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Doubling time by return
| Annual return | Rule of 72 | Exact (annual compounding) | $10,000 becomes $20,000 in |
|---|---|---|---|
| 1% | 72.0 yrs | 69.66 yrs | 70 years |
| 2% | 36.0 yrs | 35.00 yrs | 36 years |
| 3% | 24.0 yrs | 23.45 yrs | 24 years |
| 4% | 18.0 yrs | 17.67 yrs | 18 years |
| 5% | 14.4 yrs | 14.21 yrs | 15 years |
| 6% | 12.0 yrs | 11.90 yrs | 12 years |
| 7% | 10.3 yrs | 10.24 yrs | 11 years |
| 8% | 9.0 yrs | 9.01 yrs | 10 years |
| 9% | 8.0 yrs | 8.04 yrs | 9 years |
| 10% | 7.2 yrs | 7.27 yrs | 8 years |
| 12% | 6.0 yrs | 6.12 yrs | 7 years |
The exact formula
Doubling time = ln(2) ÷ ln(1 + r), where r is the annual return as a decimal. At 7%: 0.6931 ÷ 0.0677 = 10.24 years. The rule of 72 is a shortcut that is closest to exact for returns around 6–10%. The rule of 70 (or 69.3) is more accurate for low rates and continuous compounding; at 2%, 70 ÷ 2 = 35 years against an exact 35.0.
What it means over a career
At 7%, money doubles roughly every 10 years, so $10,000 left alone for 30 years grows to about $81,165 with monthly compounding: about three doublings. At 4% it doubles every 18 years, reaching about $33,135. The difference is why the long-run return matters more than almost anything else.
Inflation doubles costs too
The same rule works in reverse. At 3% inflation, prices double in about 24 years (72 ÷ 3), meaning a dollar buys half as much. Real (after-inflation) returns are what grow your purchasing power: a 7% return with 3% inflation doubles real value in about 18 years (72 ÷ 4).
Rates in the tables are a range for comparison, not current market quotes. Payments are principal and interest only unless stated.
Related
Frequently asked questions
How long does it take to double money at 7%?
About 10.2 years (rule of 72: 10.3).
How long does it take to double money at 10%?
About 7.3 years (rule of 72: 7.2).
How long to double money at 5%?
About 14.2 years.
What is the rule of 72?
A shortcut: divide 72 by the annual return in percent to estimate the years needed to double an investment.