Rule of 72: The Shortcut That Tells You How Fast Your Money Actually Doubles
6 min read
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6 min read
If your savings grow at 10% a year, how long until they double? Most people either guess or reach for a calculator. There is a faster way: divide 72 by the growth rate. At 10%, that is 72 ÷ 10 = 7.2 years. This is the Rule of 72, a mental-math shortcut that has been used by savers and lenders for centuries, and it is accurate enough to trust for a real decision. Here is where the number 72 comes from, how close it actually gets to the real compound-interest formula, and what it says when applied to a real Bank Indonesia rate, a real long-run stock market return, and a real Indonesian credit card interest cap.
The rule is one division: take the annual growth rate as a plain number (not a decimal), divide it into 72, and the answer is roughly how many years it takes for a sum of money to double, assuming the rate stays constant and any returns are reinvested rather than withdrawn.
Nothing here is specific to stocks or bank deposits. The same division works for a savings account, a bond, a loan you owe, or an economy's GDP growth rate. It only assumes compounding: that whatever was earned last period gets added to the base before the next period's growth is calculated.
The Rule of 72 is an approximation of a real formula. The exact number of periods it takes an amount to double at a periodic rate r is:
The two do not give identical answers, but they stay close across the range of rates a saver or investor actually encounters:
| Annual rate | Rule of 72 estimate | Exact formula | Difference |
|---|---|---|---|
| 2% | 36.0 years | 35.0 years | +1.0 year |
| 5.75% (BI's benchmark rate) | 12.5 years | 12.4 years | +0.1 year |
| 8% | 9.0 years | 9.0 years | ~0 |
| 10% (long-run S&P 500 average) | 7.2 years | 7.3 years | −0.1 year |
| 15% | 4.8 years | 5.0 years | −0.2 year |
| 20% | 3.6 years | 3.8 years | −0.2 year |
The shortcut is tightest right around 8%, and drifts a little in both directions as the rate moves away from there. At very low rates it slightly overstates how long doubling takes. At high rates it slightly understates it. For almost any rate a retail saver or investor deals with, the error is a few months on a multi-year estimate, which is close enough to plan around.
Bank Indonesia held its BI 7-Day Reverse Repo Rate, the central bank's own benchmark policy rate, at 5.75% at its July 2026 board meeting, and it remained unchanged into August. This is not what a savings account pays you directly; actual bank deposit rates are set independently and usually sit below it. But it is a clean, real, current number to run through the shortcut: 72 ÷ 5.75 ≈ 12.5 years. The exact formula agrees closely, at 12.4 years. A rate in this range roughly matches money's growth if it were compounding at something close to the policy rate.
The S&P 500, the benchmark US large-company stock index, has returned close to 10% a year on average since 1957 when dividends are reinvested, a figure that converges across multiple independent sources including officialdata.org's own historical return series and Fidelity's investor education material. That average smooths over individual years that swing far wider in both directions. At a flat 10%, 72 ÷ 10 = 7.2 years to double, against the exact formula's 7.3 years. The gap between 12.5 years at the BI benchmark rate and 7.2 years at a long-run equity average is itself the case for taking on some market risk with money that will not be needed for a decade or more, since the difference compounds into a large gap over multiple doubling cycles.
Compounding does not only work in a saver's favor. Bank Indonesia caps credit card interest at 1.75% a month, a ceiling first set in July 2021 and still in force in 2026. Because the rate is monthly, the Rule of 72 can be applied directly to the monthly figure to get months rather than years: 72 ÷ 1.75 ≈ 41 months, or about 3.4 years, for an unpaid balance to double. The exact monthly formula agrees closely, at about 40 months. A balance left to carry at the regulatory maximum roughly triples the pace at which the S&P 500 example above compounds, in the wrong direction for whoever owes it.
The Rule of 72 is a rough approximation, not an exact formula, and it is worth knowing where it stops being close enough. Below about 2% to 3% a year, the estimate runs noticeably long, by a full year or more at the low end of the table above. Above roughly 15% to 20%, it runs noticeably short, understating how long doubling really takes by a few months. Neither error is large enough to change a decision most people make with it, choosing between two rough options, sanity-checking a number a bank or an app quoted, or getting an intuitive feel for how much a rate difference actually matters over time, but it is not the tool for a figure that needs to be exact to the day, like a loan amortization schedule or a retirement projection with a fixed end date.
The Rule of 72 is only useful once it is applied to a real rate, not a hypothetical one. Any listed stock's own long-run annualized return can be checked directly on its NetWort Asset Detail page, which is also where you can see how far that real historical return diverges from a flat, evenly-compounding assumption in practice. The same compounding math that drives a doubling-time estimate is also what sits underneath a retirement withdrawal plan, covered in more depth in how the 4% withdrawal rule actually works.