In Short
The Rule of 72 estimates how long money takes to double: divide 72 by the yearly rate [1]. At 8%, that's 9 years; the exact answer with yearly compounding is 9.01 years. To double in 10 years takes about 7.2% (exactly 7.18%). At 3% inflation, prices double in about 24 years.
How to Use the Rule of 72 Calculator
- Pick what to work out: years to double at a rate, the rate needed to double, or how fast inflation doubles prices.
- Enter the yearly rate (or the number of years), plus an optional starting amount for the chart.
- Read the exact answer next to the Rule of 72, 114 and 144 estimates, and see the 2×, 3× and 4× marks on the chart.
- Or tap Say It All: “I have 10,000 earning 8 percent a year.”
The Formula
The rules divide a fixed number by the rate in percent. The exact answers come from compound growth at that rate, once a year [2].
- Rule of 72: years to double ≈ 72 ÷ rate
- Rule of 114: years to triple ≈ 114 ÷ rate
- Rule of 144: years to quadruple ≈ 144 ÷ rate
- Exact years to multiply by m = ln(m) ÷ ln(1 + rate)
- Exact rate to double in Y years = 2^(1 ÷ Y) − 1
Worked Examples
| Scenario | Inputs | Result |
|---|---|---|
| A 6% return | 6% a year | Doubles in 12 years by the rule (exact 11.9) · triples in 18.85 · quadruples in 23.79 |
| An 8% return | 8% a year, $10,000 | $20,000 in 9.01 years · $30,000 in 14.27 · $40,000 in 18.01 |
| A 10-year target | Double in 10 years | Rule of 72: 7.2% · exact 7.18% · triple needs 11.61% · quadruple 14.87% |
| Inflation at 3% | 3% inflation, $1,000 of groceries | Prices double in about 24 years (exact 23.45) |
| Where the rule drifts | 20% a year | Rule says 3.6 years; exact is 3.8 years |
Illustrative examples, not projections. Figures use the tax year shown and the assumptions above.
What Is the Rule of 72?
The Rule of 72 is a quick way to estimate how long an investment takes to double: divide 72 by the expected yearly rate of return [1]. Investor.gov's example: at 9%, money doubles about every 8 years.
It works because doubling time is ln(2) ÷ ln(1 + r), and for everyday rates that is close to 72 ÷ the rate in percent. It is most accurate between about 4% and 12%; at 2% or 20% it drifts by a few tenths of a year.
What Are the Rules of 114 and 144?
They are the same idea for bigger multiples, and also rules of thumb. Divide 114 by the rate for years to triple, and 144 for years to quadruple. At 6%, that's 19 and 24 years; the exact figures are 18.85 and 23.79.
How Does the Rule of 72 Work for Inflation?
The same math tells you how fast prices double. At 3% inflation, something that costs $1,000 today would cost about $2,000 in 24 years. At the latest 12-month change in the Consumer Price Index, about 3.7%, prices double in roughly 19 years [3]. Put another way, the same dollars buy half as much.
Frequently Asked Questions
How long does it take to double money at 7%?
About 10.3 years by the Rule of 72 (72 ÷ 7). The exact figure with yearly compounding is 10.24 years.
What interest rate doubles money in 5 years?
About 14.4% by the Rule of 72 (72 ÷ 5). The exact rate is 14.87% a year, compounded yearly.
Is the Rule of 72 accurate?
It is close for rates between about 4% and 12%. At 8% it says 9 years and the exact answer is 9.01. At 20% it says 3.6 years against an exact 3.8.
How long does it take to triple money?
Divide 114 by the rate for a quick estimate (the Rule of 114, a rule of thumb). At 8%, about 14.25 years; exactly 14.27.
Does the Rule of 72 account for taxes and fees?
No. Use your return after fees and taxes for a more realistic estimate. Returns on investments also vary from year to year [2].
Sources
- What Is Compound Interest? (Rule of 72) — U.S. Securities and Exchange Commission (Investor.gov)
- Compound Interest Calculator — U.S. Securities and Exchange Commission (Investor.gov)
- CPI for All Urban Consumers (CPI-U), U.S. city average, all items, series CUUR0000SA0 — U.S. Bureau of Labor Statistics
Official sources only: the IRS, SSA, BLS and other government agencies. Read how Zentavos researches.