The Napkin Math That Changed My Investing
I was 28, sitting in a Starbucks with a friend who worked in finance. He asked how long I thought it would take my savings to double at 7% annual return. I pulled out my phone to calculate.
He laughed. "Just divide 72 by 7. About 10 years."
I stared at him. "That is... that is it?"
He nodded. "Rule of 72. Works for any interest rate. 72 divided by the rate gives you the doubling time. Been using it since college."
That 30-second trick has saved me hundreds of calculator sessions. More importantly, it made compound interest intuitive in a way spreadsheets never did.
Why 72? (It Is Not Random)
The Rule of 72 is a shortcut for the actual compound interest formula. The real math for doubling time looks like this:
The Actual Formula
Where is time in years and is the interest rate as a decimal.
Natural logarithms. Not exactly napkin-friendly. But for interest rates between 6% and 10% — where most investments live — this formula spits out numbers very close to 72 divided by the rate.
Why 72 specifically? Because , and when you work through the algebra for small rates, 72 has more divisors (1, 2, 3, 4, 6, 8, 9, 12...) than 69 or 70, making mental math cleaner. It is accurate and convenient.
The 7% Reality Check
The S&P 500 has averaged about 10% annually since 1926. After inflation (roughly 3%), that is 7% real return. Plug it into the Rule of 72:
Doubling Time at 7%
Your money doubles roughly every decade.
Start with $10,000 at age 25. By 35, it is $20,000. By 45, $40,000. By 55, $80,000. By 65, $160,000. You contributed once. Time did the rest.
This is why financial advisors obsess over starting early. The first decade of doubling is worth more than the last because it compounds forward through every subsequent doubling. That is the same principle behind maxing your 401k early — the money you invest at 25 works harder than the money you invest at 45.
The Debt Side: Why 18% Credit Cards Are Brutal
The Rule of 72 works both ways. If you are earning interest, it shows your wealth doubling. If you are paying interest, it shows your debt doubling.
years to double
$5,000 becomes $10,000 in 9 years. Passive growth working for you.
years to double
$5,000 debt becomes $10,000 in 4 years if you only pay minimums. Compound interest working against you.
A $5,000 credit card balance at 18% APR doubles in 4 years. That is why minimum payments feel like running on a treadmill — the interest compounds faster than you can pay it down. The math is identical to investment growth, just pointed the wrong direction.
The Inflation Trap Most People Miss
Your savings account pays 0.5% interest. Inflation is running at 3%. You are not treading water — you are sinking. The Rule of 72 makes this visceral:
At 3% inflation, your purchasing power cuts in half every years. That $100,000 in a checking account? It buys $50,000 worth of stuff in 2050.
This is the hidden cost of "safe" money. A 0.5% savings account does not protect you from inflation — it just loses slower than cash under a mattress. Real safety means beating inflation, which requires taking on some level of investment risk.
The same math explains why CDs paying 5% were such a big deal in 2023-2024 — they finally beat inflation by a meaningful margin.
When the Rule of 72 Breaks Down
The shortcut works best between 6% and 10%. Outside that range, the error grows:
| Rate | Rule of 72 | Actual | Error |
|---|---|---|---|
| 2% | 36.0 years | 35.0 years | +2.9% |
| 6% | 12.0 years | 11.9 years | +0.8% |
| 8% | 9.0 years | 9.0 years | 0.0% |
| 12% | 6.0 years | 6.1 years | -1.6% |
| 20% | 3.6 years | 3.8 years | -5.3% |
For very low rates (under 4%), use the Rule of 70. For very high rates (above 15%), use the Rule of 69. But for the vast majority of real-world scenarios — stock market returns, mortgage rates, CD yields — 72 nails it.
Frequently Asked Questions
Does the Rule of 72 work for monthly compounding?
Yes, but use the annual percentage rate (APR), not the monthly rate. If your account compounds monthly at 6% APR, it still takes roughly 12 years to double. The rule approximates the effective annual rate automatically for typical compounding frequencies.
Can I use the Rule of 72 for tripling or quadrupling?
For tripling, use 114 (since ). For quadrupling, just double the doubling time — if it takes 10 years to double, it takes 20 to quadruple. The Rule of 72 is specifically optimized for doubling because that is the most common question.
What if I am adding money every month, not just a lump sum?
The Rule of 72 only works for lump sums. For regular contributions (like a 401k), you need the full compound interest formula with periodic payments. Use a future value calculator instead — the math gets significantly more complex.