Rule of 72 Calculator

The Rule of 72 is a simple mental math shortcut for estimating how long it takes an investment to double in value at a fixed annual return rate. The formula: Years to Double = 72 ÷ Annual Interest Rate (%). Examples: at 6% return: 72 ÷ 6 = 12 years to double. At 8% return: 72 ÷ 8 = 9 years to double. At 10% return: 72 ÷ 10 = 7.2 years to double. Reverse: to find the rate needed to double in a given time: Rate = 72 ÷ Years. "I need to double my money in 8 years" → 72 ÷ 8 = 9% annual return needed. Why 72? The exact formula for doubling time is: T = ln(2) / ln(1 + r) ≈ 0.693 / r (when r is small). 0.693 / r is approximately 70/r or 72/r for practical purposes. The number 72 was chosen because: it's close to 69.3 (the precise value). It has many factors (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72), making division by common interest rates (like 3%, 4%, 6%, 8%, 9%, 12%) come out to clean whole numbers. Accuracy: the Rule of 72 is most accurate for annual rates between 6% and 10%. It slightly overestimates doubling time at low rates and slightly underestimates at high rates. For most financial planning purposes, this level of precision is more than adequate. Applications beyond investing: population growth. Inflation (doubling of prices). Economic growth (GDP doubling time). Debt growth (how quickly debt doubles if unpaid at a given interest rate).

The Rule of 72 is a mathematical approximation — it's accurate enough for practical financial planning but not perfectly precise. Accuracy analysis: at 1% interest rate: Rule of 72 gives 72 years; exact answer is 69.66 years (3.4% error). At 6% interest rate: Rule of 72 gives 12 years; exact answer is 11.90 years (0.8% error). At 8% interest rate: Rule of 72 gives 9 years; exact answer is 9.01 years (0.1% error — almost perfect). At 10% interest rate: Rule of 72 gives 7.2 years; exact answer is 7.27 years (1% error). At 20% interest rate: Rule of 72 gives 3.6 years; exact answer is 3.80 years (5.3% error). At 50% interest rate: Rule of 72 gives 1.44 years; exact answer is 1.71 years (16% error). The sweet spot: the Rule of 72 is most accurate at 8% — where it's nearly exact. It slightly overestimates at low rates and underestimates at high rates. For rates above 20–30%, consider using the Rule of 69.3, which uses ln(2) ≈ 0.693 as the numerator (more precise for any rate, but harder mental math). For most people's financial decisions — evaluating investment returns between 4% and 15% — the Rule of 72 provides accuracy within 1–2 years, which is sufficient for planning purposes given that actual returns are uncertain anyway.

The Rule of 72 applies to inflation just as well as to investment returns — it tells you how many years until prices double (and equivalently, how long until your money's purchasing power is cut in half). Inflation doubling time examples: 2% inflation (near Fed target): 72 ÷ 2 = 36 years for prices to double. $100 of groceries in 2024 → $200 in 2060. 3% inflation (historical US average): 72 ÷ 3 = 24 years for prices to double. 5% inflation: 72 ÷ 5 = 14.4 years. 7% inflation (recent US peak, 2022): 72 ÷ 7 ≈ 10 years. What this means for your money: at 3% average inflation, money kept in a mattress (0% return) loses half its purchasing power every 24 years. This is why financial planners emphasize that cash savings in low-interest accounts (earning below the inflation rate) lose value in real terms over time. Comparing investment returns to inflation: if your investments return 7% and inflation runs at 3%, your real return is approximately 7% − 3% = 4%. At 4% real return: 72 ÷ 4 = 18 years to double real wealth (purchasing power). If investments return only 2% during 3% inflation: real return = −1%. Your money is slowly losing purchasing power. Salary growth and inflation: the Rule of 72 also applies to salary negotiations. If inflation is running at 4% and you receive a 2% raise, your real wage dropped. At 2% inflation, you need a raise every 36 years just to stay even in real terms. At 4% inflation, you need a 4%+ raise each year to maintain purchasing power.

Yes — the Rule of 72 works for debt just as well as for investments. It tells you how long until your debt doubles if left unpaid (with no payments) at a given interest rate. Debt doubling examples: credit card at 24% APR: 72 ÷ 24 = 3 years to double. $5,000 credit card debt → $10,000 in 3 years without payment. Credit card at 18% APR: 72 ÷ 18 = 4 years. Student loan at 6.8%: 72 ÷ 6.8 ≈ 10.6 years. Mortgage at 7%: 72 ÷ 7 ≈ 10.3 years. Payday loan at 400% APR: 72 ÷ 400 = 0.18 years ≈ 65 days! Why this matters: the visualization of debt doubling time is one of the most powerful tools for motivating debt repayment. A credit card at 20% APR doubles debt in 3.6 years. Someone who carries $5,000 in credit card debt for 7–8 years (making only minimum payments) effectively watches it grow to nearly $20,000 before seeing meaningful paydown. Rule of 72 and debt payoff motivation: make the numbers visceral: "at 22% APR, every $1,000 becomes $2,000 in 3.3 years." This reframing (debt as a growing obligation) can motivate prioritizing high-interest debt payoff over investing — especially when debt interest rates exceed expected investment returns. Rule of thumb: pay off any debt whose interest rate exceeds your expected investment return. At 20%+ credit card APR, there's no investment that reliably beats that guaranteed "return" you get from paying it off.