The rule of 72 is a mental-math shortcut for compound growth, and it is accurate enough that most people never check it. We did. The table below compares the rule with the exact doubling time at every whole rate from 1% to 20%, then explains where the number 72 comes from, when 69.3, 70, 114 or 144 work better, and how to apply the rule to savings yields and inflation without the common mistakes. For the rest of the interest math, see the safe investments hub.
What is the rule of 72?
The rule of 72 is a shortcut for compound growth: divide 72 by the annual rate in percent to estimate how many years money takes to double.
Years to double ≈ 72 ÷ annual rate in percent
At 6% that gives 72 ÷ 6 = 12 years, and at 9% it gives 8 years, the example Investor.gov uses when it teaches compound interest. The rule also runs in reverse: to double money in 10 years you need roughly 72 ÷ 10 = 7.2% a year.
It works for anything that grows at a steady compound rate, including savings balances, debt left unpaid and consumer prices. It does not apply to simple interest, where a 4% rate takes a full 25 years to double the deposit because interest never earns interest. And 72 has a practical advantage over more precise numbers: it divides evenly by 1, 2, 3, 4, 6, 8, 9 and 12, so most estimates need no calculator.
How accurate is the rule of 72?
From 4% to 20%, the rule of 72 lands within a third of a year of the exact doubling time, and at 8% it is almost exact.
The exact answer for annual compounding at rate r, written as a decimal, is ln(2) ÷ ln(1 + r). Here is the comparison at every whole rate from 1% to 20%:
| Annual rate | Rule of 72 (years) | Exact (years) | Difference | 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% |
| 11% | 6.55 | 6.64 | −0.10 | −1.5% |
| 12% | 6.00 | 6.12 | −0.12 | −1.9% |
| 13% | 5.54 | 5.67 | −0.13 | −2.3% |
| 14% | 5.14 | 5.29 | −0.15 | −2.8% |
| 15% | 4.80 | 4.96 | −0.16 | −3.2% |
| 16% | 4.50 | 4.67 | −0.17 | −3.6% |
| 17% | 4.24 | 4.41 | −0.18 | −4.1% |
| 18% | 4.00 | 4.19 | −0.19 | −4.5% |
| 19% | 3.79 | 3.98 | −0.20 | −4.9% |
| 20% | 3.60 | 3.80 | −0.20 | −5.3% |
Three patterns are worth knowing. The rule overestimates below about 7.85% and underestimates above it, crossing zero error between 7% and 8%. Measured in years, the biggest misses are at low rates: at 1% the rule is 2.34 years too long. Measured as a percentage, the error grows at both ends, reaching −5.3% at 20%. For the savings and bill yields most people deal with, roughly 3% to 6%, the rule runs one to seven months long: cautious for a savings goal, slightly optimistic for inflation.
Why does the rule of 72 work?
Exact doubling time is ln(2) ÷ ln(1 + r), and because ln(1 + r) is close to r for modest rates, the answer is near 69.3 ÷ the rate.
Here is the derivation in four steps:
- Money doubles when (1 + r)^t = 2.
- Taking logarithms gives t = ln(2) ÷ ln(1 + r), and ln(2) is about 0.693.
- For small r, ln(1 + r) is roughly r − r² ÷ 2, which makes t about 69.3 ÷ R × (1 + r ÷ 2), with R the rate in percent.
- At 8%, the correction factor 1 + 0.08 ÷ 2 = 1.04 turns 69.3 into about 72.
So 72 is 69.3 adjusted for the rates where people most often use it, and rounded to a number with many divisors. The same expansion gives a sharper version that needs one more step:
Years to double ≈ 69.3 ÷ R + 0.35
That refinement stays within 0.02 year of the exact answer at every whole rate from 1% to 20%. For continuous compounding no correction is needed: doubling time is exactly ln(2) ÷ r, or 69.3 ÷ R.
When should you use the rule of 69.3 or 70 instead?
Use 70 for low rates, around 1% to 3%, and 69.3 when a rate compounds daily or continuously, because each divisor is exact at a different point.
| Annual rate | Exact (years) | 72 ÷ R | 70 ÷ R | 69.3 ÷ R | 69.3 ÷ R + 0.35 |
|---|---|---|---|---|---|
| 1% | 69.66 | 72.00 | 70.00 | 69.30 | 69.65 |
| 2% | 35.00 | 36.00 | 35.00 | 34.65 | 35.00 |
| 3% | 23.45 | 24.00 | 23.33 | 23.10 | 23.45 |
| 4% | 17.67 | 18.00 | 17.50 | 17.33 | 17.68 |
| 6% | 11.90 | 12.00 | 11.67 | 11.55 | 11.90 |
| 8% | 9.01 | 9.00 | 8.75 | 8.66 | 9.01 |
| 10% | 7.27 | 7.20 | 7.00 | 6.93 | 7.28 |
| 12% | 6.12 | 6.00 | 5.83 | 5.78 | 6.12 |
| 15% | 4.96 | 4.80 | 4.67 | 4.62 | 4.97 |
| 20% | 3.80 | 3.60 | 3.50 | 3.47 | 3.82 |
The rule of 70 is exact at about 1.98%, which makes it the usual choice for inflation and economic growth rates. The rule of 69.3 never matches annual compounding, because it ignores the correction term, but it is the right tool when a quoted rate compounds daily. At 4% compounded daily, the exact doubling time is 17.33 years, and 69.3 ÷ 4 gives 17.33. Converting that rate to its 4.08% APY and using 72 gives 17.6 years, the usual few months long.
What are the rules of 114 and 144?
The rule of 114 estimates tripling time and the rule of 144 estimates quadrupling time, using the same division as the rule of 72.
| Annual rate | 114 ÷ R | Exact tripling | 144 ÷ R | Exact quadrupling |
|---|---|---|---|---|
| 2% | 57.00 | 55.48 | 72.00 | 70.01 |
| 4% | 28.50 | 28.01 | 36.00 | 35.35 |
| 6% | 19.00 | 18.85 | 24.00 | 23.79 |
| 8% | 14.25 | 14.27 | 18.00 | 18.01 |
| 10% | 11.40 | 11.53 | 14.40 | 14.55 |
| 12% | 9.50 | 9.69 | 12.00 | 12.23 |
Quadrupling is two doublings, so 144 is simply 2 × 72 and shares its sweet spot at about 7.85%. The rule of 114 is exact at about 7.63%. For continuous compounding the matching constants are 100 × ln(3) = 109.9 for tripling and 100 × ln(4) = 138.6 for quadrupling. Any other multiple follows the same pattern: the exact time to grow by a factor F is ln(F) ÷ ln(1 + r).
How long will savings take to double at today's rates?
At yields near 4%, money takes roughly 17 to 18 years to double before tax, and about five years longer once federal tax is taken out.
Worked example: Doubling times at October 2026 rates
- A savings account paying a 4.00% APY: 72 ÷ 4.00 = 18.0 years; exact 17.67. After 18 years, $10,000 grows to $10,000 × 1.04^18 = $20,258
- The 13-week Treasury bill at a 4.08% investment rate on October 30, 2026, which is about a 4.14% APY if rolled at the same rate: 72 ÷ 4.14 = 17.4 years; exact 17.08
- The 4.00% APY after a 22% federal tax rate: 4.00% × 0.78 = 3.12%, and 72 ÷ 3.12 = 23.1 years; exact 22.56
- Working backward: doubling in 5 years takes 72 ÷ 5 = 14.4% by the rule (14.87% exact), and doubling in 20 years takes 3.6% (3.53% exact)
The bill example uses the APY because the rule assumes annual compounding; APY vs APR shows the conversion, and current bill yields are on the T-bill rates page. The 22% bracket applies to 2026 taxable income over $50,400 for single filers and $100,800 for married couples filing jointly. Treasury bill interest is exempt from state and local income tax, so a bill's after-tax doubling time can be shorter than a bank account's at the same yield. To see the full growth path rather than one milestone, use the compound interest calculator.
How fast does inflation halve purchasing power?
Divide 72 by the inflation rate: at September 2026's 3.74%, prices would double, and a dollar's purchasing power halve, in about 19 years.
Worked example: Inflation at three rates
- At 3.74%, the CPI-U change for the 12 months to September 2026: 72 ÷ 3.74 = 19.3 years; exact 18.88; rule of 70, 18.72. After 19.25 years at that rate, $1,000 would buy what about $493 buys today
- At 2%: 72 ÷ 2 = 36 years, while the exact answer is 35.00, the rule of 70's estimate
- At 9.1%, the 12-month rate reached in June 2022: 72 ÷ 9.1 = 7.9 years; exact 7.96
History offers a real-world check. The CPI-U stood at 168.3 in December 1999 and 336.94 in September 2026, so prices doubled in 26.75 years, an average of about 2.63% a year. The rule of 72 at 2.63% gives 27.4 years, about eight months long, in line with its error at low rates; the rule of 70 gives 26.6.
These are what-if figures, not forecasts. They show why a yield that beats inflation by a small margin builds purchasing power very slowly. A 4.00% APY against 3.74% inflation is a real return of about 0.25% a year, and at that pace purchasing power would take about 277 years to double. The real returns guide works through that calculation with live CPI data.
What are the risks of relying on the rule of 72?
The rule is only as good as the rate you feed it, and most mistakes come from rates that are not steady, compounded or after tax.
- Using an APR on a daily-compounded balance. A 24% card APR charged daily doubles an unpaid balance in 2.89 years. 72 ÷ 24 says 3.0 years, too long, and 72 ÷ 27.11, the effective yearly rate, says 2.66, too short. 69.3 ÷ 24 = 2.89 gets it right.
- Ignoring tax. A taxable 4.00% APY doubles in about 18 years before tax and about 23 years after a 22% federal tax.
- Mixing nominal and real. Doubling your dollars is not doubling your purchasing power. After 22% tax, the 3.12% yield trails 3.74% inflation, so purchasing power shrinks about 0.60% a year and would halve in about 116 years.
- Assuming the rate holds. Savings rates change, bills and CDs reset when they mature, and the rule assumes one rate for the whole period, so treat the result as a scenario, not a plan.
- Plugging in an average return. Volatile returns compound more slowly than their average. Gains of 20% and losses of 10% in alternating years average 5%, but compound at 3.92%, so the rule's 14.4 years becomes an actual 18.0.
- Using it at high rates. At 20% the rule is already 5.3% short, and the error keeps growing at higher rates; use ln(2) ÷ ln(1 + r) instead.
- Simple interest. Accounts and bonds that pay interest out rather than reinvesting it do not compound, so a 4% simple rate takes 25 years to double, not 18.
For the mechanics behind all of these, the compound interest guide shows the year-by-year tables.