Compound Interest and the Rule of 72
How money makes money, and a mental-math shortcut
The most powerful force in long-term investing turns out to be surprisingly simple: compound interest — the idea that money you’ve already earned goes on to earn more money. Even at the same rate of return, having this mechanism or not creates a gap that widens dramatically over time, and the difference becomes obvious the moment you put compound interest side by side with simple interest.
Simple interest vs. compound interest
Simple interest only accrues on your original principal. Leave $1,000 at 10% simple interest, and you earn a flat $100 every year — after 10 years, that’s 1,000 + (10 × 100) = $2,000. Because interest is always proportional to the same original principal, the growth is a steady ‘straight line.’
Compound interest earns interest on the interest. Leave that same $1,000 at 10% compound interest, and after 1 year you have $1,100; in year 2, that $1,100 earns another 10% — $110 — bringing you to $1,210. Because the grown balance itself becomes the base for next year’s interest, the curve gets steeper and steeper over time. After 10 years, it’s about $2,594 — nearly $590 more than simple interest ($2,000).
The snowball effect of compounding
Compound interest’s real power shows up in the later stretches. It’s like rolling a small snowball — the first few turns barely change anything, but as it grows, each additional turn packs on a dramatically bigger amount of snow. At 10% compound interest, it takes about 7 years for your principal to double. Doubling again — to 4x — doesn’t take another 7 years on top of that; it takes another 7, for 14 years total. An 8x multiple takes 21 years. But the same 7-year stretch produces a wildly different amount in absolute dollars depending on whether it’s turning $1,000 into $2,000, or $10,000 into $20,000.
That’s why compounding makes time just as important a variable as the rate of return. At the same rate, a dollar that started one year earlier ends up contributing the single largest chunk of growth in the final year.
The Rule of 72
So how many years does it take for your money to double? Calculating that exactly requires logarithms, but a simple shortcut called the Rule of 72 gets you close enough.
- Years to double ≈ 72 ÷ annual return (%)
- 8% a year → 72 ÷ 8 = about 9 years
- 6% a year → 72 ÷ 6 = about 12 years
- 12% a year → 72 ÷ 12 = about 6 years
Why 72, specifically? The exact condition for compound doubling is (1 + r)n = 2. Taking the log of both sides gives n = ln 2 ÷ ln(1 + r). ln 2 is about 0.693, and when the return isn’t too large, ln(1 + r) is roughly equal to r itself. So n ≈ 0.693 ÷ r, which becomes n ≈ 69.3 ÷ return (%) once you switch to percentage terms. But 69.3 is awkward to calculate in your head, so 72 — which has far more divisors and splits evenly by common rates like 6, 8, 9, and 12 — became the conventional shortcut instead. In the 6–10% range, the error stays within about a year, which is plenty accurate for practical use.
Combining DCA with compounding
The Rule of 72 shows how a single lump sum grows over time. But real-world investing is often DCA — putting in new money every month. Under DCA, the dollars you invested earliest have had the most time for compounding to work, so they grow the most; the dollars you just contributed this month are still worth almost exactly what you paid. In other words, every dollar in the same account has a different “age,” and it’s the oldest dollars that drive most of the overall growth.
Because of this, a DCA portfolio’s final value doesn’t cleanly reduce to “total contributions × some multiplier” — the price at the time of every single monthly purchase, and everything that happened afterward, are all tangled together. To get a real feel for how much compounding is actually doing under DCA, run your own ticker and monthly amount through the calculator, which replays it against real historical data.
What this means for long-term investing
Compounding and the Rule of 72 teach two lessons. First, starting earlier is a real advantage, because the very last doubling (say, $500K to $1M) creates as much new money as every doubling before it combined. Second, a small bump in your rate of return matters more than it sounds. Push your rate from 6% to 9%, and the time to double drops from 12 years to 8 — meaning your money completes twice as many “doubling cycles” in the same stretch of time. Just remember that a higher expected return almost always comes bundled with higher volatility.
The limits — reality isn’t a straight line
The Rule of 72 assumes the exact same rate of return, year after year. But real stock and ETF returns bounce around from year to year, and some years are negative. When a loss enters the picture, compounding works in reverse too — recovering from one big drop requires an even bigger gain. For example, an asset that falls 50% needs +100%, not +50%, to get back to even. Leveraged ETFs in particular are prone to this kind of compounding volatility loss (decay) — see Leveraged ETF Risk for more.
- Volatility — even with the same average return, bigger swings can leave you worse off in the end.
- Taxes — taxes on realized gains or dividends shrink the principal available for reinvestment, chipping away at the compounding effect.
- Inflation — an 8% nominal annual return is closer to a 5% real (purchasing-power) return if inflation is running at 3% a year.
So the Rule of 72 is best used not as a precise forecast but as a rough intuition tool. Real returns swing year to year, and the fact that something compounded at a certain pace in the past is no guarantee it will keep doing so going forward.
This content is for general information only, not investment advice or a solicitation.