The Rule of 72 and Compounding Interest
Are you familiar with the Rule of 72? It’s always something that has fascinated me. Here’s the jist, if you take 72 and divide it by your rate of return you get the approximate time to double your investment. Conversely, if you divide 72 by the number of years you want to double, you get an approximate rate of return.
This is not a 100% accurate, number, but it is a great “back of the envelope” estimate. I’ve always kind of wondered why this works. Math is a cool thing and there really must be a reason for it… right?
I did some investigation and found this website that shows the mathematical formula for the interest rate calculation and how to solve for N when you are doubling your present value. In the end, they suggest you graph the formula and the Rule of 72 formula and see how close they are. So, I did just that.
While you can see the answers are quite close, the absolute percent error increases as the interest rate increases. This is really only attributed to the fact that your base time is decreasing and so a small error looks larger in comparison. Though the absolute error does increase when you get outside of the typical range for interest rates. When you are in the most likely range of 6% to about 10% the estimate is very close to being accurate (within .1 years).
The graph is also a little telling. You can see the general shape of the line and realize that the curve is a very typical inverse relationship curve. From that, I would assume there are probably a number of formulas that could come close to approximating this phenomenon, but with one simple division, this one seems good enough to do the job.
January 7th, 2008 at 3:36 am
[…] from Real World Finance$ has put together a great overview and graphical display of The Rule of 72 and Compounding Interest. The rule of 72 applies to halving or doubling of money. Even if you’re not a numbers geek […]
January 7th, 2008 at 7:30 am
Curtis,
The rule of 72 is a great forecasting tool for interest bearing investments that compound, such as bonds and cd’s.
The mathematical equation to determine what an investment will grow to is:
F = P x (1 + r)^n
Where F is the future value, p is the present value, r is the interest rate, and n is the number of years
So, if you invested $10,000 in a CD that paid 5% compounded annually and reinvested all interest payments (paying taxes out of other income), your investment will grow to:
F = 10,000 x (1 + .05)^10 = $16,288.95
January 7th, 2008 at 8:03 am
[…] article on The Rule of 72 was featured on this week’s Carnival of Personal Finance over at Mrs. Micah. Wander over and […]
January 8th, 2008 at 8:45 pm
That is neat. With cheap hand-held calculators a lot of these rules of thumbs are falling by the wayside.
Best Wishes,
D4L
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