Rule of 72

The time required for a given principal to double (assuming  conversion period) for compound interest is given by solving

(1)

or

(2)

where ln is the natural logarithm. This function can be approximated by the so-called "rule of 72":

(3)

The above plots show the actual doubling time  (left plot) and the difference between the actual doubling time and the doubling time calculated using the rule of 72 (right plot) as a function of the interest rate .

REFERENCES:

Avanzini, J. F. Rapid Debt-Reduction Strategies. Fort Worth, TX: HIS Pub., 1990.