The Rule of 72... or 70, 69.3

If you have no idea what that title means then I guarantee (ironic global and personal events withstanding) that this is the most important thing you will learn today.

This is something my dad talked about constantly since I can remember, so when a lecturer at IIT today stated the "rule of 70" I chuckled to myself with my usual dorky demeanor. It was one architectural PhD talking to a bunch of other MA's and PhD's who don't know basic finance... which is of course why they design the objects that contain more of humanities combined wealth than any other profession by far. But that's not the point.

The point is that I wanted to know why he said rule of 70 and not 72. Upon further research I learned all sorts of cool things, and as usual Wikipedia and a subsequent Google search taught me more in fifteen minutes than I learned all day at my fancy school (sorry school, I still love you and your sweet sweet buildings and wood shop).


The rule of 72 is a quick and fairly accurate way of determining how long it will take an investment to double. Simply divide 72 by the interest rate and the result is the amount of time it takes the principle to double due to compounding interest. For example: if you are receiving an interest rate of 8% on $1 it will take 72/8 = 9 years for that dollar to double. Simple enough.

Here's the actual calculations (from Wikipedia):

Rate ↓ Actual Years ↓ Rule of 72 ↓ Rule of 70 ↓ Rule of 69.3 ↓
0.25% 277.605 288.000 280.000 277.200
0.5% 138.976 144.000 140.000 138.600
1% 69.661 72.000 70.000 69.300
2% 35.003 36.000 35.000 34.650
3% 23.450 24.000 23.333 23.100
4% 17.673 18.000 17.500 17.325
5% 14.207 14.400 14.000 13.860
6% 11.896 12.000 11.667 11.550
7% 10.245 10.286 10.000 9.900
8% 9.006 9.000 8.750 8.663
9% 8.043 8.000 7.778 7.700
10% 7.273 7.200 7.000 6.930
11% 6.642 6.545 6.364 6.300
12% 6.116 6.000 5.833 5.775
15% 4.959 4.800 4.667 4.620
18% 4.188 4.000 3.889 3.850
20% 3.802 3.600 3.500 3.465
25% 3.106 2.880 2.800 2.772
30% 2.642 2.400 2.333 2.310
40% 2.060 1.800 1.750 1.733
50% 1.710 1.440 1.400 1.386
60% 1.475 1.200 1.167 1.155
70% 1.306 1.029 1.000 0.990

72 is used because it's the multiple of many numbers and hence easy to use. The "appropriate", if that's the right word to use (pun definitely intended), number to use is 70 because ln(2) = 69.3; rounded up. Although it depends on what interest rate you're working with. For the numbers I tend to use, say... the real rate of return on an investment in the stock market which is about 6-7%; 72 works best. For small numbers use the others.

Use that link above and play with the stock markets numbers. I learned quite a bit. I did 1955-2002. My thinking was an era post-WWII and the boom afterwords and the period before we went totally nuts in the last few years. Average rate of return? About 10.6% (this is the geometric mean, not arithmetic - there's an explanation on the site and the number I give is far more accurate) and when it's adjusted for inflation the "real" rate of return is about 6.3%.

72/6.3 = 11.4 years

The take away from that is this. Say you have a kid and you decide it'd be nice if one day they had money to give their kids, you know, patience and forethought. Well, if when they were born you set up an IRA (savings account that doesn't get taxed) and put in a $100 bill by the time they could withdraw it at 59.5 it'd be worth roughly $40,000. Keep in mind this is already adjusted for inflation. So say you skipped buying that Acura and instead bought the Toyota and put the savings of roughly $15,000 in that account (over several years, you can only put in $6,000 a year currently) and they didn't withdraw it until they were 65.5 (using the 1871-2008 geometric mean of the average rate of return on the US S&P 500 adjusted for inflation which is 6.6%). They'd have $960,000 (again, in present value) tax free. That's a truly conservative estimate based off of the largest sample size available to anyone is the US that I'm aware of.

Capitalism may be brutal and inhumane, but over the long run it certainly doesn't have to be. Just think of how you live now - and the giant's shoulders we stand on to do so. The rich get richer because they know simple financial tricks like the rule of 72 that enables them to create a mental picture strong enough to allow them to invest in something that they will most likely never see come to fruition. But in the long run... $15,000? That was my tuition this semester. When we spend money in the present it has a great effect on the future that few ever give thought to. My decision to go to grad school is essentially me saying "with the knowledge I gain here I will effect the world in a more significant way than if I were to invest the money (3 years at over $30K per year) and bequeath to six people of my choosing one million dollars apiece in roughly 65 years." Understanding this relationship adds new meaning to these actions, or detracts it if you consider what most people spend their money on.

So yes, that's why I wear Hanes white tees and bring my lunch to class.