GMAT Focus EditionQuantitative ReasoningHard
A certain investment grows at an annual rate of 'r' compounded annually. If the investment doubles in 6 years, what is the approximate annual interest rate 'r'?
- A10%
- B8%
- C14%
- D12%
Show answer & explanationAnswer & explanation
Correct answer: D. 12%
We can use the Rule of 72 for approximation. If an investment doubles in 'N' years, the approximate annual interest rate 'r' is given by r = 72 / N. Here, N = 6 years, so r = 72 / 6 = 12%. The actual calculation (1+r)^6 = 2 implies r = 2^(1/6) - 1 ≈ 0.12246, which is approximately 12%.
Why the other options are wrong
- A. This is incorrect; it might be a result of misremembering the Rule of 72 or an incorrect calculation.
- B. This is incorrect; it might be a result of misremembering the Rule of 72 or an incorrect calculation.
- C. This is incorrect; it might be a result of misremembering the Rule of 72 or an incorrect calculation.
Rule of 72 (Approximation)
A quick and simple rule to estimate the number of years required to double an investment or the interest rate needed for an investment to double in a given number of years.
- Years to double ≈ 72 / (annual interest rate as a whole number).
- Interest rate ≈ 72 / (years to double).
- Works best for interest rates between 6% and 10% but is a useful approximation for GMAT.
Memory trick: 72 on top, time or rate below, for doubling, that's how you know!