Dated assumptions · transparent formulas
Rule of 72
The rule of 72 is a fast mental estimate for doubling time. This guide shows the math behind it, where it is accurate, and how to check it with the calculator.
Educational calculator. Inputs stay in your browser. Historical ranges are not forecasts or investment advice.
Inputs
Estimate comparison
| Assumption | Rate | Nominal FV | Real FV |
|---|---|---|---|
| Lower estimate1-year Treasury constant maturity | 4.28% | $7,915.29 | $6,716.21 |
| Middle estimateS&P 500 rolling 30-year total-return median | 10.80% | $9,621.50 | $8,163.95 |
| Higher estimateS&P 500 rolling 30-year total-return 75th percentile | 12.04% | $9,996.02 | $8,481.74 |
Growth curve and yearly schedule
The same projection engine draws each estimate and feeds the collapsible year-by-year detail.
- Lower estimate
- Middle estimate
- Higher estimate
Show year-by-year detail
| Year | Opening | Deposits | Interest | Ending |
|---|---|---|---|---|
| 1 | $1,000.00 | $1,200.00 | $174.73 | $2,374.73 |
| 2 | $2,374.73 | $1,200.00 | $330.77 | $3,905.50 |
| 3 | $3,905.50 | $1,200.00 | $504.53 | $5,610.03 |
| 4 | $5,610.03 | $1,200.00 | $698.01 | $7,508.04 |
| 5 | $7,508.04 | $1,200.00 | $913.45 | $9,621.50 |
Rate assumptions and sources
Lower / Middle / Higher estimates · reviewed 2026-09-12
- Lower estimate
4.28%
- FRED: 1-Year Treasury Constant Maturity Rate (DGS1)
Retrieved 2026-09-12 · observation 2026-09-10
Dated benchmark snapshot.
- Middle estimate
10.80%
- Damodaran historical returns, 1928-2025
Retrieved 2026-09-12
Median of 69 overlapping 30-year S&P 500 total-return windows through 2025.
- Higher estimate
12.04%
- Damodaran historical returns, 1928-2025
Retrieved 2026-09-12
75th percentile of 69 overlapping 30-year S&P 500 total-return windows through 2025.
- Inflation: 3.34%
- FRED: Consumer Price Index for All Urban Consumers (CPIAUCSL)
Compound annual change from August 2016 to August 2026; user input can replace it.
The formula and worked examples
Divide 72 by the annual percentage return to estimate the number of years a balance takes to double. At a 6% return, 72 / 6 = 12 years; at 8%, 9 years; at 10%, 7.2 years.
The exact doubling time is ln(2) / ln(1 + r). At 6% that is about 11.9 years, at 8% about 9.0 years, and at 10% about 7.3 years. The rule of 72 stays within a few months of the exact answer across the range of ordinary investment returns.
The same division works in reverse for required growth: to double in 10 years, you need roughly a 7.2% annual return. Treat that as a screening estimate, not a promised rate.
From doubling time to future value
Each doubling multiplies the balance by 2, so a horizon with n doublings projects a future value of roughly the present balance times 2^n. A $50,000 balance growing at 7.2% doubles every 10 years: about $100,000 in 10 years, $200,000 in 20 years, and $400,000 in 30 years.
For recurring deposits, estimate the lump-sum doubling first, then check the deposit stream with the calculator. Deposits early in the horizon compound through more doublings than deposits made late, which is why contribution timing changes results so much.
Where the rule of 72 breaks down
The estimate is tuned for rates between about 4% and 12%. At 2% it says 36 years when the exact answer is about 35 years, and at 24% it says 3 years when the exact answer is about 3.4 years, so very high or very low rates drift from reality.
It also assumes a constant annual return. A portfolio that averages 7% can still spend years below its starting value, and a sequence of poor early returns delays every planned doubling. Variable annuity growth and inflation-adjusted returns each need the full calculator treatment rather than one division.