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Rule of 72 & Understanding Compounding Interest
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Originally published on March 8th, 2005.
One of the most well known rules of thumb regarding interest rates (really, any rate) is the “Rule of 72.” The Rule of 72 is that you take the interest rate and divide it into 72 (that is divide 72 by the rate) and that’s roughly how many years it will take to double your principal.
3% rate – 72/3 = 24 years
6% rate – 72/6 = 12 years
12% rate = 72/12 = 6 years
Okay, now we’ve set the table for something really magical. You know how they say that the power of “compounding interest” is incredible? Well, every time I was told that I just thought they were crazy, interest is interest and I understand that you keep the appreciation in and so your investment gets more momentum (3% of $13 is more than 3% of $10, obviously!). Well, let’s put that together with our quick calculating rule of thumb….
– You start with 3% and a $1,000 principal. In 24 years, it’s $2,000. In 48 years, it’s $4,000. In 72-some-odd years… a mere $8,000.
– If you do it with 6%, you get $2,000 in 12 years, $4,000 in 24 years, … ultimately $64,000 in 72-ish years.
– Finally, with 12%, you end up with $4,096,000 in 72 (or so) years.
So 12% interest isn’t double 6% when you look into the future, it’s actually significantly more ($4M more!). Also, if you look at the results from the 3% and imagine inflation grows at roughly that rate (which is accurate enough), in 72 years you will need $8 dollars to equal the purchasing power of $1 now, the $4M is actually only worth $504,000 now. But still… compounding interest is pretty sweet.
I’m sure I messed up something in there so please let me know if I have.
{ 6 comments, please add your thoughts now! }
Good one, didn’t know about the rule of 72. could have used some more meat in the story but I suppose you were going for a quick and simple article.
Rule of 72 Explained
I learned about the Rule of 72 as a way of quickly determining how long it would take to double your money at a given interest rate. A relatively new financial weblog that I’ve been following, Blueprint for Financial Prosperity, seems to explain it…
Great!– Where can I sign up for this 12% interest rate for my savings? ðŸ˜‰
The only investment that i know of reaching the 10-12% dividend yield are Oil Royality Trusts; see BPT or San Juan Basin.
It’s a depleting commodity so it fluxuates; you also have to trust the reserve math.
Foob
It’s worth noting that the “Rule of 69” is more accurate (since the ln(2)=.6931…), but many people choose the Rule of 72 since it is easier to divide by more numbers in your head. 72 is divisible by 2,3,4,6,8,9,18,24,36 whereas 69 is divisible only by 3 and 23 (excluding the trivial divisibility by 1 and the number itself, of course). if you are allowed a calculator, divide using 69 instead for better accuracy…
Very true, but if you have a calculator you might as well do the math out.