Rule of 72

The rule of 72 exists because compound growth is hard to do in your head and doubling is easy to picture. Divide 72 by a yearly rate and the answer is the years a balance takes to double at that rate; divide 72 by a number of years and the answer is the rate it would take to double in them. The rule lands within a year of the exact answer at every rate from 2% to 24%, and it is nearly exact at 8%, which covers savings accounts, investment returns, inflation and most loans. At 7% the rule says 10.3 years and the exact figure is 10.2; at 4% it says 18 and the exact figure is 17.7.

In a sentence

• "By the rule of 72, money earning 7% a year doubles in about ten years, so $10,000 is roughly $20,000 by then."
• "The rule of 72 cuts both ways: at 3% inflation, prices double in about twenty-four years, so a dollar buys half as much."
• "A carried balance at 18% doubles in about four years by the rule of 72, if nothing is paid on it."

How it works

Years to double ≈ 72 ÷ yearly rate, with the rate as a whole number, 6 for 6%

Rate needed to double ≈ 72 ÷ years

1. Take the yearly growth rate as a whole number: 6 for 6%, 7 for 7%.
2. Divide 72 by it. The result is the years to double.
3. Add the same span for each further doubling. The balance quadruples in twice the time and grows eightfold in three times the time.

The exact doubling time is ln 2 ÷ ln(1 + r), and for small rates that is close to 69.3 ÷ r. Seventy-two is used instead because it is a closer fit at the rates people meet, where interest is credited yearly rather than continuously, and because it divides evenly by 2, 3, 4, 6, 8, 9 and 12. Its error is small and predictable: the rule runs slightly long at low rates and slightly short at high ones. It also assumes the rate holds steady, which a savings account or a loan does over its term and an investment return does not.

An example

$10,000 invested at a steady 7% a year, the example's assumption. The rule puts a doubling every 72 ÷ 7, or 10.3, years, so the balance should be near $20,000 after ten years, $40,000 after twenty-one, $80,000 after thirty-one and $160,000 after forty-one.

Four doublings in a little over forty-one years, and the rule is off by a few months per doubling and by less than 1% of the balance at the end. The same $10,000 at 4% takes eighteen years per doubling and is about $50,000 after the same forty-one years, which is the rule's real use: it makes the cost of three percentage points visible without a spreadsheet.

Why it matters

The rule turns a rate into a span of time, which is the form in which a rate means something. A 7% return and a 4% return are three points apart on paper and eight years apart per doubling, and over forty years that is the difference between about two doublings and about four. It prices inflation and debt in the same units: at 3% inflation the purchasing power of cash halves in about twenty-four years, and a card balance at 24% with nothing paid on it doubles in about three.

The mistake it prevents is treating a small difference in rate as a small difference in outcome. Its limit is the steady rate it assumes: an investment that averages 7% with swings does not double on a schedule, and the rule gives the average path rather than any particular decade.

Rule of 72 versus the exact doubling time

The rule is an approximation of years to double = ln 2 ÷ ln(1 + r), and the table shows how close it comes. A positive difference means the rule runs long.

Use the exact formula, or a calculator, when the answer is going into a plan, and the rule when the answer is going into a conversation. For continuous compounding the exact constant is 69.3, and 72 is the better fit for interest credited yearly at rates from about 6% up; below that, dividing 70 by the rate comes slightly closer. See Compound interest for the mechanism the rule approximates.

Common questions

Is the rule of 72 accurate? Within a year of the exact answer at any rate from 2% to 24%, and within four months at rates from 4% to 24%. It runs a little long at low rates and a little short at high ones, and it is nearly exact at 8%. For a plan, use the formula or a calculator; for a sense of scale, the rule is enough.

Does the rule of 72 work for inflation? Yes, in reverse. Divide 72 by the inflation rate for the years until prices double, which is the years until a fixed sum buys half as much. At 3% that is about twenty-four years by the rule and 23.4 exactly; at 2% it is thirty-six by the rule and thirty-five exactly.

Does the rule of 72 work for debt? Yes, for a balance nothing is being paid on. Divide 72 by the rate: a balance at 18% doubles in about four years and one at 24% in about three. Any payment slows the doubling, and a payment larger than the month's interest reverses it.

Is there a rule for tripling? Quadrupling is two doublings, so twice the time. For tripling the matching shortcut is the rule of 114, 114 divided by the rate: at 6% that is nineteen years, against twelve for doubling, and the exact figure is 18.9.

Where does the 72 come from? From the exact formula. The doubling time is ln 2 ÷ ln(1 + r), which for small rates is close to 69.3 ÷ r; 72 is used instead because it is slightly closer for interest credited yearly at everyday rates, and because so many of those rates divide into it evenly.

Go deeper

• The Compound interest calculator shows how a starting balance and a monthly contribution grow at a given return over the years, year by year, so the doublings the rule estimates are visible as a table.
• The Retirement calculator projects what your retirement savings could grow to by the age you plan to stop working, what that is worth in today's dollars, and the monthly income it could support.
• Why net worth grows slowly at first and then faster draws the same curve on a whole net worth, with the share of each year's growth that comes from the balance rather than from you.