At 8% effective annual growth, your money doubles in about 9 years.
Rule of 72: 72 ÷ 8 = 9 years
Assumes a constant return, annual compounding, reinvested earnings, and no deposits or withdrawals.
Rule of 72 is convenient near typical investment rates; Rule of 70 is a rounder low-rate shortcut; Rule of 69.3 is the natural match for continuous compounding. The highlighted row is currently closest to the exact result.
| Method | Years | Difference | Best use |
|---|
Core assumption: doubling time requires a constant compounded return, all earnings reinvested, and no deposits or withdrawals.
The Rule of 72 divides 72 by a percentage; the reverse calculation divides 72 by years.
Estimated years = 72 ÷ annual rate (%)
Estimated annual rate (%) = 72 ÷ years
For effective annual growth g, exact doubling time uses a natural logarithm. Exact required growth reverses the equation.
Exact years = ln(2) ÷ ln(1 + g)
Exact g = 2^(1 ÷ years) − 1
For nominal APR r compounded n times per year, APY is (1 + r/n)^n − 1. Continuous compounding uses e^r − 1. The calculator then subtracts annual fee percentage points and converts to real growth with (1 + net growth) ÷ (1 + inflation) − 1.
Inputs: $10,000, 8% effective annual growth, no fees or inflation.
72 ÷ 8 = 9 years
ln(2) ÷ ln(1.08) = 9.01 years
The shortcut differs by only 0.01 years (0.07%). If the rate stays constant and earnings are reinvested, $10,000 becomes $20,000.
Inputs: 3% constant inflation, interpreted as the rate at which prices grow.
72 ÷ 3 = 24 years
ln(2) ÷ ln(1.03) = 23.45 years
A fixed amount of cash loses about half its purchasing power when prices double: about 24 years by the rule, versus 23.45 years exactly. Actual inflation changes over time.
Inputs: 18% nominal APR, monthly compounding, no payments, purchases, or added fees.
(1 + 0.18 ÷ 12)^12 − 1 = 19.56% APY
72 ÷ 19.56 = 3.68 years
ln(2) ÷ (12 × ln(1 + 0.18 ÷ 12)) = 3.88 years
After putting APR and the exact result on the same effective-rate basis, the shortcut is about 0.20 years low (5.13%). This illustrates compounding, not a payoff schedule; real balances change with payments and charges.
| Effective rate | Rule of 72 | Exact years | Error |
|---|---|---|---|
| 1% | 72.00 | 69.66 | 3.36% |
| 2% | 36.00 | 35.00 | 2.85% |
| 3% | 24.00 | 23.45 | 2.35% |
| 4% | 18.00 | 17.67 | 1.85% |
| 5% | 14.40 | 14.21 | 1.36% |
| 6% | 12.00 | 11.90 | 0.88% |
| 7% | 10.29 | 10.24 | 0.40% |
| 8% | 9.00 | 9.01 | 0.07% |
| 9% | 8.00 | 8.04 | 0.54% |
| 10% | 7.20 | 7.27 | 1.00% |
| 11% | 6.55 | 6.64 | 1.45% |
| 12% | 6.00 | 6.12 | 1.90% |
| 13% | 5.54 | 5.67 | 2.34% |
| 14% | 5.14 | 5.29 | 2.78% |
| 15% | 4.80 | 4.96 | 3.22% |
| 16% | 4.50 | 4.67 | 3.64% |
| 17% | 4.24 | 4.41 | 4.07% |
| 18% | 4.00 | 4.19 | 4.49% |
| 19% | 3.79 | 3.98 | 4.90% |
| 20% | 3.60 | 3.80 | 5.31% |
| Target | Rule of 72 rate | Exact effective rate | Error |
|---|---|---|---|
| 5 years | 14.40% | 14.87% | 3.16% |
| 7 years | 10.29% | 10.41% | 1.18% |
| 10 years | 7.20% | 7.18% | 0.32% |
| 12 years | 6.00% | 5.95% | 0.90% |
| 15 years | 4.80% | 4.73% | 1.49% |
| 20 years | 3.60% | 3.53% | 2.08% |
Chart values assume a constant effective annual rate with annual compounding and no fees, taxes, inflation adjustment, deposits, or withdrawals.
Use the Rule of 72 to sense-check investment growth, estimate how inflation erodes purchasing power, or illustrate how an unpaid debt balance compounds. It is an educational shortcut, not a forecast.
We calculate APY from the selected nominal APR and frequency, subtract the entered annual fee percentage points, adjust for inflation geometrically, and solve the compound-growth equation with logarithms. Reverse mode algebraically solves the required real growth and converts it back to the displayed annual rate. Values are calculated in the browser with full JavaScript precision and rounded only for display.
References: the U.S. SEC's Rule of 72 and compound-interest explanation, the CFPB's official APY calculation guidance, and the SEC's investor bulletin on fees and returns.
Educational use only: this calculator provides general information, not financial, investment, tax, or legal advice.
The Rule of 72 is a mental-math shortcut: divide 72 by a constant annual percentage return to estimate doubling time, or divide 72 by a target number of years to estimate the required return.
For effective annual rates from about 6% to 10%, it is usually within about 1% of the exact annual-compounding result. Accuracy declines at very low or high rates, so use the exact result for decisions.
Yes. Choose Years to rate. The shortcut is 72 divided by years; the exact effective annual rate is 100 × (2^(1/years) − 1). Advanced settings convert that requirement to a nominal APR when needed.
Yes. Open Advanced assumptions and choose monthly, quarterly, daily, or continuous compounding. The rate field then represents nominal APR, and the calculator derives APY before finding the exact doubling time.
Yes. Enter an inflation rate to estimate when purchasing power doubles in real terms. The calculator converts nominal net growth to real growth using (1 + nominal net growth) ÷ (1 + inflation) − 1.
It can illustrate how quickly an unpaid balance could double at a constant compounded rate, but real debt may have payments, purchases, penalties, fees, and variable rates that this simple model does not capture.
A balance cannot double under this constant-return model when the adjusted growth rate is zero or negative. The calculator reports that no finite doubling time exists.
No. It assumes one starting amount, reinvested earnings, and no deposits or withdrawals. Use a compound interest or savings calculator for recurring cash flows.
APR is the nominal annual rate before within-year compounding; APY is the effective one-year growth after compounding. With annual compounding they are equal, but with more frequent compounding APY is higher when the rate is positive.
Yes. Everything runs locally in your browser and is not uploaded.