Money doubles faster as the assumed annual rate rises, but the exact timeline depends on compounding. This guide uses annual compounding as the main benchmark, with a constant hypothetical rate and no taxes, fees, contributions, withdrawals, inflation, or rate changes.
The Rule of 72 is a mental shortcut: divide 72 by the assumed annual rate. It is useful for quick estimates, not forecasts or guarantees. If you start from an APY or effective annual return, do not divide that rate across compounding periods again.
Quick Answer:
With annual compounding, money doubles in about 11.90 years at 6%, 9.01 years at 8%, and 6.12 years at 12%. The Rule of 72 rounds those to 12, 9, and 6 years. Other compounding assumptions can produce different exact results, so use the Rule of 72 Calculator for a custom calculation based on your inputs.
How we approached this analysis
The main table uses annual compounding and the formula
t = ln(2) ÷ ln(1 + r), whereris the annual rate as a decimal. Examples assume a constant rate before taxes, fees, cash flows, inflation, and volatility. They are educational scenarios, not expected or guaranteed returns.
TL;DR
- Higher assumed rates shorten modeled doubling time.
- Exact annual-compounding results for 1% to 20% are shown below.
- Higher expected market returns usually involve higher risk.
- Use exact calculations when compounding, cash flows, or decisions matter.
How Does the Rule of 72 Estimate Doubling Time?
The shortcut is:
Doubling Time ≈ 72 ÷ Assumed Annual Rate (%)
Those figures are easy to calculate mentally. The exact annual-compounding formula uses logarithms, so the shortcut and exact result are close but not identical.
Doubling Time by Interest Rate
The exact column below assumes annual compounding. It uses t = ln(2) ÷ ln(1 + r), where r is the annual rate in decimal form.
| Assumed annual rate | Rule of 72 estimate | Exact annual-compounding time |
|---|---|---|
| 1% | 72.00 years | 69.66 years |
| 2% | 36.00 years | 35.00 years |
| 3% | 24.00 years | 23.45 years |
| 4% | 18.00 years | 17.67 years |
| 5% | 14.40 years | 14.21 years |
| 6% | 12.00 years | 11.90 years |
| 7% | 10.29 years | 10.24 years |
| 8% | 9.00 years | 9.01 years |
| 9% | 8.00 years | 8.04 years |
| 10% | 7.20 years | 7.27 years |
| 11% | 6.55 years | 6.64 years |
| 12% | 6.00 years | 6.12 years |
| 13% | 5.54 years | 5.67 years |
| 14% | 5.14 years | 5.29 years |
| 15% | 4.80 years | 4.96 years |
| 16% | 4.50 years | 4.67 years |
| 17% | 4.24 years | 4.41 years |
| 18% | 4.00 years | 4.19 years |
| 19% | 3.79 years | 3.98 years |
| 20% | 3.60 years | 3.80 years |
Illustrative - actual results vary.
The Rule of 72 is especially close around 6% to 10% with annual compounding. For details on when accuracy changes and how monthly, daily, or continuous compounding affects the exact result, see When Does the Rule of 72 Stop Being Accurate?.
Why Small Rate Differences Matter
In the math model, a higher assumed rate shortens doubling time. If those assumed rates were actually earned consistently, they would produce substantially different modeled balances over long periods. In real markets, higher expected returns often come with higher risk, fees and taxes can reduce net return, and an investment should not be chosen only because its theoretical doubling time is shorter.
Illustrative Examples
Savings Accounts
Consider hypothetical savings rates of 3%, 4%, and 5%.
The Rule of 72 gives about 24, 18, and 14.4 years. Actual bank rates change, and quoted APYs already reflect compounding.
Stock Market Investing
Consider hypothetical long-term return assumptions of 7%, 8%, and 10%.
The Rule of 72 gives about 10.29, 9, and 7.2 years. Market returns vary, losses are possible, and actual results do not follow a fixed compounding path. A higher assumed return does not imply a better or appropriate investment.
Inflation
The Rule of 72 can roughly illustrate how long prices might take to double at a constant inflation rate: 36 years at 2%, 24 years at 3%, and 12 years at 6%. Actual inflation changes over time. At low annual rates, the Rule of 70 may be closer; for that comparison, read Rule of 70 vs. Rule of 72 vs. Rule of 69.3.
Scenario Analysis
Imagine three scenarios that each start with $50,000 and use hypothetical assumed annual rates of 4%, 7%, and 10%. The Rule of 72 estimates doubling in 18.00, 10.29, and 7.20 years. Under these constant-rate assumptions, the modeled balances would double at different speeds. The starting amount does not affect proportional doubling time when the rate and compounding method are the same and there are no contributions or withdrawals. Once cash flows are added, doubling the account balance becomes a different calculation.
When the Rule of 72 Isn't Enough
Use exact compound-interest calculations when you need to model contributions, withdrawals, taxes, fees, a specific time horizon, different compounding methods, or a nominal annual rate versus an APY.
An exact calculation provides a more precise result for the stated assumptions, but it does not make uncertain market returns reliable.
Run Your Own Scenario
Rather than relying only on shortcut estimates, test your assumptions directly.
The Rule of 72 Calculator lets you compare the shortcut with exact annual, periodic, or continuous compounding.
You may also find these calculators helpful:
For the broader set of compounding guides and calculators, visit the Compound Interest and Growth topic page.
Key Takeaways
- Higher assumed rates shorten modeled doubling time, but they are not free or guaranteed.
- The main table uses annual compounding for every rate from 1% to 20%.
- The Rule of 72 is a shortcut; exact results depend on the compounding assumption.
- Savings, inflation, and market examples should be treated as hypothetical scenarios.
- For planning, model the actual rate, timing, cash flows, fees, and taxes.
Frequently Asked Questions
How long does money take to double at 8%?
Using the Rule of 72, about 9.00 years. With annual compounding, the exact result is about 9.01 years.
Does money double exactly when the Rule of 72 says?
Not necessarily. The Rule of 72 is an approximation; exact results depend on the rate and compounding method.
Does inflation follow the Rule of 72?
Only as a rough illustration under a constant inflation rate. Actual inflation changes, and the Rule of 70 can be closer at low rates.
Does the starting amount affect doubling time?
Not if the rate, compounding method, and cash-flow assumptions are identical. Contributions, withdrawals, fees, and taxes can change the actual path.
Should I use the Rule of 72 or an investment calculator?
Use the Rule of 72 for quick estimates and a calculator when comparing scenarios or making financial decisions.
This article is for informational purposes only and does not constitute financial advice. Please consult a qualified financial advisor before making financial decisions.