The rule of 72 is a shortcut to estimate the number of years/days required to double your money at a given annual/daily rate of return. The rule states that you divide the rate, expressed as a percentage, into 72:
Years required to double investment = 72 ÷ compound annual interest rate
The rule of 72 is a useful shortcut, since the equations related to compound interest are too complicated for most people to do without a calculator. To find out exactly how long it would take to double an investment that returns 8% annually, one would have to use this equation:
T = ln(2) / ln(1.08) = 9.006
Most people cannot do logarithmic functions in their heads, but they can do 72 ÷ 8 and get almost the same result. If it takes 9 years to double a Rs.1,000 investment, then the investment will grow to Rs.2,000 in Year 9, Rs.4,000 in Year 18, Rs.8,000 in Year 27, and so on. Conveniently, 72 is divisible by 2, 3, 4, 6, 8, 9, and 12, making the calculation even simpler.
The unit does not necessarily have to be money: the rule could apply to any thing that grows, such as population. If GDP grows at 4% annually, the economy will be expected to double in 72 ÷ 4 = 18 years. Also, in regards to fees that cut into investment gains, the rule of 72 can be used to demonstrate the long-term effects of these costs. A mutual fund that has 3% in annual expense fees will cut the investment principal in half over 24 years. A borrower that pays 12% interest on his credit cards will double the amount he owes in 6 years.
The rule of 72 is reasonably accurate for interest rates between 6% and 10%. When dealing with rates outside this range, the rule can be adjusted by adding or subtracting 1 from 72 for every 3 points the interest rate diverges from 8%. So for 11% annual compounding interest, the rule of 73 is more appropriate; for 14%, it would be the rule of 74; for 5%, the rule of 71.