A certain sum of money is invested at an annual interest rate of 8% compounded quarterly. Approximately how many years will it take for the investment to triple?
- A12 years
- B14 years
- C16 years
- D10 years
Show answer & explanationAnswer & explanation
Correct answer: B. 14 years
For compounding quarterly, the effective annual rate is slightly higher than the nominal rate. However, for approximation with the Rule of 72/Rule of 114, we often use the nominal rate. For tripling, the Rule of 114 is used: Years to triple ≈ 114 / (annual interest rate as a whole number). Here, Rate = 8%. Years to triple ≈ 114 / 8 = 14.25 years. The closest option is 14 years. (For more precise calculation, (1 + 0.08/4)^(4n) = 3 => (1.02)^(4n) = 3. Taking natural log: 4n * ln(1.02) = ln(3) => 4n * 0.0198 = 1.0986 => 4n = 55.48 => n = 13.87 years).
Why the other options are wrong
- A. This is incorrect; it might be a result of misremembering the Rule of 114 or incorrect calculation.
- C. This is incorrect; it might be a result of misremembering the Rule of 114 or incorrect calculation.
- D. This is incorrect; it might be a result of misremembering the Rule of 114 or incorrect calculation.
Rule of 114 (Tripling Time Approximation)
A quick and simple rule to estimate the number of years required for an investment to triple in value.
- Years to triple ≈ 114 / (annual interest rate as a whole number).
- Similar to the Rule of 72 but for tripling instead of doubling.
- Provides a reasonable approximation for GMAT purposes, especially when options are spaced out.
Memory trick: 114 on top, rate below, for tripling, that's how you know!