Investments

How To Calculate Rule of 72

By David Krug David Krug is the CEO & President of Bankovia. He's a lifelong expat who has lived in the Philippines, Mexico, Thailand, and Colombia. When he's not reading about cryptocurrencies, he's researching the latest personal finance software. 6 minute read

How long do you think it will take for your money to double? Invested wealth can rise exponentially over time, apparently by magic, as you may have heard from financial professionals. Where do they get these preconceived notions?

Sometimes it’s helpful to know the doubling time for your current or initial investment if you were to stop putting fresh money toward it, whether you’re saving for an emergency fund, a down payment, or an early retirement.

You can do the Time Value of Money calculation, which is a bit more involved. Alternatively, you can employ the rule of 72, which is a convenient shortcut.

What Is the Rule of 72?

Using a constant annual rate of return and compounding growth, the rule of 72 can be used to quickly estimate how long it will take for your investment to double.

Although it is not 100% correct, as a general rule of thumb it will serve you well. After all, your actual returns on investment are likely to deviate somewhat from the annual rate of return you anticipate. However, when returns are expected to be in the typical range of 6% to 12%, the rule of 72 provides surprisingly accurate results.

How well the rule of 72 predicts how long it will take an investment to double is broken down by various rates of return as follows:

Rate of ReturnYears to Double Estimated by Rule of 72Exact Years to DoubleDifference (in Years)
2%36.0351.28
3%24.023.450.6
5%14.414.210.2
7%10.310.240.0
9%8.08.040.0
12%6.06.120.1
25%2.93.110.2
50%1.41.710.3
72%1.01.280.3
100%0.710.3

In other words, the rule of 72 offers you an estimate that is most precise between the percentages of 5% and 25% but is still close enough to 100% to be useful in most situations.

The Formula for Rule of 72

Calculate the time it will take for your investment to double by dividing 72 by the expected annual return rate.

The formula for this is as follows: 

Years to double = 72 return on investment (annual%)

It’s the kind of math that can be done on a cocktail napkin. Even after having a couple of those beverages.

Illustration of the Rule of 72

Think about putting your money into an index fund that tracks the S&P 500. Investors can expect a long-term return on their investment of about 10%, based on the market’s historical average.

If you divide 72 by 10, you get a figure of 7.2 years for your investment to double. I mean, it’s not like this is a complicated question.

When using the rule of 72, remember that the return rate is not divided by 100. Excel doesn’t accept decimals, therefore you can’t enter 10% as 0.10 or 10% as 10%. The number is entered exactly as it appears on the page. Simply divide by 10 to get a 10% return.

It would take twice as long, or 14.4 years (72 5 = 14.4), for your money to double if you were only to get a 5% return instead of a 10% one. And the same reasoning can be used for various other rates of return.

Application of the Rule of 72

Saving for a house down payment, retirement, and other long-term financial goals are all things that we work for. Understanding the potential impact of compound interest on your investments is important regardless of your end aim.

To that aim, it’s important to determine how rapidly your current investments will double in value. Let’s say you’re 55 years old and you’re considering quitting your stressful work for a less demanding one that pays less. You’re wondering if it’s safe to cease making contributions to your Roth IRA and instead let your existing investments grow on their own.

Let’s pretend you’ve amassed half of the retirement fund you’ll need. In this situation, a quick mental calculation using the rule of 72 tells you that it will take another 10 years (72 7.2 = 10) for your Roth IRA amount to double at an average return of 7.2%. 

In other words, if you start saving at age 25 and are halfway there by age 55, you should reach your goal balance and retire comfortably by age 65 with no more contributions required.

Also, let’s say you’re wondering if and when you can cease making payments into your kid’s 529 plan. You estimate that your investment returns will average around 9% each year, so you divide your current balance by 9 to get an estimate of how long it will take for your money to double (72 9 = 8). 

If your child is 10 years old now, you can expect to have nearly twice the present balance by the time they are 18 if you don’t make any additional contributions. The actual world definitely has more chaos than neatly organized numbers. To estimate how quickly your assets will double if you stop adding to them, you can use the rule of 72.

Calculating the Loss of Spending Power Due to Inflation

The rule of 72 can be used to estimate how long it will take for inflation to halve the value of your money. All the calculations are correct. It would take around 36 years for the value of the dollar to decrease by half if inflation were to average 2% every year. 

It’s a gentle nudge to invest your savings rather than let them sit in a savings account doing nothing. In figuring up your potential profits, don’t forget to factor in that decline in value. A return of 8% would only amount to a real return of 6% if inflation were running at 2%.

The Rule of 72 alternatives

While the rule of 72 is a basic and useful tool for estimating the growth of any investment, it is not the only method for doing so. If you’re up for the extra mental effort, here are a few commonly used alternatives that offer slightly better accuracy.

Money Has a Time Value.

Using Time Value of Money, you might determine with precision how long it would take for an investment to generate a return equivalent to its initial outlay. 

This equation describes the process:

FV = PV*(1+r)t

FV is the value in the future, PV is the value right now, r is the rate of return, and t is the time frame. Solving for t would require some complicated mathematical manipulations. Which, even to someone as interested in finance as I am, sounds like a lot of extra effort that isn’t necessary.

Rule of 69.3

For annual compounding, the rule of 72 is a good guideline, but for daily or continuous compounding, a smaller numerator is more appropriate. Divide by 69.3 rather than 72 if you anticipate a daily or continual compounding of your investment. Even with a calculator, that’s beyond the realm of mental calculation at this point.

Calculator for Compound Interest

Rule 72 predicts the amount of time it will take for an initial investment to provide a return of 100% without any further capital infusions. Nevertheless, you should usually keep putting money into your assets regularly. 

It is more accurate to utilize a compound interest calculator that takes into account regular new contributions to a portfolio than the rule of 72.

Bottom Line

It’s true that the rule of 72 isn’t 100% precise, but in most situations, you won’t even notice. The rule of 72 is a conservative estimate, therefore it’s likely that your projection of future returns will be even off. 

The rounding mistake involved in utilizing the rule of 72 is more than offset by the fact that a conservative estimate of 10% annual return would result in a longer period of time for your money to double. If you can’t afford to add to your investments every month, the rule of 72 can help you figure out how long you can get by on what you already have.

For instance, coast FI is a term used by members of the FIRE (Financial Independence, Retire Early) community to describe the situation in which one has amassed sufficient retirement savings to allow them to coast until they reach retirement age without making any more contributions. By using Coast FI, you can take the job of your dreams, even if it doesn’t pay as much, and still feel secure about your retirement.

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