Scenario presets
Compounding Inputs
Doubling & Growth Timelines
Calculating compounding...
- Doubling time (Rule of 72)
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- Exact doubling time (logarithmic)
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- Tripling time (Rule of 115)
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- Quadrupling time (Rule of 144)
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- Inflation halving time (50% purchasing power loss)
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- Real (inflation-adjusted) doubling time
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- Required return to double in target years
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Sensitivity Analysis 1: Return % vs. Inflation % on Real Doubling Time
Years required to double purchasing power across nominal investment returns and inflation rates.
| Nominal Return \ Inflation | -1.0% | -0.5% | Base | +0.5% | +1.0% |
|---|
Sensitivity Analysis 2: Target Horizon vs. Growth Multipliers on Required Return %
Annual compound rate of return required to achieve wealth multiplication milestones within set time horizons.
| Horizon (Years) \ Growth Goal | 2x (Double) | 3x (Triple) | 4x (Quadruple) | 5x (5-Fold) | 10x (10-Fold) |
|---|
Geometric Wealth Milestone Progression
| Multiple | Doubling Steps | Timeline | Nominal Portfolio Balance | Real Purchasing Power |
|---|
Formulas and worked example
- Rule of 72 Doubling Time: tdouble ≈ 72 / R
- Exact Doubling Time: texact = ln(2) / ln(1 + r)
- Rule of 115 Tripling Time: ttriple ≈ 115 / R
- Rule of 144 Quadrupling Time: tquad ≈ 144 / R
- Inflation Purchasing Power Halving: thalve ≈ 72 / π
- Real Rate of Return: rreal = (1 + r) / (1 + π) - 1
An investor allocates $10,000 to an equity index earning 10.0% annually with 2.5% expected inflation. Using the Rule of 72, the portfolio doubles in 72 / 10 = 7.20 years (exact: 7.27 years). It triples in 115 / 10 = 11.50 years (exact: 11.53 years) and quadruples in 144 / 10 = 14.40 years. Inflation halves purchasing power every 72 / 2.5 = 28.8 years, meaning real purchasing power doubles every 9.8 years.
Self-check quiz
1. At an 8% annual compound return, an investment will double in approximately:
2. The Rule of 144 calculates:
3. When interest rates are very high (e.g. 25% or 30%), the Rule of 72:
4. If inflation averages 4% per year, the purchasing power of cash will be halved in about:
Frequently asked questions
What is the Rule of 72 and how does it work?
The Rule of 72 is a financial shortcut used to estimate the number of years required to double an investment at a fixed annual rate of return: divide 72 by the annual return percentage.
What are the Rule of 115 and Rule of 144?
The Rule of 115 estimates how many years it takes for an investment to triple (115 divided by annual return). The Rule of 144 estimates how many years it takes for an investment to quadruple (144 divided by annual return), which equals two full doublings.
Why does the Rule of 72 work mathematically?
Under continuous compounding, the natural logarithm of 2 is approximately 0.693 (69.3%). For annual compounding at realistic interest rates between 6% and 10%, 72 provides a more accurate approximation and is easily divisible by 2, 3, 4, 6, 8, 9, 12, and 18.
How does the Rule of 72 apply to inflation and purchasing power?
Dividing 72 by the annual inflation rate estimates how many years it will take for the purchasing power of money to be cut in half. For example, at 3% inflation, money loses 50% of its buying power in approximately 24 years.