Rule of 72: How Accurate Is It? Table vs Exact Doubling Times
The Rule of 72 estimates how long money takes to double. See how accurate it is at rates from 1% to 30%, the exact formula, and when to use 69.3 or 70.
By Awais, Founder and editor-in-chiefPublished
The Rule of 72 says you can estimate how many years it takes for money to double by dividing 72 by the annual interest rate. At 8% a year, 72 ÷ 8 = 9, and the exact answer is 9.01 years, so the rule is almost perfect there.
It is less precise at very low and very high rates. Below is the exact formula, a table comparing the rule with the true doubling time from 1% to 30%, and the variations to use when you need more accuracy.
How the Rule of 72 works
Investor.gov, the SEC’s investor education site, gives the same shortcut in its compound interest explainer: at 9%, money doubles in about 72 ÷ 9 = 8 years.
You can also run it backwards to find the rate you need:
To double your money in 6 years, you need about 72 ÷ 6 = 12% a year. The exact figure is 12.25%.
The exact formula
The rule is a shortcut for this calculation, which assumes interest compounds once a year:
r = annual rate as a decimal; ln = natural logarithm
Example at 8%: ln(2) = 0.693147 and ln(1.08) = 0.076961, so 0.693147 ÷ 0.076961 = 9.01 years. Check: 1.089 = 1.999, just short of double.
Rule of 72 vs exact doubling time
Exact times assume annual compounding. The error column shows how far the rule’s estimate is from the true value.
| Annual rate | Rule of 72 (years) | Exact (years) | Error |
|---|---|---|---|
| 1% | 72.00 | 69.66 | +2.34 (+3.4%) |
| 2% | 36.00 | 35.00 | +1.00 (+2.8%) |
| 3% | 24.00 | 23.45 | +0.55 (+2.3%) |
| 4% | 18.00 | 17.67 | +0.33 (+1.9%) |
| 5% | 14.40 | 14.21 | +0.19 (+1.4%) |
| 6% | 12.00 | 11.90 | +0.10 (+0.9%) |
| 7% | 10.29 | 10.24 | +0.04 (+0.4%) |
| 8% | 9.00 | 9.01 | −0.01 (−0.1%) |
| 9% | 8.00 | 8.04 | −0.04 (−0.5%) |
| 10% | 7.20 | 7.27 | −0.07 (−1.0%) |
| 12% | 6.00 | 6.12 | −0.12 (−1.9%) |
| 15% | 4.80 | 4.96 | −0.16 (−3.2%) |
| 18% | 4.00 | 4.19 | −0.19 (−4.5%) |
| 20% | 3.60 | 3.80 | −0.20 (−5.3%) |
| 25% | 2.88 | 3.11 | −0.23 (−7.3%) |
| 30% | 2.40 | 2.64 | −0.24 (−9.2%) |
What the table shows
- Between about 5% and 12%, the rule is within 2% of the exact answer. That covers most savings, bond and long-run stock market return assumptions.
- It is most accurate near 8%, where the error is almost zero.
- At low rates it overestimates the doubling time slightly; at high rates it underestimates it. At 30%, it is off by more than 9%.
Why 72?
The exact doubling time for small rates is close to 69.3 ÷ rate, because ln(2) is about 0.693. So why use 72? Two reasons:
- 72 is easy to divide. It splits evenly by 1, 2, 3, 4, 6, 8, 9 and 12, so mental maths is quick.
- It corrects for annual compounding. At typical rates of 6% to 10%, the true doubling time with yearly compounding sits slightly above 69.3 ÷ rate, and 72 happens to land closer.
Rule of 72, 70 or 69.3?
Different numerators work better in different situations:
| Rule | Best for | Example at 5% |
|---|---|---|
| Rule of 72 | annual compounding at about 6% to 10%, easy mental maths | 14.40 years |
| Rule of 70 | low rates, such as inflation or GDP growth | 14.00 years |
| Rule of 69.3 | continuous or daily compounding | 13.86 years |
The exact doubling time at 5% with annual compounding is 14.21 years, and with continuous compounding it is 13.86 years. If you need more than an estimate, use the compound interest calculator, which works out the precise balance for any rate, period and compounding frequency.
Other uses of the rule
How fast inflation halves your money
The rule works for anything that grows at a steady percentage, including prices. At 6% inflation, prices double in about 72 ÷ 6 = 12 years (exactly 11.9). That means the buying power of cash kept under the mattress halves in the same time. Our guide on compound interest shows how to calculate real returns after inflation.
How fast debt grows
A credit card balance at 24% a year, left unpaid with interest compounding, doubles in about 72 ÷ 24 = 3 years. The rule makes it obvious why high-interest debt should be paid first.
How much fees cost
With no growth at all, a 2% annual fee would eat half of a portfolio in roughly 72 ÷ 2 = 36 years (exactly 34.3, because the rule is less precise for shrinking amounts). Over a working life, that is a large drag. Small percentage differences matter when they compound for decades.
Tripling and quadrupling
- Rule of 114 for tripling: at 8%, 114 ÷ 8 = 14.25 years (exact 14.27).
- Rule of 144 for quadrupling: two doublings, so 144 ÷ 8 = 18 years.
Limits of the rule
- Returns are rarely steady. Stock market returns vary from year to year. The rule assumes a constant rate, so it describes an average path, not a promise.
- Taxes and fees reduce the rate. Use your expected return after costs.
- It ignores new contributions. For regular monthly investing, use the SIP calculator instead.
FAQ
What is the Rule of 72?
A shortcut to estimate how many years it takes money to double at a fixed annual rate: divide 72 by the rate in percent. At 6%, money doubles in about 12 years.
How accurate is the Rule of 72?
Within about 2% of the exact answer for rates from 5% to 12% with annual compounding, and nearly exact at 8%. It becomes less accurate below 3% and above 15%.
Why is it 72 and not 70?
72 divides easily by many numbers and gives better estimates for annual compounding at common rates. For continuous compounding or low rates, 69.3 or 70 is more accurate.
Can I use the Rule of 72 for inflation?
Yes. Divide 72 by the inflation rate to estimate how many years it takes for prices to double, which is also how long it takes for cash to lose half its buying power.