The Number That Can Help You Predict The Future

I’ve mentioned before that I can’t tell the future. That’s still completely true. But I can make an educated guess about my financial future using the number 72. Specifically, I can predict the future by using the Rule of 72.

What is the Rule of 72? Only everybody’s favorite mathematical equation! Okay, that’s probably not true. But savvy investors like it.

The Rule of 72

Personal finance nerds love numbers. I think that’s probably pretty true across the board. But that’s not necessarily the same thing as being good at math. For those of you that don’t love complicated equations to figure out financial concepts, we have the Rule of 72.

The Rule of 72 shows you – in a very simple way – how many years it will take you to double your money based on a steady rate of return.

Conversely, you can figure out what rate of return you need to earn with your money to double it, based on how long you have to invest!

To figure out how long it will take to double your money, you simply divide 72 by the return rate. So if you are predicting an average return of 8% in your 401k or TSP, for instance, it would take you 9 years to double your money.

72 divided by 8 = 9

The Rule of 72 assumes you are not adding any additional contributions – you are only accounting for returns from interest or earnings. If you do add contributions, your money will double faster.

Need proof?

Let’s run a simple experiment.

Let’s say you invest $10,000 today, and expect it to earn an average of 8% each year. It would take you approximately 9 years to get to $20,000. Here’s the yearly breakdown. If you want to follow along with a calculator, multiply $10,000 by 1.08 a total of 9 times.

• End of year 1: $10,000.00 times 1.08 = $10,800.00 ending balance
• End of year 2: $10,800.00 times 1.08 = $11,664.00 ending balance
• End of year 3: $11,664.00 times 1.08 = $12,597.12 ending balance
• End of year 4: $12,597.12 times 1.08 = $13,604.89 ending balance
• End of year 5: $13,604.89 times 1.08 = $14,693.28 ending balance
• End of year 6: $14,693.28 times 1.08 = $15,868.74 ending balance
• End of year 7: $15,868.74 times 1.08 = $17,138.24 ending balance
• End of year 8: $17,138.24 times 1.08 = $18,509.30 ending balance
• End of year 9: $18,509.30 times 1.08 = $19,990.05 ending balance

Boom! Off by slightly less than $10! That’s a 99.9% accuracy.

This is obviously a very simplistic example that doesn’t account for sequence of returns, variable returns, etc. Just go with it for now.

Example #2

Lest you think I chose 8% because it works out that way only for that number, let’s use a different example. Looking at the US Treasury Daily Treasury Long Term Data Rate it looks like right now (August 18, 2017) you can expect to get about a 2.6% return on long term Treasury bonds. So how long would it take to double $100 at that rate of return?

72 divided by 2.6 = 27.69 years. Let’s call that 28 years.

• End of year 1: $100.00 times 1.026 = $102.60
• End of year 2: $102.60 times 1.026 = $105.27
• End of year 3: $105.27 times 1.026 = $108.00
• End of year 4: $108.00 times 1.026 = $110.81
• End of year 5: $110.81 times 1.026 = $113.69
• End of year 6: $113.69 times 1.026 = $116.65
• End of year 7: $116.64 times 1.026 = $119.68
• End of year 8: $119.68 times 1.026 = $122.79
• End of year 9: $122.79 times 1.026 = $125.99
• End of year 10: $125.99 times 1.026 = $129.26
• End of year 11: $129.26 times 1.026 = $132.62
• End of year 12: $132.62 times 1.026 = $136.07
• End of year 13: $136.07 times 1.026 = $139.61
• End of year 14: $139.61 times 1.026 = $143.24
• End of year 15: $143.24 times 1.026 = $146.96
• End of year 16: $146.96 times 1.026 = $150.78
• End of year 17: $150.78 times 1.026 = $154.71
• End of year 18: $154.71 times 1.026 = $158.73
• End of year 19: $158.73 times 1.026 = $162.85
• End of year 20: $162.85 times 1.026 = $167.09
• End of year 21: $167.09 times 1.026 = $171.43
• End of year 22: $171.43 times 1.026 = $175.89
• End of year 23: $175.89 times 1.026 = $180.46
• End of year 24: $180.46 times 1.026 = $185.16
• End of year 25: $185.16 times 1.026 = $189.97
• End of year 26: $189.97 times 1.026 = $194.91
• End of year 27: $194.91 times 1.026 = $199.98***
• End of year 28: $199.98 times 1.026 = $205.18

See? It maybe not be the sexiest bar trick, but it’s reliable as hell.

***Okay, so we are actually closest at 27 years. Keep reading.

Side note! Did you notice how at the halfway year point (year 14) you were only 43% of the way to doubling the money? And how you weren’t halfway there money-wise until year 16 ($150)? That’s because of the miracle of compounding returns. That’s definitely a whole post in itself, but worth remembering for now.

The Rule of 72-ish

Why was the answer closest at 27 years? Well, the Rule of 72 is most accurate for return rates between 6% and 10%. If you are using returns that are higher or lower, you can adjust the rule slightly to account for that. You do this by adjusting the number 72 up or down by 1 for every 3% difference in return.

For rates higher than 10%, you will add 1 to 72 for every 3% above 8%. That means if you are finding the number of years it will take your money to double at 11% earnings, you will use the Rule of 72+1, or 73. 73 divided by 11 is 6.64, so your money will double in approximately 6 years 8 months (~6.64 years).

For rates lower than 6%, you want to subtract 1 from 72 for every 3% under 8%. So looking back at our 2.6% example, we see that 2.6% is (roughly) 6% less than 8%. So you will subtract 2 from 72 to use the Rule of 70. 70 divided by 2.6 is (drumroll!!!) 26.92 years. Boom!! Pretty close to the 27 years we found by doing the year-to-year math, no?

Also, everything I’ve described up until this point is based on a once-annually compounded return. If your money is compounded daily, as it is with most investment accounts, the magic number is 69.3. For simplicity’s sake, you can use the Rule of 69 or 70. It’ll be close enough. For interest rates higher or lower than 6-10%, adjust from 69.3 instead of from 72. Hopefully that makes sense.

Using Years to figure out Interest Rates

I mentioned above that you can also use 72 divided by the number of years you have to invest to figure out what interest/earnings rate you need to achieve to double your money. Here’s how that works.

Just like you divide 72 by the return rate to get the number of years it takes to double money, you can also flip the equation around. You’re just solving for y instead of x.

For instance, say you want to retire in 10 years and you currently have $400,000 in your retirement accounts. Your money will double in that time if you earn a 7.2% return on your money because 72 divided by 10 is 7.2. Now let’s prove it.

• End of year 1: $400,000.00 times 1.072 = $428,800.00
• End of year 2: $428,800.00 times 1.072 = $459,673.60
• End of year 3: $459,673.60 times 1.072 = $492,770.10
• End of year 4: $492,770.10 times 1.072 = $528,249.55
• End of year 5: $528,249.55 times 1.072 = $566,283.51
• End of year 6: $566,283.51 times 1.072 = $607,055.93
• End of year 7: $607,055.93 times 1.072 = $650,763.95
• End of year 8: $650,763.95 times 1.072 = $697,618.96
• End of year 9: $697,618.96 times 1.072 = $747,847.52
• End of year 10: $747,847.52 times 1.072 = $801,692.54

I love math.

Using the Rule of 72 to predict the future

Okay. Now let’s talk about how this helps you predict the future.

By knowing how long it will take to double your money, you can figure out roughly how much your investments will be worth in the future. This is a HUGE advantage in your financial planning.

For instance, let’s say I have $100,000 in my retirement accounts and I think I need $800,000 to retire. That requires me to double my money three times.

$100,000 x 2 = $200,000

$200,000 x 2 = $400,000

$400,000 x 2 = $800,000

At an 8% rate of return, I know my money will double every 9 years even if I don’t put in another dime. So, in this scenario I could stop saving money and, based on my current calculations, I would be able to retire in 27 years.

I feel like this is another good spot to put in a reminder that these examples are based on steady rates of return, which is not what happens in the stock market. Keep that in mind. I’ll work on a “sequence of returns” post in the meantime.

If I keep contributing to my retirement accounts, I would be able to retire even sooner because I would be adding money both from my contributions and the returns. Or, I could choose a less risky investment that has a lower potential return, and still retire in 27 years.

Therefore, knowing the Rule of 72 and how to modify it for lower or higher returns gives you a fairly accurate, very simple way to predict future values of your investment portfolio. And you can use that information to either determine when you are able to retire (based on portfolio value) or how much retirement money you will have (if you base it on a certain retirement year). Pretty cool, right?

If you are ready to step it up to the next step of personal finance nerdiness, you can even create tables that show various results at different rates of return. Nerds love a good spreadsheet!

I love the Rule of 72 because it provides an extremely easy way to visual future results. What are some other rules of thumb you use for your personal financial planning?