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Rule of 72 Approximation:
Exact Formula:
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The time to double formula calculates how many years it will take for an investment to double in value given a fixed annual rate of return. The exact formula uses natural logarithms, while the Rule of 72 provides a quick approximation.
The calculator uses two formulas:
Exact Formula:
\[ t = \frac{\ln(2)}{\ln(1 + r)} \]Rule of 72 Approximation:
\[ t \approx \frac{72}{r \times 100} \]Where:
Explanation: The exact formula precisely calculates the doubling time using the mathematical properties of exponential growth, while the Rule of 72 provides a mental math shortcut.
Comparison: The Rule of 72 is accurate for interest rates between 6% and 10%. For rates outside this range, the exact formula should be used for better precision.
Tips: Enter the annual interest rate as a percentage (e.g., enter 5 for 5%). The calculator will show both the exact result and the Rule of 72 approximation.
Q1: Why does the Rule of 72 work?
A: It's derived from the mathematical properties of logarithms and provides a good approximation for typical interest rates.
Q2: How accurate is the Rule of 72?
A: It's within 1% of the exact value for rates between 6-10%, but becomes less accurate for very high or very low rates.
Q3: Can I use this for monthly compounding?
A: The formula assumes annual compounding. For more frequent compounding, the time will be slightly shorter.
Q4: What's the Rule of 69.3?
A: This is the exact continuous compounding version (ln(2) ≈ 0.693). Rule of 72 is adjusted for easier mental math.
Q5: Does this account for inflation?
A: No, this calculates nominal doubling time. For real returns, use the inflation-adjusted interest rate.