how to use the rule of 72
the rule of 72 could apply to anything that grows at a compounded rate such as population macroeconomic numbers charges or loans if the gross domestic product gdp grows at 4 annually the economy will be expected to double in 72 4 18 years with regards to the fee that eats into investment gains the rule of 72 can be used to demonstrate the long term effects of these costs a mutual fund that charges 3 in annual expense fees will reduce the investment principal to half in around 24 years a borrower who pays 12 interest on their credit card or any other form of loan that is charging compound interest will double the amount they owe in six years the rule can also be used to find the amount of time it takes for money s value to halve due to inflation if inflation is 6 then a given purchasing power of the money will be worth half in around 12 years 72 6 12 if inflation decreases from 6 to 4 an investment will be expected to lose half its value in 18 years instead of 12 years additionally the rule of 72 can be applied across all kinds of durations provided the rate of return is compounded annually if the interest per quarter is 4 but interest is only compounded annually then it will take 72 4 18 quarters or 4 5 years to double the principal if the population of a nation increases at the rate of 1 per month it will double in 72 months or six years who came up with the rule of 72 the rule of 72 dates back to 1494 when luca pacioli referenced the rule in his comprehensive mathematics book called summa de arithmetica 2 pacioli makes no derivation or explanation of why the rule may work so some suspect the rule pre dates pacioli s novel 3