Rule of 72
The rule of 72 is one of the most useful formulas to understand when it comes to managing our investments. So I want to help you understand how this rule works and we will also review several use case scenarios so you can start applying it to your own investing journey.
What is the Rule of 72?
Simply, the Rule of 72 enables us to estimate how long it will take to double our money given a certain interest rate. The higher the interest rate, the faster we can double an initial investment. Lower the interest rate and doubling of our money takes a little longer
Here’s how it works. We divide our expected rate of return on our investments into 72. The result is an estimate of how many years it will take us to double our initial investment. For example, if we earn 8% annual interest on an investment, it will take us about 9 years to double our money. 72 divided by 8 equals 9. If we earn a 10% interest rate on our investment, the time to double our money shrinks to about 7 years. 72 divided by 10 equals 7.2.
This simple rule of thumb allows us to easily calculate the impact of a rate of return or an interest rate on our money. Literally on the back of the envelope. Now a limit to this rule of 72 is that it doesn’t account for additional investments. It assumes you invest one lump sum of money at the start. However, it still gives us a glimpse into the power of compounding.
Because in this example that we just went over, a difference between 8% and 10% may not seem like much. But when we put it in the perspective of doubling our money in 7 years versus 9 years, we quickly see the scale of its impact. And when you multiply this impact over many decades, the difference grows exponentially.
For example, let’s take a 30 year period. An initial investment will double approximately 3 times at a 8% rate of return. Once every 9 years. But with a 10% return, the investment will have doubled approximately four times. Once every 7.2 years. Initial investment of $10,000 at a 8% return will have grown to approximately $100,000. However, the same investment of $10,000 at a 10% return will have grown to approximately $175,000.
Again the difference between 8 and 10% on the surface may not seem like much, but when we apply the rule of 72 to it, we see that 2% makes a lot of difference. Alright, now that we have a good general understanding of the rule of 72, let’s see it in action in a few use case scenarios.
Use Case #1 - Time Impact
The first use case scenario where the rule of 72 is most useful is when we are trying to understand the time impact of an estimated rate of return. When you have an average rate of return and a current balance of your investment, you can use the rule of 72 to see what your money will be in the near future. For example, let’s say you have $200,000 in investments today. And let’s say you are estimating approximately 10% rate of return on your investment for the foreseeable future. Bit high but not undoable when we look at the market returns of the past 30 years.
And let’s say you are 20 years from retirement. When you want to access your money. As we calculated earlier, at a 10% interest rate your money will double approximately every 7.2 years. Which means in 7 years, your investment will have doubled to $400,000. In 14 years, to $800,000. And in 21 years, to $1.6 million dollars.
Not a bad amount for your retirement nest egg given you are starting with only $200,000 and in this scenario you didn’t contribute any more money to your investment. Of course this is a very simplistic calculation because we are not incorporating inflation, change in rate of return and any additional contribution. However the purpose of the rule of 72 is to give us a general sense of the future, not an accurate forecast. If you need more money because of inflation or your interest rate changes due to your risk tolerance, you can quickly use the rule of 72 to estimate how long it will take to get to your goal.
Use Case #2 - Evaluate Risk vs Reward
A second good use case for the rule of 72 is to evaluate risk and reward choices. For example, let’s say that you are risk averse and you are thinking about putting all your money in an investment that yields an average rate of return of 3%. Maybe a well diversified bond index fund. When we apply the 3% to the rule of 72, 72 divided by 3, it will take us approximately 24 years before our investment will double in value. Compare that to an investment that yields a 10% rate of return which will double every 7.2 years.
The 3% investment will take three times longer to double than an investment that could yield a 10% rate of return. This is where as an investor you can use the rule of 72 to decide if the risk level you are taking is in alignment with the reward you want to receive. Is 24 years too long for your investment to double? Or is that enough for you to retire on? If not, do you need to take additional risks?
If you are young. In your 20s or 30s, it's advisable to take bigger risks in your investments because of the opportunity to take advantage of high rates of return for multiple doubling cycles. Yes, there are risks associated with higher rates of return such as market dips and downturns. However, you have time on your side and you have the ability to ride all the ups and downs of the market in order to take advantage of the higher risk and higher rate of return.
If you are nearing retirement, you might want to opt for lower-risk investments such as bonds. Because at this stage in your life, doubling your money is less important than keeping your money. Regardless, the rule of 72 is a quick and dirty method to assess the result of your risk tolerance. If you are starting out with a small nest egg and have time on your side, you have the ability to take more risks and thus a high rate of return. If you have a sizable nest egg and are more concerned about protecting it, take less risk because you don’t need your money to double every few years.
Use Case #3 - Evaluate Impact of Cost
The number three useful use case of the rule of 72 to evaluate the impact of costs to your investment. If you’ve read any of my other posts you know I detest high investment expenses. But often it's hard to assess its detrimental impact. However the rule of 72 can quickly show us how damaging even a 1% additional expense could be for our portfolio.
Let’s say that we hired a fancy investment manager to manage our money. And he or she charges 1% to manage our money for us. This means that when our investment portfolio had a 10% rate of return, in actuality, we only got to keep $0.09 of every dollar we earned because we paid the investment manager $0.01 to manage our money. Now, you might be thinking that 1% and the 1 cent doesn’t sound like much. However when we apply rule 72 it's actually quite tremendous.
Let’s say that we started out with $200,000 in investments. If our investment was invested in rock bottom funds like a solid low cost index fund such as Vanguard’s total stock market index fund, our expenses are essentially zero compared to a 1% expense ratio. Vanguard’s total stock market index charges an expense ratio of 0.04%.
At a 10% rate of return, it would take about 29 years for our money to double 4 times. At which point our original investment of $200,000 would be close to $3.2 million dollars. But if we had given 1% to a fund manager, effectively making our rate of return 9%, how long do you think it will take to get the same $3.2 million dollars? 32 years. 3 additional years. And with time, the gap grows bigger. The rate of return on our investments is crucial. And seemingly small changes, like a 1% investment manager fee can have a huge life changing effect on our future if we don’t watch our costs carefully.
Use Case #4 - Evaluate Impact of Inflation
The fourth useful case for the rule of 72 is to evaluate the impact of inflation. Inflation is the rate that the costs of products and services increase over time. Essentially lowering the value of the money that you have today. I remember watching Jurassic Park, the original one in theaters in 1993. I was in elementary school and it was one of the coolest experiences in my life. My friend’s dad was kind enough to pay for our tickets and I distinctly remember it costing $3 per kid. And for a 3rd grader with no money, $3 was a lot of money.
Fast forward to today, the latest Jurassic Park movie, Jurassic World Dominion is planned to be released in theaters this summer. And if we were to watch this in the theaters, it would cost us more than $10 per person. In a period of 30 years, movie ticket prices have tripled in cost. This is what is called inflation. In 2022, the latest rate of inflation is around 8% nationally.
But what does this mean to us in the long run? We can use the rule of 72 to see how many years it will take to cut in half our purchasing power due to inflation. For example, when inflation is around 8 percent, we can divide 72 by the rate of inflation to get 9 years until the purchasing power of your money is reduced by 50 percent. 72/8 = 9 years to lose half your purchasing power. With this quick formula, we evaluate the severity of inflation concretely. The hope is that inflation might not remain elevated for an extended period of time, but it's good to know how it can really impact the value of our current dollars.
Bottom Line
The Rule of 72 is an important guideline to keep in mind when considering how much to invest. Investing even a small amount can make a big impact if you start early, and the effect can only increase the more you invest, as the power of compounding works its magic. You can also use the Rule of 72 to assess how quickly you can lose purchasing power during periods of inflation.
