Rule Of 72

Gunnar Lindqvist asks his representative for a quick mental estimate of how long a 150,000 dollar portfolio would take to double if it compounds at an assumed 8 percent per year. Using the Rule of 72, the approximate answer is:

1. A.About 12 yearsThis would correspond to a 6 percent return; the rate and the answer have been transposed.
2. B.About 8 years, because the return and the doubling period are the same numberThe Rule of 72 divides 72 by the rate; the rate itself is not the answer.
3. C.About 6 yearsThis would correspond to a 12 percent return, not 8 percent.
4. D.About 9 yearsCorrect. 72 divided by 8 equals 9.

Why: The Rule of 72 estimates a doubling time by dividing 72 by the annual percentage rate of return. Here 72 divided by 8 gives approximately 9 years. The starting balance is irrelevant to the calculation, which is why the 150,000 dollar figure does not enter the arithmetic. The rule is a mental approximation of compounding, useful for illustrating a mathematical principle to a customer, and it becomes less accurate at very high rates of return.

Beatrix Lindqvist has $200,000 set aside and will need $400,000 in nine years to buy out her business partner. She will make no further contributions. Using the rule of 72, what average annual return must the account earn, and what should the adviser conclude?

1. A.About 8%, a return that will require significant equity exposure and may be difficult to reconcile with a firm nine-year deadlineCorrect. 72 / 9 = 8%, and flagging the conflict between a required return and a fixed horizon is the substantive planning point.
2. B.About 6%, applying the rule of 72 to a twelve-year planning horizon72 / 12 = 6%, but the stem gives nine years, not twelve. Using the wrong horizon understates the required return by two full percentage points.
3. C.About 22.2%, since the ending value is 200% of the starting value spread across nine yearsThis divides the ENDING VALUE percentage by the years rather than the gain, and also ignores compounding. Both errors push the figure far too high.
4. D.About 11.1%, since the account must grow 100% over nine yearsThis divides the total percentage gain by the number of years, treating the growth as simple rather than compound. Compounding does much of the work, so the required rate is lower.

Why: The rule of 72 estimates the return needed to double money over a given number of years by dividing 72 by the number of years: 72 / 9 = 8%. An 8% average annual return with no additional contributions requires a substantially equity-weighted portfolio, which puts the required return in tension with a hard nine-year deadline. The adviser should surface that tension rather than simply build an 8% portfolio.