What is the Rule of 72?

The Rule of 72 is a simple calculation that helps you estimate how long it will take for your investments to increase twofold. In order to use the rule, you just need to divide 72 by your expected annual rate of return. Here’s what that formula looks like:

Years to double = 72 / expected annual rate of return.

What’s an example of the Rule of 72?

Let’s say you have an investment portfolio that’s worth $200,000. You want to know how long it will take for your portfolio to hit $400,000 if your expected annual rate of return is 9%. According to the Rule of 72, just divide 72 by 9%.

72 / 9% = eight years

So, in eight years, your $200,000 will double to $400,000. Now, if you wanted a more accurate calculation, you could use the enhanced Rule of 72, which requires a bit more math (for expected rates of return that are less than 6% and greater than 9%, the enhanced version will give you a more accurate calculation).

The advanced equation looks like this:

T = ln(2)/ ln(1+r)

Here, “T” equals the time it takes for an investment to double and “r” equals your expected annual rate of return. The “ln(x)” is simply a logarithmic function that you can find on most smartphones (turn it to landscape) and scientific calculators.

So, for our example, here’s what the enhanced calculation would look like:

T = ln(2) / ln(1+.09)

T= ln(2) / ln(1.09)

T= 8.04

In this case, your investment will double in eight years and 12 days. As you can see, the simple Rule of 72 (without logarithms and scientific calculators) was only off by 12 days.

How to make the Rule of 72 work harder for you

One great application of the Rule of 72: if you know how many years you have until you retire, the Rule of 72 can help you calculate how many times your investments will double.

For example, let’s say you have 32 years before you retire. If we take the example from above, we know your money will double every eight years (72/9%). That means your money has the potential to double four times before you actually withdraw it (32 years / eight years = four doubling periods). So, in this case, every $1,000 you invest could potentially turn it into $16,000. Here’s a breakdown of that math:

First doubling period: $1,000 turns to $2,000
Second doubling period: $2,000 turns to $4,000
Third doubling period: $4,000 turns to $8,000
Fourth doubling period: $8,000 turns to $16,000

This, in essence, is why you should start investing as soon as you’re financially able to. By giving your money 32 years to grow, you can potentially turn every $1,000 into $16,000. That alone will help you build a solid nest egg on which to retire.

Conversely, if you started investing later than most, the Rule of 72 can help you adjust your financial planning. For example, let’s say instead of 32 years, you have eight years until you retire. With the same annual rate of return (9%), you only have one doubling period left. That means that every $1,000 you invest will potentially turn into $2,000.

Seen in that way, those eight years left until retirement might seem closer than you thought, as you realize your money doesn’t have that much time to grow.

What are the shortcomings of the Rule of 72?

Like any rule of thumb, the Rule of 72 isn’t meant to be a hard and fast law. Your investments could take longer to double, or they may double faster than the rule predicts. Certain factors make the Rule of 72 only a “fairly accurate” rule:

1. Market volatility

No one can predict how the market will behave. Even though the highs of the market typically balance out the lows, there’s no telling if a market crash (or market high) will affect your investment portfolio. While you may use the historic rate of return for an index for your law of 72 calculation (9% to 10% for the S&P/TSX Composite index), your actual rate of return may be higher or lower than that.

2. Inflation rates

The Rule of 72 doesn’t factor in inflation (though, as we’ll see below, it can help you calculate how much you lose to inflation). In general, the longer you allow your money to double, the more time inflation has to eat into your spending power.

3. Investment fees

Lastly, the Rule of 72 doesn’t take into account the investment fees you might pay, such as annual fees, trading commissions, or even fees paid to a financial advisor or fiduciary. Likewise, it doesn’t take into consideration the taxes you might have to pay for capital gains.

How else can you apply the Rule of 72?

Though most investors use the Rule of 72 for investments, you can use it for any calculation that involves compound interest. Three other useful financial calculations include the following:

1. Inflation rates

Instead of calculating how long it takes for an investment to double, you could calculate how long it takes for inflation to reduce an investment by half its current value. If inflation is 2%, then according to the Rule of 72, it would take around 36 years for your $200,000 investment portfolio to be worth essentially $100,000 in today’s dollar values.

2. Loan interest

The law of 72 can also help you calculate how long it will take a loan to double based on its APR (annual percentage rate). If you have a car loan with a 12% APR, it would take just six years before the loan amount doubled.

3. Annual expense fees

Finally, you can use the Rule of 72 to figure out how long it will take investment fees to reduce your portfolio by half its current value. For example, let’s say you have a mutual fund with a 3% management expense ratio (MER). According to the Rule of 72, it would take 24 years for the mutual fund fees to eat away half of your principal investment.

Bottom line

As with any rule of thumb, the Rule of 72 isn’t perfect. Despite its shortcomings, however, it can help you see if you’re on track to hit your financial goals or if you need to adjust your contributions.

What is the Rule of 72?