For example, $100 invested at 6% compounded annually would double to $200 in approximately 72 / 6 or 12 years.

The Compound Interest Formula is:

where P is the Principal invested at r, and compounded m times per year for n years. A is the total earned in the account after n years. Note that r is the annual interest rate divided by 100, but that in the Rule of 72, R is the annual interest rate.

For Annual Compounding (where m is 1), the formula becomes:

In the example above, the actual time required for $100 to double is 11.89 years and can be solved in the following manner:

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But why does this Rule of 72 seem to work?

Take the Compound Interest Formula, and solve for n:

Now, take the Rule of 72 and solve for n (remember to divide R by 100 to get r):

Graph these two functions on a graphing calculator to see why the values of n are very close. Use the trace function and change the domain (values for r) and the range (values for n) to be:
XMIN = 0
XMAX = .12
XSCAL = .01
YMIN = 0
YMAX = 100
YSCAL = 10