th Wonder of The World for a reason; it’s got one hell of a powerful ability to build wealth off wealth, and it’s hard to fathom.
Let’s recount a story that will help us be able to visualize the power of compounding a bit better.
The Power of Compounding: A Story of the King and a Peasant
As an old folklore story goes, there once was a King who ruled the people and land of his country.
He was responsible for trying and convicting criminals for any and all crimes committed. When he was faced with a local burglar, who was about to take advantage of the King’s kindness, he learned a quick yet harsh lesson on the power of compound interest.
Moments before the King was presented with the burglar, he was in the middle of a chess game, which he set aside to take care of the criminal matter. The burglar, who would be sentenced to death, requested one wish from his King. He asked that the King temporarily take care of his family by supplying them with rice for the following few days. The King agreed and asked how much rice they would need. The burger wished for the sum of rice equal to the total number of squares on his chessboard (64 squares in all) beginning with one grain on the first square.
But that wasn’t all; he requested that the rice be doubled with every square, meaning 1 grain of rice on the first square, 2 grains on the second, 4 grains on the third, and so on until all 64 squares have been accounted for.
The King, not understanding the power of compounding, gracefully agreed because what’s the harm in a few grains of rice anyway?
Shortly after, when the King’s treasurer calculated how many rice grains would be needed, he realized that the country did not have enough rice to give to the burglar’s family. Since this was an agreement between the kind and the burglar, the King, who could not meet his obligations, was forced to surrender his kingdom to the burglar and his family, and the burglar was acquitted of the death penalty.
Although there are varying versions of the king and rice story, the math of compounding interest stays the same. The moral of the story here is that as insignificant as your initial investment may appear, when you apply the power of compounding to it, you’re giving it the power to grow to a sum it otherwise would not be able to.
Money holds its true value when compound interest is applied to it. No matter how little the compounding interest is, don’t under estimate it. Time is what makes the power of compounding work, the longer you can invest, the more money you will end up with.
To take advantage of the rule of 72, check out the 4% rule to help you retire early.
Examples of How the Rule of 72 Work
To break it down, let’s go over the most basic example.
Every $1.00 invested with an annual fixed interest rate of 5% would take 14.4 years to grow to $2.00. The simple computation is as follows:
- 72 (rule) ÷ 5 (interest rate) = 14.4
The list below will give you a clearer picture of how the Rule works in real-time.
- At 1%, it will take 72 years for any dollar value to double (72 ÷ 1 = 72)
- At 3%, it will take 24 years for any dollar value to double (72 ÷ 3 = 24)
- At 6%, it will take 12 years for any dollar value to double (72 ÷ 6 = 12)
- At 9%, it will take 8 years for any dollar value to double (72 ÷ 9 = 8)
- At 12%, it will take 6 years for any dollar value to double (72 ÷ 12 = 6)
Somewhere between 9% and 12% is an average rate of return that doubles your money in 7 years. Let’s say for simplicity’s sake that it’s around 10%.
The stock market, and specifically the index, provide returns of roughly 10% a year on average. If you simply place your money in an index fund and let it run for 7 years, there’s a good chance that your money will double or come quite close to it.
According to investment experts, The Rule of 72 provides an accurate representation when applied to relatively low-interest rates. On the flip side, when the interest increases, you start to see a growth in the margin of error, making it too imprecise to be trusted.
When does the rule of 72 not work?
A point to consider with The Rule of 72 is that an 8% interest rate provides the most realistic and accurate result. Therefore, for every three points that an interest rate strays from 8%, you can adjust 72 by “1” in the direction of the rate change. This is important as it will produce a more accurate estimation.
For example, if you invest $1.00 with an annual interest rate of 5% (3 interest points below 8%), you will adjust the equation by reducing 72 down to 71. Conversely, suppose the annual interest rate is 11% (3 interest points above 8), you would increase the Rule to 73.
And from here, you simply plug in the adjusted numbers:
- $1.00 invested with a 5% interest rate will take 14.2 years to double (71 / 5 = 14.2)
- $1.00 invested with an 11% interest rate will take 6.64 years to double (73 / 11 = 6.64)
Now consider if you don’t adjust for the margin of error:
- $1.00 invested with a 5% interest rate will take 14.4 years to double (72 / 5 = 14.4)
- $1.00 invested with an 11% interest rate will take 6.54 years to double (72 / 11 = 6.54)
As is displayed above, there is some margin of error, but whether it is significant to you or not is a personal choice. For some, it may aid in future decisions, and for others, it may not make a single bit of difference.
It’s best to know your own situation when deciding between accuracy vs. simplicity. When applying the Rule of 72, it’s no different. Feel free to make appropriate adjustments as you see fit.
The Rule of 72 is an excellent resource to help offer you a rough estimate of how long it will take to double your money when invested with a fixed annual rate of interest.
When you know the average rate of return, you can easily project how long your investments will take to double.
The beauty of this rule is you can reverse engineer it by working backward from your desired goal, and you can determine how much more you should invest to reach your goal by a specific time.
This is an excellent tool for many investment goals, including retirement planning, a future home purchase, your child’s school tuition, or simply for a long-term savings goal.