Method Deck / finance
Rule of 72 and exact doubling time
Estimates the years to double an investment with the Rule of 72 approximation and computes the exact doubling time with logarithms.
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Inputs
- annual_rate_percent (number, %, required) min 0 : Annual compound growth rate
Outputs
- approx_years (years): Rule of 72 approximation: 72 / rate
- exact_years (years): Exact doubling time using logarithms
Steps
- Rule of 72 approximation: approx_years = 72 / annual_rate_percent.
- Convert the rate to a decimal: r = annual_rate_percent / 100.
- Exact doubling time: exact_years = ln(2) / ln(1 + r).
- Round approx_years and exact_years to 2 decimals.
Constants
- rule_of_72_numerator = 72 dimensionless (source: Principles of Corporate Finance)
Sources
- Principles of Corporate Finance (McGraw-Hill, 2026-09-30T19:31:29Z) - Rule of 72 approximation and the exact doubling-time formula t = ln(2)/ln(1+r)
Worked example and test vectors
| Name | Inputs | Answer |
|---|
| worked example | {"annual_rate_percent":8} | Approximately 9.00 years (Rule of 72); exactly 9.01 years |
| test vector: low rate | {"annual_rate_percent":3} | Approximately 24.00 years (Rule of 72); exactly 23.45 years |
Published card
- Address:
604e3fffadfa40c7bc7aadacb51d6677
- Made at:
2026-09-30T22:39:30.722Z
- Method sha256:
fa1e6742ec6dc7659251d22c510305ba110c9258a403dae71eb6aa3c4f220acf