Rule of 72 Calculator
Use the Rule of 72 to quickly estimate how long it takes to double your money at a given interest rate — or find the rate needed to double in a target number of years. Includes a reference table of common rates.
Rule of 72 Results
The Rule of 72 Explained
Divide 72 by the annual interest rate to estimate how many years it takes to double your money. It's a useful mental math shortcut that works well for rates between 5% and 15%.
Formula: Years ≈ 72 ÷ Rate
Example: At 8% per year, 72 ÷ 8 = 9 years to double.
The Precise Formula
For exact doubling time: Years = ln(2) ÷ ln(1 + r) = 0.6931 ÷ ln(1 + r). The Rule of 72 is accurate within 1% for rates in the typical investment range.
Application to Debt
At 24% APR (some credit cards), your balance doubles in just 3 years. At 18%, it doubles in 4 years. Understanding this makes it clear why high-interest debt should be eliminated as quickly as possible.
Rule of 72 for Inflation
You can apply the same formula to inflation. At 3% inflation, prices double in about 24 years. At 7% (2022 peak), prices double in roughly 10 years. This makes it easy to visualize how inflation erodes the real value of fixed incomes, savings accounts, and any asset that doesn't grow to keep pace.
Worked Examples Across Common Rates
Credit card debt at 22% APR: 72 ÷ 22 = 3.3 years to double. A $5,000 credit card balance left unpaid becomes $10,000 in just over 3 years. Mortgage at 7%: 72 ÷ 7 = ~10.3 years — if you have a $300,000 outstanding principal and somehow let it compound without payments, it would reach $600,000 in a decade. S&P 500 at 10%: 72 ÷ 10 = 7.2 years to double. $25,000 invested today becomes $50,000 in 7.2 years, $100,000 in 14.4 years, and $200,000 in 21.6 years — all at a 10% annual return without adding a cent.
Rule of 72 Quick Reference Table
| Annual Rate | Rule of 72 (Years) | Exact Years | Common Use |
|---|---|---|---|
| 2% | 36.0 | 35.0 | Low-yield savings |
| 4% | 18.0 | 17.7 | High-yield savings |
| 6% | 12.0 | 11.9 | Conservative portfolio |
| 8% | 9.0 | 9.0 | Diversified portfolio |
| 10% | 7.2 | 7.3 | S&P 500 historical avg |
| 18% | 4.0 | 4.2 | Credit card APR |
| 24% | 3.0 | 3.2 | High-rate credit card |
Frequently Asked Questions
Why 72 and not another number?
72 is a mathematical approximation derived from the natural logarithm of 2 (≈ 0.693). It works because ln(2) ÷ ln(1 + r) ≈ 0.693 ÷ r for small values of r, and 72 is close enough to 69.3 while being far more divisible — you can divide it evenly by 1, 2, 3, 4, 6, 8, 9, 12, and 18. For very low rates, the Rule of 69.3 is more accurate; for higher rates, some analysts use 74.
How accurate is the Rule of 72?
At rates between 5% and 15%, the Rule of 72 is accurate within about 1% of the exact answer. At lower rates (1–2%) it slightly overestimates doubling time; at very high rates (25%+) it underestimates. For most personal finance and investing purposes, the approximation is more than close enough for quick mental math.
Can the Rule of 72 be used for halving time?
Yes — the Rule of 72 also tells you how long before something halves in value. At 6% inflation, the purchasing power of a fixed sum halves in about 12 years. This is useful for understanding how quickly the real value of a pension, annuity, or fixed income stream declines over time without cost-of-living adjustments.
Yes — rearrange the formula: Rate = 72 ÷ Years. To double money in 6 years, you need a 72 ÷ 6 = 12% annual return. To double in 10 years, you need 7.2%. To double in 20 years, 3.6%. This reverse application helps set realistic expectations — if a salesperson promises your money will double in 3 years, the Rule of 72 tells you that requires a 24% annual return, which should prompt serious skepticism.