Doubling Time & Rule of 72 Calculator - Compound Interest Growth & Interest Rate
Doubling Time Calculator
Instructions: Enter any 1 parameters and leave 1 parameter empty to calculate the missing value.
Calculation Results
Doubling time
Mathematical Formula
Exact Formula: t = ln(2) / ln(1 + r)
Where:
- t = doubling time (in periods)
- r = interest rate per period (as decimal)
- ln = natural logarithm
Reverse Formula (Calculate Interest Rate): r = exp(ln(2) / t) - 1
Rule of 72 Approximation: t ≈ 72 / (interest rate as percentage)
How to Use This Calculator
- Calculate Doubling Time: Enter an interest rate (e.g., 6.5%) and click Calculate to find how many periods it takes to double your investment.
- Calculate Required Interest Rate: Enter the number of periods (e.g., 10) and click Calculate to find what interest rate you need to double your money in that timeframe.
- The calculator automatically disables the unused input field to prevent confusion.
- Results include both exact calculations and Rule of 72 approximations for comparison.
Investment Examples - Common Doubling Time Scenarios
- 6% Annual Return: Money doubles in approximately 11.9 years
- 8% Annual Return: Money doubles in approximately 9.0 years
- 10% Annual Return: Money doubles in approximately 7.3 years
- 12% Annual Return: Money doubles in approximately 6.1 years
How Long Will It Take for $10,000 to Double at 7 Compound Interest?
It will take approximately 10.24 years for $10,000 to double at 7% compound interest annually. This matches closely with the Rule of 72 estimate of about 10.29 years.
References and Further Reading
- U.S. Securities and Exchange Commission - Investment Basics
- Federal Reserve - Compound Interest Information
- U.S. Department of Treasury - Financial Markets
- Bureau of Labor Statistics - Consumer Price Index (for inflation considerations)
Frequently Asked Questions (FAQ)
What Is the Rule of 72?
The Rule of 72 is a quick rule to estimate doubling time by dividing 72 by the annual interest rate.
What Is the Exact Formula for Doubling Time?
The exact formula is t = ln(2) / ln(1 + r), where r is the interest rate in decimal form.
Is the Rule of 72 Accurate?
It’s an approximation that works best for interest rates between 6% and 10%. Use the exact formula for precision.
Write Reply