Rule of 72 Calculator
Calculate how long it takes for your investments to double using the Rule of 72. This simple rule provides a quick estimate of investment growth and helps with retirement planning.
Rule of 72 Results
Investment Projections
Rule Accuracy
Rule of 72 Estimate: 0 years
Actual Calculation: 0.0 years
Difference: 0.0 years
Note: Rule of 72 is most accurate for rates between 5-10%
Understanding the Rule of 72
The Rule of 72 is a simple mathematical shortcut used to estimate how long it takes for an investment to double in value. It's a quick way to understand the power of compound interest and make rough retirement projections.
How the Rule of 72 Works
The Rule of 72 states that you can estimate the number of years it takes for an investment to double by dividing 72 by the annual rate of return.
Years to Double = 72 ÷ Annual Rate
Example: 8% return rate ? 72 ÷ 8 = 9 years to double
Rule of 72 Examples
| Return Rate | Rule of 72 | Actual Time | Accuracy |
|---|---|---|---|
| 3% | 24 years | 23.45 years | Very Accurate |
| 5% | 14.4 years | 14.21 years | Very Accurate |
| 7% | 10.29 years | 10.24 years | Very Accurate |
| 10% | 7.2 years | 7.27 years | Very Accurate |
| 12% | 6 years | 6.12 years | Good |
Why 72?
The number 72 comes from the mathematical relationship in compound interest calculations. For rates between 5-10%, 72 provides the most accurate estimates.
The formula is derived from:
(1 + r)^t = 2
Taking natural log: t × ln(1+r) = ln(2) ˜ 0.693
For small r: t ˜ 0.693/r, or t ˜ 69.3/r
Rounded to 72 for easier calculation
Other Rules of Thumb
- Rule of 69: For continuous compounding (69 ÷ rate)
- Rule of 70: For rates with inflation (70 ÷ real rate)
- Rule of 71: Alternative for some calculations
- Rule of 73: For rates over 8%
- Rule of 74: For tax-deferred accounts
Applications in Retirement Planning
- Investment Growth: Estimate portfolio doubling time
- Retirement Savings: Calculate required savings rate
- Inflation Impact: Adjust for purchasing power changes
- Goal Setting: Set realistic investment targets
- Risk Assessment: Evaluate investment strategy returns
Limitations of the Rule
- Accuracy Range: Most accurate for rates between 5-10%
- Simple Interest: Doesn't account for compounding frequency
- Variable Rates: Assumes constant annual return
- Taxes and Fees: Doesn't include real-world costs
- Market Volatility: Historical averages may not predict future
Real-World Examples
Retirement Savings Example:
If you invest $10,000 at 7% annual return:
Rule of 72: 72 ÷ 7 = 10.29 years to double
Actual: Approximately 10.24 years
Final amount: $20,000
College Savings Example:
$5,000 invested at 6% for college savings:
Rule of 72: 72 ÷ 6 = 12 years to double
Future value: $10,000 for college expenses
Pro Tip: The Rule of 72 is a powerful mental shortcut for understanding compound interest. Use it for quick estimates, but always verify with detailed calculations for important financial decisions. Remember that past performance doesn't guarantee future results.