CalculateY
Quick Answer
At 8% annual return, the Rule of 72 estimates that money doubles in approximately 9 years. The exact calculation yields approximately 9.01 years. To double in 5 years, an estimated annual return of approximately 14.87% is needed.
Years to Double
Rate Needed to Double
Common Examples
| Input | Result |
|---|---|
| 6% annual rate | Estimated 12 years to double (Rule of 72), 11.90 years exact |
| 8% annual rate | Estimated 9 years to double (Rule of 72), 9.01 years exact |
| 10% annual rate | Estimated 7.2 years to double (Rule of 72), 7.27 years exact |
| Double in 5 years | Estimated 14.4% rate needed (Rule of 72), 14.87% exact |
| Double in 10 years | Estimated 7.2% rate needed (Rule of 72), 7.18% exact |
How It Works
The Rule of 72 (Approximation)
Years to Double = 72 / Annual Rate
Rate Needed = 72 / Target Years
This quick mental math shortcut works because 72 is divisible by many common numbers (2, 3, 4, 6, 8, 9, 12), making it easy to compute in your head. The rule is most accurate for rates between 2% and 15%.
Exact Doubling Time Formula
Years to Double = ln(2) / ln(1 + r/100)
Where ln is the natural logarithm and r is the annual rate as a percentage. This formula is derived from the compound interest equation: 2P = P(1 + r)^t, which simplifies to 2 = (1 + r)^t, and solving for t gives t = ln(2) / ln(1 + r).
Exact Rate Needed
Rate = (2^(1/years) - 1) x 100
This is derived from the same equation, solving for r instead of t.
Worked Example
Years to double at 8%:
Rule of 72: 72 / 8 = 9 years. Exact: ln(2) / ln(1.08) = 0.6931 / 0.07696 = 9.006 years. The Rule of 72 estimate of 9 years is off by less than 0.1%.
Rate needed to double in 5 years:
Rule of 72: 72 / 5 = 14.4%. Exact: (2^(1/5) - 1) x 100 = (1.1487 - 1) x 100 = 14.87%. The Rule of 72 slightly underestimates the required rate for shorter time periods.
At lower rates, the rule is also accurate: At 4%, Rule of 72 gives 18 years; the exact answer is 17.67 years. At 12%, Rule of 72 gives 6 years; the exact answer is 6.12 years.