Rule of 72

The time required for a given Principal to double (assuming $n=1$ Conversion Period) for Compound Interest is given by solving

$$2P=P(1+r)^t,$$ (1)

or

$$t={\ln 2\over\ln(1+r)},$$ (2)

where Ln is the Natural Logarithm. This function can be approximated by the so-called ``rule of 72'':

$$t\approx {0.72\over r}.$$ (3)

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

See also Compound Interest, Interest

References

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