Rule of 72 Explained — How Long to Double Your Money?
Published July 1, 2026 · 7 min read
Divide 72 by your annual interest rate and you get the approximate number of years it takes to double your money. That is the entire Rule of 72.
At 7%, your money doubles in 10.3 years. At 10%, it doubles in 7.2 years. At 3%, it takes 24 years. The rule works in your head — no spreadsheet, no calculator, no finance degree required.
Albert Einstein is often (apocryphally) credited with calling compound interest the eighth wonder of the world. Whether or not he said it, the Rule of 72 is the fastest way to see why it deserves that title. A 25-year-old who invests $10,000 in an index fund earning 7% per year will see that money double three times by age 65 — from $10,000 to $80,000, without adding a single extra dollar.
This guide explains how the rule works, walks through a full examples table, compares the rule to exact compound interest calculations, and shows how to use it for 401(k) and Roth IRA planning. To run the exact numbers for your situation, use our free Rule of 72 calculator.
What Is the Rule of 72?
The Rule of 72 is a mathematical approximation rooted in the formula for compound interest doubling time. The exact formula is:
Where t is years to double and r is the decimal interest rate. For r = 0.07: t = 0.693 / 0.0677 = 10.24 years.
The Rule of 72 approximates ln(2) ≈ 0.693 as 72/100 and simplifies the logarithm with a linear approximation, giving:
The number 72 is used instead of 69.3 (the exact value) because 72 has more divisors — it is evenly divisible by 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 — making mental arithmetic cleaner. For 6%: 72/6 = exactly 12. For 8%: 72/8 = exactly 9.
The rule is accurate to within 1 year for interest rates between 3% and 15% — which covers virtually every savings account, bond portfolio, index fund, and retirement account scenario an individual investor faces.
Rule of 72 Examples: $10,000 at Different Rates
How long $10,000 takes to double, triple, and what it grows to after 10 and 20 years at various annual return rates.
| Annual Rate | Doubles In | Triples In | After 10 yrs | After 20 yrs |
|---|---|---|---|---|
| 3% | 24.0 yrs | 38.0 yrs | $13,439 | $18,061 |
| 5% | 14.4 yrs | 22.8 yrs | $16,289 | $26,533 |
| 7% | 10.3 yrs | 16.3 yrs | $19,672 | $38,697 |
| 10% | 7.2 yrs | 11.4 yrs | $25,937 | $67,275 |
| 12% | 6.0 yrs | 9.5 yrs | $31,058 | $96,463 |
Starting principal: $10,000. No additional contributions. Compounded annually.
The table makes the power of rate selection viscerally clear. Earning 10% instead of 5% does not just double your return — it turns $10,000 into $67,275 vs $26,533 over 20 years. Rate selection is the single biggest lever an individual investor has after time itself.
Rule of 72 vs Actual Compound Interest: How Accurate Is It?
The Rule of 72 is an approximation, not an exact formula. The table below compares the rule's estimate to the exact doubling time calculated using ln(2)/ln(1+r):
| Rate | Rule of 72 | Exact | Difference |
|---|---|---|---|
| 2% | 36.0 yrs | 35.0 yrs | 1.0 yr |
| 5% | 14.4 yrs | 14.2 yrs | 0.2 yrs |
| 7% | 10.3 yrs | 10.2 yrs | 0.1 yrs |
| 10% | 7.2 yrs | 7.3 yrs | 0.1 yrs |
| 15% | 4.8 yrs | 4.96 yrs | 0.16 yrs |
| 25% | 2.9 yrs | 3.11 yrs | 0.21 yrs |
The rule is most accurate between 5% and 15% — the range covering virtually all investment decisions. It loses precision at the extremes (very low rates like savings accounts during low-rate environments, or very high rates like early-stage startup investments), but even there the error rarely exceeds half a year.
For exact compound interest calculations — including monthly contributions, different compounding frequencies, and year-by-year breakdowns — use the full compound interest calculator.
Using the Rule of 72 for 401(k) and Roth IRA Planning
The Rule of 72 is particularly powerful for retirement planning because most retirement accounts compound over decades. Here is how to use it for common scenarios:
401(k) at 7% (Index Fund)
A 30-year-old with $50,000 in a 401(k) earning 7% will see that balance double to $100,000 by age 40.3, then to $200,000 by age 50.6, then to $400,000 by age 60.9. That is three doublings — 8× growth — before reaching 65, before adding any new contributions.
Roth IRA at 7% (Tax-Free)
A 22-year-old maxing a Roth IRA at $7,000/year has roughly $70,000 saved by age 32. At 7%, that $70,000 doubles every 10.3 years: $140,000 by 42, $280,000 by 52, $560,000 by 62. This only counts the first decade of contributions — the compounding on subsequent deposits pushes the total much higher.
The Cost of Starting Late
Starting at 25 vs 35 means losing one full doubling cycle. At 7%, money doubles in 10.3 years. Starting $10,000 at 25 instead of 35 means having $80,000 vs $40,000 at 65 — from the same initial investment. The Rule of 72 makes this cost tangible and immediate.
The key insight: every year you delay investing is not just one year of lost returns — it is the loss of an entire future doubling for every dollar not invested. The Rule of 72 is the fastest way to quantify this cost for any real conversation about retirement savings.
Calculate Your Exact Doubling Time
Enter any interest rate and starting balance to see doubling time, tripling time, and a full comparison table.