The Rule of 72 – How It Helps, And How It Doesn’t
Would you like an easy way to approximate the rate of return or amount of time needed to achieve a financial goal?
The Rule of 72 is a great tool to use for this purpose.
This rule can estimate the time it takes to double your money when the interest rate on your investment is known. Additionally, it can estimate the interest rate needed to double your money if your time horizon is known.
How It Works
If you know the interest rate of an investment, the length of time it takes to double your money is calculated by simply dividing 72 by the interest rate. So if the interest rate is 6%, then 72 / 6 = 12. It’ll take you about 12 years to double your money at 6% interest.
One the other hand, if you know that you need to double your money in 9 years, divide 72 by 9 to get 8. You’d need about an 8% interest rate to double your money within this time.
How It Helps
The Rule of 72 is a very helpful tool if you just want a quick approximation. If you don’t have a calculator available, this is a great substitute.
Examples of the Rule of 72
| Interest Rate | Approximate Years Needed To Double Your Money |
|---|---|
| 1% | 72 |
| 2% | 36 |
| 3% | 24 |
| 4% | 18 |
| 8% | 9 |
| 9% | 8 |
| 12% | 6 |
| 18% | 4 |
| 72% | 1 |
So let’s say you open up a Roth IRA with $5,000, and you expect to earn 12% interest a year. From the Rule of 72, it’ll take about 6 years to grow your money to $10,000.
Or maybe you’ve been contributing to your 401k and have $500,000 saved up. If you plan on retiring in 16 years with $1 million, you’ll need an average return of about 4.5% on your investments.
How It Doesn’t Help
Although the Rule of 72 is a useful tool, it still is only an approximation. As such, there are errors in it. Specifically, at extremely low or high interest rates, the error is quite sizable.
For instance, according to the Rule of 72, the time it would take to double $50,000 to $100,000 at the rate of 72% is 1 year (72 / 72 = 1). But if you calculate the actual return after 1 year, you would only receive $86,000. This is a $14,000 difference, or an error rate of 14%.
Conversely, if the interest rate was 1%, according to the rule of 72, it would take 72 years for $50,000 to double. Yet if you calculate the actual return after 72 years, you’d receive over $102,300, more than $2,300 than the expected amount. This results in an error rate of 2.4%.
Where It Works Best
Taking these errors into consideration, the Rule of 72 works best for interest rates between 7 and 10%. Within this range, the time it takes to double your money as calculated from the Rule of 72 is accurate within one month of the actual time frame.
| Interest Rate | Rule of 72 Time To Double | Actual Time To Double | Difference |
|---|---|---|---|
| 7% | 10 years, 104 days | 10 years, 89 days | 15 less days |
| 8% | 9 years | 9 years, 2 days | 2 more days |
| 9% | 8 years | 8 years, 16 days | 16 more days |
| 10% | 7 years, 73 days | 7 years, 99 days | 26 more days |
Outside of this range, the actual time period needed to double your money can vary by a year or more!
For example, if your investment is earning 2% interest, the Rule of 72 says that you’ll double your money in 36 years. But if you actually do the math, it’ll really take about 35 years, saving you almost 365 days of needing to wait for your money.
And if your investment is only earning 1%, the Rule of 72 says that you’ll double your money in 72 years. But after doing the math, it’ll actually take under 70 years, saving you over 2 years of needing to wait for your money.
That being said, if the interest rate is outside the range of 7 to 10%, it’s better to calculate the actual time needed to double your money, so that you get a more accurate answer.
So although the Rule of 72 isn’t 100% accurate, using it is an easy way to get a good estimate of when and how you’ll be able to double your money.
Would knowing how long it takes to double your money, or the rate of return needed to double your money make a difference in how you save and invest?
This article was included in the Carnival of Personal Finance during the week of June 14, 2010. Check out Pop Economics for a variety of great articles!
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Filed under Investing, Saving by on Jun 12th, 2010. Comment. 
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Comments on The Rule of 72 – How It Helps, And How It Doesn’t
Monterey Marketing Lab (Neal) @ 11:21 pm
Cool post Darren,
It’s good to have some quick numbers like that in your back pocket. As I have studied physics we had a few like that. Like the number of seconds in a year is approximately pi x 10^7.
-Neal
Darren @ 11:28 pm
Thanks Neal! Never heard of that approximation for seconds in a year. Nice tip!
FinEngr @ 2:13 pm
Nice write-up & graphics. Very important to understand that these are approximations, and actual results can vary significantly based on your parameters.
Over-simplifying the results can have very real effects. For example, I went through and entered similar data into different retirement calculators. The time it would take me to reach $1M varied by about 12 years!
To answer your question – I think the power of the rule comes in product comparison, when you’re looking at different investment vehicles for a specific time frame.
Darren @ 3:26 pm
Thanks FinEngr. Yeah, because they’re approximations, it helps to know how to compute actual future value, time horizon, interest rate, and other similar variables.
Just curious, what inputs did you use that led you to a 12-year time difference?
FinEngr @ 3:43 am
@Darren:
It wasn’t the inputs per se, but the calculators. I started with the same variables, then some asked more than others – so I tried to keep it as consistent as possible.
Some asked for tax bracket while others asked what type of accounts (taxable/non-tax) for example.
Darren @ 4:51 am
FinEngr – You brought up a good point. These calculations also don’t take taxes into account, or inflation for that matter. For that, you’d need a fancy calculator like the HP 12C or TI BA II Plus!
mat @ 4:28 pm
Hey, Very interesting points, loved everything about it…
Is there a way to come up with a formula for the lower then 7% or higher then 10% ??
Darren @ 5:41 pm
Hey mat,
Thanks for stopping by. Yep, the way to calculate the actual time to double is pretty simple. Using Excel’s NPER function, you put in your desired percentage in the Rate field, put -1 in the Pv field, and 2 in the Fv field. Leave the Pmt and Type fields blank.
If this is a bit confusing and you want the actual spreadsheet, let me know and I’ll send it to you!