Rule of 72: The Fastest Way to Calculate How Long to Double Your Money

The Rule of 72 is one of the most useful mental math shortcuts in personal finance. No calculator required — just divide 72 by your annual interest rate and you instantly know roughly how many years it takes to double your money.

For precise projections, use our Compound Interest Calculator. But the Rule of 72 is perfect for back-of-the-envelope comparisons on the fly.

How the Rule of 72 Works

Years to double = 72 ÷ Annual Interest Rate

That is it. The simplicity is the point. Need to flip it around? If you know how many years you have:

Required Rate = 72 ÷ Years to Double

So if you need your money to double in 8 years, you need roughly a 9% annual return (72 ÷ 8 = 9).

Examples at Common Interest Rates

Annual Rate	Years to Double	What This Looks Like
2%	36 years	High-yield savings at rock-bottom rates
3%	24 years	Typical I-Bond or Treasury note yield
4%	18 years	Conservative bond portfolio
6%	12 years	Balanced stock/bond portfolio
8%	9 years	Aggressive stock index fund
10%	7.2 years	Historical S&P 500 average
12%	6 years	Small-cap stock funds, emerging markets
24%	3 years	Credit card debt (working against you)

Real Dollar Examples

Starting with $20,000:

• At 4%: doubles to $40,000 in 18 years → $80,000 in 36 years
• At 6%: doubles to $40,000 in 12 years → $80,000 in 24 years
• At 8%: doubles to $40,000 in 9 years → $80,000 in 18 years
• At 10%: doubles to $40,000 in 7.2 years → $80,000 in 14.4 years

The difference between 4% and 8% is not just 2× the return — it cuts the doubling time in half, which means your money doubles twice as many times over the same 36-year horizon.

Why the Rule of 72 Works (The Math Behind It)

The exact formula to solve for doubling time comes from the compound interest equation:

2P = P(1 + r)^t

Solving for t:

t = ln(2) / ln(1 + r)

For small values of r, ln(1 + r) ≈ r, and ln(2) ≈ 0.693. So:

t ≈ 0.693 / r

Multiply numerator and denominator by 100 to work with percentages:

t ≈ 69.3 / rate%

The number 72 is chosen instead of 69.3 because it is easier to divide mentally (more whole-number factors) and slightly overestimates doubling time, giving a conservative estimate.

Accuracy: When Is the Rule of 72 Most Precise?

The Rule of 72 is most accurate between 6% and 10%. At very low or very high rates, the approximation drifts:

Rate	Rule of 72 Estimate	Actual Years	Error
1%	72 years	69.7 years	+3.3%
4%	18 years	17.7 years	+1.7%
6%	12 years	11.9 years	+0.8%
8%	9 years	9.0 years	+0.0%
10%	7.2 years	7.3 years	-1.4%
20%	3.6 years	3.8 years	-5.3%
50%	1.44 years	1.71 years	-15.8%

At typical investment rates (4%–12%), the error is under 2% — close enough for planning purposes.

The Rule of 69: More Precise for Continuous Compounding

When interest compounds continuously (as in many financial derivatives and theoretical models), use 69.3 instead of 72:

Years to double = 69.3 / rate%

Some financial professionals use 69 for easy mental division, splitting the difference between accuracy and simplicity.

For discrete compounding (annual, monthly, daily), 72 remains the most practical choice.

Applying the Rule of 72 to Debt

The rule works in reverse for debt — and the results are sobering:

• Credit card at 20% APR: balance doubles in 3.6 years with no payments
• Personal loan at 12%: doubles in 6 years
• Student loan at 6%: doubles in 12 years
• Mortgage at 7%: doubles in ~10 years

If you carry a $10,000 credit card balance at 20% and make only minimum payments, compound interest alone could push you past $20,000 before you make meaningful progress on the principal.

Check your take-home pay and find room to accelerate debt payments with our Paycheck Calculator.

Rule of 72 for Inflation

At 3% inflation, purchasing power halves every 24 years.

That means $100,000 of purchasing power today becomes effectively $50,000 in 24 years if your money earns less than inflation. Keeping a large cash emergency fund in a zero-interest account is not “safe” — it is a guaranteed slow loss.

Use our Compound Interest Calculator to model inflation-adjusted returns and see your real purchasing power over time.

Quick Reference: Rule of 72 in One Table

Goal	Formula	Example
How long to double?	72 ÷ rate	72 ÷ 6% = 12 years
What rate do I need?	72 ÷ years	72 ÷ 10 years = 7.2%
How long for debt to double?	72 ÷ APR	72 ÷ 18% = 4 years
When does inflation halve my cash?	72 ÷ inflation	72 ÷ 3% = 24 years

Bottom Line

The Rule of 72 is the fastest way to gut-check any investment, savings, or debt scenario. It does not replace a proper financial model, but it gives you instant intuition for what rates and time horizons actually mean in dollar terms. Commit it to memory, and you will have a financial superpower in every meeting, conversation, and planning session.