Rule of 72 Calculator — How Many Years to Double Your Money
The Rule of 72 is the classic mental-math shortcut for compound growth: divide 72 by your annual return and you get the approximate years it takes to double your money. This calculator does it instantly — and also shows the exact logarithmic result, tripling and quadrupling times, so you can compare how different rates accelerate your savings. Works for investment returns, inflation impact, debt growth, or any compounding rate.
The Rule of 72 says: divide 72 by your annual interest rate to get the years it takes to double your money. Example: at 8% annual rate, 72 ÷ 8 = 9 years to double. Exact formula: n = ln(2) / ln(1 + r).
When to use this calculator
- Compare how quickly a savings account vs. an index fund doubles your money
- Understand the true cost of inflation on purchasing power
- Evaluate investment return promises for plausibility
- Retirement planning: how many doublings before you retire
- Teaching compound interest visually with real numbers
Example: $10,000 at 8% annual compound
- Annual rate: 8%
- Rule of 72: 72 ÷ 8 = 9 years to double
- Exact formula: ln(2) / ln(1.08) = 9.01 years
- $10,000 becomes $20,000 in ~9 years
- To triple ($30,000): ln(3) / ln(1.08) = 14.3 years
- To quadruple ($40,000): 18 years (two doublings)
How it works
2 min readWhat Is the Rule of 72
The Rule of 72 is a quick mental-math shortcut to estimate how long it takes an investment to double under compound interest:
Years to double = 72 ÷ Annual Rate (%)Example: You invest at 6% annual. 72 ÷ 6 = 12 years. Money doubles in 12 years.
Rule of 72 Reference Table
| Annual Rate | Years to Double (Rule of 72) | Exact Years |
|---|---|---|
| 1% | 72.0 years | 69.7 years |
| 2% | 36.0 years | 35.0 years |
| 3% | 24.0 years | 23.4 years |
| 4% | 18.0 years | 17.7 years |
| 4.5% (high-yield savings) | 16.0 years | 15.7 years |
| 5% | 14.4 years | 14.2 years |
| 6% | 12.0 years | 11.9 years |
| 7% | 10.3 years | 10.2 years |
| 8% | 9.0 years | 9.0 years |
| 10% (S&P 500 hist. avg) | 7.2 years | 7.3 years |
| 12% | 6.0 years | 6.1 years |
| 15% | 4.8 years | 5.0 years |
| 20% | 3.6 years | 3.8 years |
The rule is most accurate between 6–10% (error under 1%). Below 3% or above 20%, use the exact formula.
Why 72 (Not 69 or 70)?
The mathematically exact numerator is 69.3 (100 × ln 2). But 72 is preferred because it divides evenly by 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 — the most common investment rates — making mental math much cleaner.
Exact Formula
n = ln(2) / ln(1 + r)Where r is the decimal rate. Examples:
r = 0.08 → 0.693 / 0.0770 = 9.01 yearsr = 0.06 → 0.693 / 0.0583 = 11.90 yearsTripling and Quadrupling
114 ÷ rate. At 8%: ~14.25 years.144 ÷ rate. At 8%: ~18 years (= two doublings).231 ÷ rate. At 8%: ~28.9 years.General formula: n = ln(target multiple) / ln(1 + r).
Practical Applications
Inflation: If inflation runs at 4%, your purchasing power halves in 18 years (72 ÷ 4). $100,000 in a checking account becomes worth $50,000 in real terms by 2044.
Debt: A credit card at 24% APR doubles your debt in 3 years (72 ÷ 24) if you make no payments.
Sanity-checking investment promises: Someone promises 36% annual returns? That doubles money every 2 years — $10,000 becomes $573,000 in 10 years. If the numbers sound implausible, they probably are.
Retirement planning: At 7% (balanced fund, net of fees), money doubles every ~10.3 years. A 30-year-old investing $20,000 today sees roughly three doublings by age 60: $20k → $40k → $80k → $160k, without adding another dollar.
Frequently asked questions
What is the Rule of 72 formula?
Years to double = 72 ÷ annual interest rate (%). Example: at 8% annual return, 72 ÷ 8 = 9 years to double your money. The exact formula is n = ln(2) / ln(1 + r), which gives 9.01 years at 8% — nearly identical to the rule-of-thumb.
How accurate is the Rule of 72?
Very accurate for rates between 6% and 10% — error under 1%. At 2%, the rule gives 36 years vs. the exact 35.0 years (2.8% error). At 20%, the rule gives 3.6 years vs. exact 3.8 years (5% underestimate). For rates below 3% or above 15%, use this calculator's exact result.
How long does it take to double money at 7%?
At 7% annual compound interest, the Rule of 72 gives 72 ÷ 7 ≈ 10.3 years. The exact formula gives 10.24 years. This is close to the historical long-term return of a diversified stock portfolio after fees.
How long to double money at 5%?
At 5% annual compound, 72 ÷ 5 = 14.4 years (rule of thumb). The exact answer is 14.21 years. A 5% return is roughly what high-yield savings accounts and short-term CDs offered in 2024–2026.
What rate do I need to double my money in 10 years?
Reverse the formula: required rate = 72 ÷ target years = 72 ÷ 10 = 7.2% annually. The exact answer is 7.18%. This means you'd need a portfolio averaging about 7–7.2% annually, which historically requires holding a meaningful equity allocation (50–70% stocks).
Can I use Rule of 72 for inflation?
Yes — it works in reverse. If inflation runs at 3%, your purchasing power halves in 72 ÷ 3 = 24 years. At 4% inflation, your cash halves in 18 years. Use the real rate (nominal return minus inflation) to find your real doubling time.
Does the Rule of 72 work for monthly compounding?
The classic rule assumes annual compounding. For monthly compounding, use the effective annual rate (EAR): EAR = (1 + nominal/12)^12 − 1. Then apply Rule of 72 to the EAR. Example: 6% nominal monthly-compounded → EAR = 6.168% → doubling time = 72 ÷ 6.168 ≈ 11.67 years, not 12.
What is the Rule of 114 and Rule of 144?
These are extensions of the same idea. Rule of 114 estimates years to triple your money (114 ÷ rate). Rule of 144 estimates years to quadruple (144 ÷ rate), which equals two doublings. At 8%: triple in 114 ÷ 8 = 14.25 years; quadruple in 144 ÷ 8 = 18 years.
Why is compound interest called the eighth wonder of the world?
The famous quote (often attributed to Einstein, though unverified) refers to the exponential nature of compound growth. At 7% annual return, $1,000 becomes $7,612 in 30 years — a 7.6× increase. The critical insight is that each year's return earns returns on prior returns, accelerating growth over time. The Rule of 72 makes this tangible: at 10%, money doubles every 7.2 years — three doublings in just over 21 years (8×).
How does the Rule of 72 apply to debt?
The rule cuts both ways. A credit card at 24% APR doubles your balance in 3 years (72 ÷ 24) if you make no payments. A student loan at 7% doubles in ~10 years. This reframing is powerful: paying off a 20% credit card is equivalent to earning a guaranteed 20% investment return — which doubles your effective net worth protection every 3.6 years.
What if my annual return varies each year?
Use the CAGR (Compound Annual Growth Rate), not the arithmetic average. CAGR = (ending value / starting value)^(1/years) − 1. Arithmetic averages overstate real growth due to volatility drag. Example: returns of +20%, −10%, +15% average 8.3% arithmetically, but the CAGR is roughly 7.8%. Apply Rule of 72 to the CAGR for realistic doubling estimates.
Is the Rule of 72 useful for non-financial metrics?
Yes. Any metric growing at a compound rate works: a SaaS company growing 36% annually doubles revenue every 2 years; a city growing 3% annually doubles population in 24 years; website traffic growing 6% monthly doubles in 12 months. The rule translates abstract growth rates into intuitive timelines for any audience.