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 
.
