Rule of 72 Calculator

The Rule of 72 is a mental arithmetic shortcut for estimating how long it takes an investment to double at a given compound annual growth rate. Divide 72 by the annual rate written as a whole number, and the answer is the number of years. At 6% growth, money doubles in approximately 72 / 6 = 12 years. At 8% it doubles in 72 / 8 = 9 years, at 9% in 8 years and at 12% in 6 years. The shortcut is most accurate for rates between 2% and 15%, and it holds for any compounding scenario, whether savings, investments, debt growth or the erosion caused by inflation.

The mathematical basis is the natural logarithm. The exact doubling time is ln(2) / ln(1 + r), which equals 0.693 / ln(1 + r). For small rates ln(1 + r) approximates to r, giving 0.693 / r, or roughly 69.3 / r%. The number 72 is used instead of 69.3 because it has more factors, being divisible by 2, 3, 4, 6, 8, 9 and 12, which makes the mental division easy, and the slight overestimate partly compensates for the approximation error. Accuracy is very good between 4% and 12%. Above 15% the Rule of 70 gets closer, and 69.3 is the mathematically exact figure.

The shortcut also works in reverse. If you want to double your money within a set number of years, divide 72 by the years to find the rate you need. To double in 10 years you need 72 / 10 = 7.2% annual growth. Applied to inflation, the same division shows how fast prices erode savings. At 3% inflation the cost of living doubles every 72 / 3 = 24 years, so your £1 buys only 50p worth of today's goods, and £100,000 in 1995 has the buying power of roughly £50,000 in 2024. Cash paying 2% against 3% inflation is a real return of minus 1%, on which £10,000 loses £1,000 of purchasing power every 5 years.

Practical UK uses run from pension projections to mortgage payoff times. Savings at 5% double every 14.4 years, so £10,000 becomes £20k after 14 years, £40k after 28 and £80k after 42. The 7% historic real return on the S&P 500 doubles every 10.3 years, which turns a £20,000 ISA into £40k after 10 years, £80k after 20 and £160k after 30 years. Seeing the horizon in years rather than percentages makes the trade-off between saving vehicles much easier to weigh up.

Debt compounds on exactly the same arithmetic, which is why the rule works as a nudge to repay. A credit card at 22% APR in 2026 doubles an unpaid balance every 3.3 years, turning £3,000 into £6,000 in 3 years and £12,000 in 6. An interest-only mortgage at 5% doubles every 14 years, which is a real concern on long-term interest-only products. Buy Now Pay Later penalty interest of 36% doubles a debt in 2 years. Framing the cost of inaction as a doubling time tends to concentrate the mind more effectively than an APR does.

Compound interest was reputedly called the eighth wonder of the world by Albert Einstein, although the attribution is disputed. Pension figures show why the phrase stuck. Investing £100/month from age 25 to 65 at 7% produces £262,481 at retirement from £48,000 contributed. Start the same £100/month at 35 and the pot is £121,997 from £36,000 contributed. Just 10 more years of compounding roughly doubles the final figure, and on that arithmetic even £25/month from 22 outperforms £100/month from 35.

Where the shortcut breaks down matters as much as where it works. It assumes a constant return, and real markets fluctuate. It assumes annual compounding, so monthly or daily compounding is slightly more favourable than the answer suggests. It leaves out contributions added each year, which need the full future value formula, and it leaves out fees and taxes, since an ISA is tax-free but platform fees of 0.2-1% still drag on growth. Inflation is absent too, and real returns matter more than headline ones. The answer is mental shorthand for a quick estimate, and a future value calculator carrying all the variables will land closer.