The Rule of 72 estimates how long money takes to double: divide 72 by the annual return. At 8 percent a year, money doubles in about 9 years, because 72 divided by 8 equals 9. At 6 percent it takes about 12 years, and at 12 percent it takes about 6 years.

Top guides state the formula and one example, then stop. They rarely check the rule against the exact answer, and they rarely show the full doubling ladder over a lifetime. This guide checks the rule against exact maths, then runs a $1,000 investment through three doublings so you can see the long-term effect.

Use the formula in two directions. To find the years to double, divide 72 by the annual return. To find the return you need, divide 72 by the years you have. If you want to double your money in 10 years, divide 72 by 10 and you get 7.2 percent a year. Both directions use the same division, so the rule works forwards and backwards.

Worked example: check the rule against exact maths at 8 percent. The rule says 72 divided by 8, which is 9 years. The exact doubling time uses logarithms: the natural log of 2 divided by the natural log of 1.08. That is 0.6931 divided by 0.0770, which equals 9.01 years. The rule is off by about 0.01 years, or roughly 2 days. Now check the money itself. Invest $1,000 at 8 percent compounded yearly for 9 years. Multiply 1,000 by 1.08 to the power of 9 and you get $1,999.00, which is $1 short of doubling. The rule is an estimate, and a very good one at this rate.

Run the doubling ladder on that same $1,000 at 8 percent. After about 9 years it becomes about $2,000. After about 18 years it becomes about $4,000. After about 27 years it becomes about $8,000. Each doubling takes the same 9 years, but each doubling adds twice as much money as the last one. The first doubling adds $1,000. The third doubling adds $4,000. That is why starting early matters more than starting big.

Compare the rule across rates. At 6 percent, the rule says 72 divided by 6, which is 12 years. The exact answer is 11.9 years. At 12 percent, the rule says 72 divided by 12, which is 6 years. The exact answer is 6.12 years. The rule stays accurate between about 6 and 10 percent. Outside that range the error grows, so treat the result as a rough guide at very low or very high rates.

The rule also works against you, on inflation and debt. At 3 percent inflation, divide 72 by 3 and you get 24 years. That is how long it takes for prices to double, and for the buying power of your money to halve. The same maths applies to a loan balance that compounds unpaid: at 12 percent, an unpaid balance doubles in about 6 years.

Remember the three conditions the rule needs. First, the return must compound, which means earnings are reinvested and earn their own returns. Second, the rate must stay roughly constant, because a changing rate breaks the estimate. Third, fees and taxes are not included, so subtract them from the return before dividing if you want a realistic answer.

Q: What is the Rule of 72 in simple terms?

A: Divide 72 by the annual return to estimate the years until money doubles. At 8 percent, 72 divided by 8 equals about 9 years.

Q: How accurate is the Rule of 72?

A: Very accurate between 6 and 10 percent. At 8 percent it says 9 years and the exact answer is 9.01 years, a difference of about 2 days.

Q: Can the Rule of 72 work for inflation?

A: Yes. Divide 72 by the inflation rate to find how long until prices double. At 3 percent inflation, prices double in about 24 years.

Q: Why is the number 72 and not 69.3?

A: The exact figure is about 69.3, from the natural log of 2, but 72 divides neatly by 2, 3, 4, 6, 8, 9, and 12, so it is easier to use in your head.