Rule of 72

The rule of 72 is an arithmetic shortcut: divide 72 by the annual rate, and the answer is roughly how many years the money takes to double. At 6% a year, 72 divided by 6 is 12, so the balance doubles in about twelve years.

The mathematically exact number is 69.3, not 72. It is 72 that gets used because 72 divides cleanly by 2, 3, 4, 6, 8, 9 and 12, so the sum can be done in your head without a calculator. The trade is a small loss of accuracy for a rule anyone can carry around. It is closest to exact at around 8% and drifts at the extremes.

Because it turns compounding from an abstract idea into a number you can picture. A rate on its own says nothing about time, and time is the variable that does the work. A doubling period says both at once.

It runs on debt exactly as it runs on savings, and that is where it earns its keep. A card at 36% doubles what you owe in about two years. A deposit paying 5% takes about fourteen years to double what you have. The same arithmetic applied to both sides of a balance sheet shows why one side moves so much faster than the other, and why the balance sheet as a whole can be going backwards while both numbers on it are growing.

It also works on prices. Divide 72 by the inflationTermInflation×التضخّمA general rise in prices over time, so one riyal today buys less than it did a year ago.Open the term rate and you have the years until the same basket of goods costs twice as much, which is the same statement as your cash buying half as much. Running it twice, once on the return and once on inflation, is where it becomes useful rather than merely neat: if the money doubles in fourteen years and prices double in twelve, the balance went up and the purchasing power went down.

The number to feed it is the one most often got wrong. The rule takes the rate actually received after fees, not the rate on the poster.

• Rearranged, it also answers the other question: 72 divided by the number of years you have gives the annual rate needed to double in that time.
• The figure it returns is for a nominal return, not a real one. Subtract inflation from the rate first if the question is when purchasing power doubles.
• Fees and taxes reduce the effective rate and so extend the timeline. The rule does not account for them: they have to be taken off the rate before it goes in.
• The estimate loses accuracy at very high and very low rates. Above roughly 20% it starts to understate the time noticeably.
• In Shariah-compliant products a profit margin or rental payment replaces interest in the calculation, and the rule works unchanged.