What the Rule of 72 says
Divide 72 by the annual interest rate, and the answer is roughly how many years it takes your money to double. At 6% a year, 72 divided by 6 is 12, so a balance that keeps compounding at 6% doubles in about 12 years.
You use the rate as a plain number, not a decimal. For 8%, you divide by 8, not by 0.08. The rule works for anything that grows at a steady percentage each year: savings, investments, prices, or an unpaid debt.
The rule also runs backward. Divide 72 by the number of years you have, and you get the rate you would need to double in that time. To double in 5 years, 72 divided by 5 gives 14.4%. The exact answer is 14.87%, so the shortcut lands close.
Example: $10,000 at 8%
The Rule of 72 says $10,000 earning 8% a year, compounded annually, doubles in about 72 ÷ 8 = 9 years. Check it with the compound interest formula: $10,000 × 1.08 to the 9th power works out to $19,990.05 after 9 years. That is within a few dollars of $20,000, so the estimate holds up well at this rate.
How close is the estimate? A side-by-side table
At common rates, the Rule of 72 is usually off by less than a year. The table compares the estimate with the exact doubling time for annual compounding, ln(2) ÷ ln(1 + r). A positive gap means the rule overestimates the time.
| Annual rate | Rule of 72 (years) | Exact (years) | Gap (years) | Rule of 70 (years) |
|---|---|---|---|---|
| 2% | 36.00 | 35.00 | +1.00 | 35.00 |
| 4% | 18.00 | 17.67 | +0.33 | 17.50 |
| 6% | 12.00 | 11.90 | +0.10 | 11.67 |
| 8% | 9.00 | 9.01 | -0.01 | 8.75 |
| 10% | 7.20 | 7.27 | -0.07 | 7.00 |
| 12% | 6.00 | 6.12 | -0.12 | 5.83 |
Two patterns stand out. First, the rule is almost exact near 8%, where 72 ÷ 8 gives 9.00 years and the true figure is 9.01. Second, the error flips sign: below about 8% the rule runs a little long, and above it the rule runs a little short. At 2% the gap reaches a full year, but on a 35-year horizon that is still under 3%.
Why 72, and the Rule of 69 and 70 variants
The math behind the rule starts with the natural log of 2, which is about 0.693. If interest compounded continuously, the doubling time would be exactly 69.3 divided by the rate. That is where the Rule of 69 (more precisely 69.3) comes from, and it is the best choice for continuous or daily compounding.
With annual compounding, the true doubling time is a little longer than 69.3 ÷ r, and the extra grows as rates rise. Bumping the numerator up to 72 makes up for that gap in the 6% to 10% range where people use the rule most. The number 72 is also easy to divide in your head. It splits evenly by 1, 2, 3, 4, 6, 8, 9 and 12.
- Rule of 72: best for annual compounding at moderate rates, roughly 6% to 10%, and the easiest to compute mentally.
- Rule of 70: a bit more accurate at low rates such as 2% to 4%. Economists often use it for population or GDP growth, where rates tend to be small.
- Rule of 69.3: matches continuous compounding exactly, and comes very close for daily compounding.
None of the three is wrong. They are all approximations of the same log formula, tuned for different conditions. For a quick answer, pick whichever divides more cleanly.
Using it for inflation and debt
The rule is just as useful for things you want to grow slowly. Apply it to inflation, and it tells you how long until prices double, which is the same as the time until a dollar buys half as much.
Example: 3% inflation
At a steady 3% annual inflation rate, 72 ÷ 3 = 24, so prices roughly double in 24 years. The exact figure is 23.45 years. In practical terms, something that costs $50 today would cost about $100 in a little under a quarter century, and cash held in a drawer would lose about half its buying power over the same stretch.
Debt works the same way, only it compounds against you. Consider a credit card balance at a 24% example APR, with no payments and no new charges. The rule gives 72 ÷ 24 = 3 years to double. Because card interest typically compounds monthly, the exact time at 2% per month is 2.92 years. Either way, the balance doubles in about three years, which shows how fast high-rate debt grows when it sits untouched.
For loans, this is a rough way to sense how much interest pressure a rate creates. It does not replace an amortization schedule, because most loans have payments that shrink the balance over time.
Where the Rule of 72 falls short
The rule is a mental shortcut, and it has limits you should keep in mind.
- High rates. The error grows as rates rise. At 36%, the rule says 2.00 years, but the exact answer is 2.25 years.
- Steady rates only. It assumes the same return every year. Real investment returns go up and down, so a long-run average does not guarantee a doubling date.
- No contributions or withdrawals. It tracks a single lump sum. Regular deposits make a balance double sooner, and withdrawals slow it down.
- Taxes and fees. A 1% annual fee on a 7% return leaves 6%, which moves the estimate from about 10.3 years to 12 years. Use the rate you actually keep.
- Nominal versus real. Doubling your dollars is not the same as doubling your buying power. Subtract inflation from your rate first if you care about what the money will buy.
Here is how the rule holds up at higher rates:
| Annual rate | Rule of 72 (years) | Exact (years) | Gap (years) |
|---|---|---|---|
| 18% | 4.00 | 4.19 | -0.19 |
| 24% | 3.00 | 3.22 | -0.22 |
| 36% | 2.00 | 2.25 | -0.25 |
A quick way to use it
Keep the steps short. Find the yearly rate that actually applies to you, after fees. Divide 72 by it. If the rate is under 4%, try 70 instead. If you need a precise number, or you plan to add money along the way, run the figures through a calculator that handles compounding and contributions.
The rule is good for comparing options at a glance. Moving from a 4% return to an 8% return cuts the doubling time from about 18 years to about 9. Doubling the rate roughly halves the time, which is a simple way to see why small differences in rates add up over decades.