GMAT Focus EditionQuantitative ReasoningMedium
An investment doubles in value approximately every 9 years. Using the Rule of 72, what is the approximate annual compound interest rate?
- A9%
- B7%
- C8%
- D6%
Show answer & explanationAnswer & explanation
Correct answer: C. 8%
The Rule of 72 states that to find the approximate number of years required to double an investment, you divide 72 by the annual compound interest rate. So, Years to Double = 72 / Interest Rate. Given Years to Double = 9, then 9 = 72 / Interest Rate. Solving for Interest Rate: Interest Rate = 72 / 9 = 8%.
Why the other options are wrong
- A. This would imply a doubling time of 8 years (72/9).
- B. This would imply a doubling time of approximately 10.28 years (72/7).
- D. This would imply a doubling time of 12 years (72/6).
Rule of 72 (Approximation)
A quick mental math trick to estimate the number of years it takes for an investment to double in value, given a fixed annual compound interest rate, or vice versa.
- Years to Double ≈ 72 / Annual Interest Rate (as a whole number).
- Annual Interest Rate ≈ 72 / Years to Double.
- It's an approximation, most accurate for rates between 6% and 10%.
Memory trick: 72 is the magic number for doubling your dough!