The Rule of 72 is a formula for estimating how many years it will take for an investment to double in value with a given interest rate. The formula is simple enough and close enough to the computed value that you can use it for
If you’re just here to quickly calculate how long it will take money to double at a given interest rate, here’s the calculator for you!
If you’re curious how this works, how accurate it is and when you should use it then read on!
What is the Rule of 72?
The actual rule of 72 formula is extremely simple:
\text{years to double an investment} = \frac{72}{\text{rate of return}}With this definition, you’ll need to make up some rate of return. In the stock market, the historic rate of return for a diversified portfolio is generally around 8%. If you’re like me, trying to guess how long it would take to double your money at 8% isn’t an easy calculation – at least without the rule of 72.
How to use the rule of 72 becomes easy with a little practice. For example, here’s how you would calculate how long does it take to double your money assuming an 8% rate of return:
\frac{72}{\text{8\%}} = \text{9 years to double an investment}The calculation of 72/8 is something easy enough to do in your head, unlike the actual compound interest calculation. 9 years is very close to the mark. This isn’t the law of 72 though – it’s only an estimate. The actual calculated answer is extremely close — 9.01 years – a difference of only 0.001%!
9 Years to double your money is pretty good. This also assumes that you don’t deposit another $1 into the account during that time. If you’re also depositing money each month the number could be quite a bit less.
Compound interest is just that cool. Even Einstein thought so!
Compound interest is the most powerful force in the universe.
Albert Einstein (maybe)
Calculating Rate of Return Needed
What’s handy about this formula is it can also be adjusted to calculate the rate of return based on a number of years. For example, if you start with a number of years, say 6 years, and want to know what rate of return you would need to double your money, you can use the same calculation,
\text{rate of return} = \frac{72}{\text{years to double}}For the 6 year example above, you can quickly work out that 72/6 = a 12% rate of return. A 12% rate of return is super high for the stock market. When calculating a rate myself, I use 7% to be conservative, or 8% if I’m being optimistic.
Do you want to get started investing and learn how to make returns like this? Check out my free Minimal Investor Course to learn how.
When Would you Need to Use the Rule of 72?
Let’s say you have calculated how much you need to retire. You know you’ll need $1.5 million and you have $100,000 saved up so far. How long would it take for your money to grow that to $1.5 million?
One way to figure this out is to go to the compound interest formula and work it out. The easier way, and the way I estimate this personally is by calculating how many times this will need to double then using the Rule of 72.
To get from $100k to $1.5 million, the money will need to double to $200k, double again to $400k, again to $800k and again to $1.6 million. That means that it will need to double 4 times. We can use the compound interest formula to see how long it will take the double our money at some interest rate (I’ll use 8% to be optimistic) then multiply it by 4.
\frac{72}{\text{8\%}}\:\times\:4 = \text{36 years to 4x your investment}So after 36 years $100,000 will turn into about $1.6 million. The actual calculated amount would be $1,596,817.18 using the actual compound interest formula, using the rule of 72 calculation within 0.2% of the real amount.
What this doesn’t take into account is the impact of periodic investments. What if you wanted to know how long it would take to grow $100k to $1.5m, but with $20,000 additional money being invested each year?
The rule of 72 won’t help with that. For that, you’d need a compound interest with periodic investments calculator. As it turns out, adding that additional $20k/year would lower the years needed from 36 down to 20! Even chipping in $10k/year would reduce the number of years needed from 36 to 25.
Rule of 72 Calculator
This calculator is super simple, but it will calculate the time to double your money. You can either edit the rate to find out the number of
The rule of 72 could also be called a “time to double money calculator” – it’s providing a very close estimate for the doubling rate.
Rule of 72 Chart
Looking at how rate affects time makes it clear – there are diminishing returns the higher you set your interest rate. The impact of increasing your returns from 4% to 5% are going to make a difference of 3.5 years. The difference from 14% to 15% is only 0.34 years — one-tenth as much!
Note: hover over to see the rate/years at any point on this chart.
My takeaway from this rule of 72 worksheet is that your first 10% is the most important. Turns out the US Stock markets historically return right around 10% too! Chasing returns higher than that have a negligible impact on how long it will take to double your money.
How Would You Use the Rule of 72?
Have you used this rule to do quick calculations? Are there other handy calculations you do in your head to save time? Let me know!
The Rule of 72 is a formula for estimating how many years it will take for an investment to double in value with a given interest rate. The formula is simple enough and close enough to the computed value that you can use it for ballpark estimate with very little effort.