The Rule of 72: A Simple Trick for Investment Math

The rule

Years to double = 72 ÷ annual interest rate (%)

At 4%  → doubles in 18 years
At 6%  → doubles in 12 years
At 8%  → doubles in  9 years
At 10% → doubles in  7.2 years
At 12% → doubles in  6 years

The rule works because 72 is close to 100 × ln(2) ≈ 69.3, and the error from rounding is small in the typical return range of 2-15%. The exact formula for doubling time is t = ln(2) / ln(1+r), where r is the decimal rate. The Rule of 72 is a practical approximation that's accurate within 1-2% for most real-world interest rates.

Using it in reverse: finding required return

The rule works in reverse too: if you know when you need your money to double, divide 72 by the number of years to find the required annual return:

Need to double in 6 years?  → need 72/6 = 12% return
Need to double in 10 years? → need 72/10 = 7.2% return
Need to double in 20 years? → need 72/20 = 3.6% return

This is useful for setting realistic return expectations. If your retirement timeline requires your portfolio to double every 6 years, you need a 12% annual return — achievable but aggressive. If you have 20 years and need the money to double once, 3.6% puts you in reach of a diversified bond portfolio or a conservative stock allocation.

Why it reveals the cost of waiting

Consider what happens with $10,000 invested at 8%, starting at different ages:

At 8%, money doubles every 9 years.

Invest $10,000 at age 25:
  Age 34: $20,000
  Age 43: $40,000
  Age 52: $80,000
  Age 61: $160,000 (retirement)

Invest $10,000 at age 34 (9 years later):
  Age 43: $20,000
  Age 52: $40,000
  Age 61: $80,000  ← half the result

Waiting 9 years cuts the final balance in half.

Each doubling period you miss costs exactly half the final outcome. This is why financial advisors relentlessly emphasize starting as early as possible — not because the advice is clever, but because the math is unforgiving.

Applying it to inflation: the cost of cash

The Rule of 72 also shows how inflation erodes purchasing power. At 3% inflation, prices double every 24 years. At 7% inflation (as seen during peak 2022), prices double every 10 years:

At 3% inflation: prices double every 24 years
  What costs $100 today costs $200 in 2050

At 7% inflation: prices double every ~10 years
  What costs $100 today costs $200 in 2036

Cash sitting in a 0% savings account loses real value at the rate of inflation. At 3%, you lose half your purchasing power in 24 years. This is the mathematical case for investing: you must earn a return at least equal to inflation just to stay in place.

The Rule of 72 and fees

The rule applies to anything that compounds — including costs. A 1% annual investment management fee halves your effective compounding. At a net 8% return, your money doubles every 9 years. With a 1% fee, your net return is 7%, and your money doubles every 10.3 years — not dramatically different per cycle, but over a 30-year career that extra year per doubling cycle means one fewer doubling: roughly 15% less final wealth. Over a 40-year career, the impact of a 1% fee versus a 0.05% index fund fee can exceed $150,000 on a typical retirement portfolio. This is the mathematical argument for low-cost index funds.