Calculadora da Regra dos 72

Rule of 72 Calculator

The Rule of 72 is one of the most practical shortcuts in personal finance. Divide 72 by any annual interest rate and you get the number of years it takes to double your money at that rate — no spreadsheet required. This calculator does the arithmetic instantly, lets you compare multiple rates side by side, and works in reverse so you can find the return rate needed to hit a doubling target within a set number of years. Whether you are evaluating a savings account, a stock portfolio, or a high-interest debt, the same formula applies.

How the Rule of 72 Is Calculated

The Rule of 72 is a fast approximation of the exact compound-interest doubling formula.

Doubling Time (years) = 72 / Annual Interest Rate (%)

The mathematically exact formula is t = ln(2) / ln(1 + r), where r is the decimal rate. Because ln(2) is approximately 0.693, and 72 is close to 69.3 after adjusting for discrete annual compounding, 72 works as a practical divisor. Its advantage over the more precise 69.3 is divisibility — 72 divides evenly by 2, 3, 4, 6, 8, 9, and 12, making mental math straightforward. The rule is most accurate between 6% and 10%, where the error is less than 0.1 years.

To use the rule in reverse — finding the required rate — simply divide 72 by the number of years you want: Required Rate = 72 / Target Years.

Worked Examples

Example 1 — Stock market index fund at 10% An investor puts $20,000 into a broad index fund averaging 10% annually. Rule of 72: 72 / 10 = 7.2 years to double. That $20,000 becomes $40,000 by year 7, $80,000 by year 14, and $160,000 by year 22 through three successive doublings — all without adding a single dollar.

Example 2 — High-yield savings account at 4.5% A saver parks $8,000 in a high-yield account at 4.5% APY. Rule of 72: 72 / 4.5 = 16 years to double to $16,000. Compared to a traditional 0.5% savings account (72 / 0.5 = 144 years), the high-yield account completes nine times as many doublings over a lifetime.

Example 3 — Credit card debt at 22% A cardholder carries a $5,000 balance at 22% APR and makes no payments. Rule of 72: 72 / 22 = 3.27 years until the balance grows to $10,000. By year 6.5 it reaches $20,000. This example illustrates why minimum payments on high-rate cards barely cover interest accumulation.

Doubling Time at Various Rates

When to Use the Rule of 72

• Comparing two investment options quickly without a calculator — “Is 7% meaningfully better than 5%?” (10.3-year vs. 14.4-year doubling tells you yes)
• Estimating how long a retirement portfolio needs to keep growing before withdrawals begin
• Checking whether a savings rate keeps pace with inflation — subtract the inflation rate from your nominal return first
• Evaluating debt payoff urgency — a 20% store credit card doubles your balance in 3.6 years if unpaid
• Teaching compound interest concepts in a way that produces concrete, memorable numbers

Common Mistakes

1. Applying the rule to simple interest — the Rule of 72 assumes compound interest. A simple-interest instrument at 6% does not double in 12 years; it takes 16.7 years (100 / 6).
2. Ignoring taxes and fees — if your investment returns 8% but you pay a 1% fund expense ratio and are in a 22% tax bracket on gains, your effective rate is closer to 5.2%, giving a doubling time of 13.8 years rather than 9.
3. Confusing nominal and real returns — a 7% return during 3% inflation has a real purchasing-power doubling time of 72 / (7 - 3) = 18 years, not 10.3 years.
4. Using it for non-annual rates — if your rate is monthly (e.g., 1.5%/month on a payday loan), convert to an annual rate first: 1.015^12 - 1 = 19.6% annually, then apply the rule.

Context and Applications

The Rule of 72 was documented as early as 1494 by the Italian mathematician Luca Pacioli in his work Summa de Arithmetica. Warren Buffett has referenced doubling-time thinking extensively to illustrate why starting early matters so much in compounding. The rule applies equally well to any exponential growth or decay process: population growth, inflation, debt accumulation, radioactive decay, and bacterial doubling times all follow the same math. In finance, it gained widespread use because investment advisors needed a quick way to show clients the practical difference between a 6% and an 8% return over a 30-year horizon — the 8% portfolio produces roughly twice the wealth.

Tips

1. Think in chains of doublings rather than absolute numbers — $10,000 at 8% passes $80,000 after three doublings (27 years) without any additional contributions
2. Subtract your fund’s expense ratio from the stated return before applying the rule — a 7% fund with a 0.8% expense ratio doubles in 9.9 years, not 9
3. Use the reverse formula (72 / years = required rate) to set realistic expectations — wanting to double money in 5 years requires a 14.4% annual return
4. Apply the rule to your debt first — a 19% credit card balance doubles in 3.8 years, making it the highest-priority target before any investing
5. For rates below 4% or above 20%, the standard formula slightly overstates or understates doubling time; use 69.3 as the divisor for better accuracy at those extremes
6. Compare the doubling time of your investments against your career timeline — someone with 30 years until retirement at 8% gets just over three full doublings, while someone with 40 years gets more than four, roughly doubling the final result