I while solving a problem in banking just thought to form a formula for the time period after which money deposited in bank at a compounded interest rate @$\alpha $ % p.a. .
Amount for compounded annually is :$$A=P[1+r]^t$$ Where t is time period in years and r is rate of interest. Now how to calculate it?
$$A=P[1+r]^t$$ So to find when $P$ has doubled, solve
$$2P=P[1+r]^t \\ \Rightarrow t = \frac{\ln 2}{\ln(1 + r)}.$$
$t$ (for doubling) is often approximated by the "rule of 72" i.e. $$t \approx \frac{0.72}{r}.$$