Rule of 72
The rule of 72 is a quick mathematical formula that helps one find the approximate time duration in which investment made doubles in value when compounded annually by a fixed interest rate.
Doubling Time (in years) = 72 / (Interest Rate (per annum))
Rule of 72 gives an “approximate” time duration and the error increases with an increasing interest rate, hence using the formula is advised for smaller interest rates. Theoretically,
Doubling Time (in years) = (ln(2)) / (ln(1+(0.01*Interest Rate)))
For more accurate calculations, instead of 72, 69.3 can be used for better approximations.
Suppose a student invests Rs.100 in a scheme which gives an interest rate of 3% compounded annually. By the rule of 72, the investment doubles (i.e becomes Rs. 200) in 72/3 = 24 years. Using the theoretical formula, the actual time duration is 23.45 years, so the approximation holds good.