Rule of 69 and continuous growth
The value 69.3 comes from 100 × ln(2). It closely estimates doubling for small annual rates and is exact for a continuously compounded rate when using 69.3147 as the numerator.
Investing
Rule of 72 Calculator
Estimate investment doubling time with the rules of 72, 70 and 69. Compare exact compound-growth time and the annual return needed for a chosen doubling period.
Exact investment doubling time
9.01 yr
Rule of 72 estimate
9 yr
Annual return needed for desired time
7.18%
Doubling-time comparison
Detailed values use the same assumptions as the summary above.
| Method | Years | Difference from exact (years) |
|---|---|---|
| Exact annual compounding | 9.01 yr | 0 |
| Rule of 72 | 9 yr | -0.006 |
| Rule of 70 | 8.75 yr | -0.256 |
| Rule of 69 | 8.63 yr | -0.381 |
Rules of 72, 70 and 69 are approximations. They do not predict investment returns or account for fees, taxes or changing rates.
Calculation method
Formula and method
r is the effective annual rate as a decimal. The required rate for a desired time t is (2^(1/t) − 1) × 100%. A ten-year doubling requires about 7.177% annually.
Detailed guide
Estimate how long money takes to double
Divide 72 by the annual percentage rate to estimate doubling time. At 8%, the rule estimates 9 years. Exact annual compounding produces about 9.006 years, so the shortcut is close for that example.
The rules of 70 and 69 use different numerator approximations. The table compares them with exact annual compounding. The calculator also solves the effective annual return needed to double within your chosen time.
Formula and method
Approximate years = 72 / annual %; exact years = ln(2) / ln(1+r)
r is the effective annual rate as a decimal. The required rate for a desired time t is (2^(1/t) − 1) × 100%. A ten-year doubling requires about 7.177% annually.
At zero or a negative growth rate, capital does not double under this model. The result reports that explicitly rather than dividing by zero.
Using the results
Annual rate convention
A nominal APR with monthly compounding differs from an effective annual rate. Convert the quoted APR to APY first if you want an annual comparison.
Frequently asked questions
Is the rule of 72 exact?
No. It approximates logarithmic compound growth. The calculator shows exact time beside each shortcut.
Which rule is best?
Accuracy depends on the rate. Compare each estimate against exact time in the table rather than assuming one rule fits every rate.
Do extra contributions change doubling time?
Yes. This page models growth of the original amount only. Use compound interest or savings-goal calculations for ongoing contributions.
Updated: October 1, 2026
Useful comparisons
Related financial calculators
Compound interest
Estimate future value with monthly contributions, flexible compounding frequency and contribution timing.
ROI and investment return
Calculate simple ROI or annualized return and profit after monthly contributions.
APY
Convert nominal APR to annual percentage yield, convert APY back to nominal APR, or project growth from a quoted APY.