6
advanced-math

$15,000 is invested at 7% compounded annually. How long until it doubles?

A

About 10 years

B

14 years

C

7 years

D

20 years

Correct Answer: A

Choice A is the correct answer. Find when the investment doubles.

  1. Target: Double means A=2×15000=30000A = 2 \times 15000 = 30000.
  2. Equation: 30000=15000(1.07)t30000 = 15000(1.07)^t, so (1.07)t=2(1.07)^t = 2.
  3. Estimate: Test values:
    • t=10t=10: (1.07)101.967(1.07)^{10} \approx 1.967 (close to 2)
    • t=11t=11: (1.07)112.105(1.07)^{11} \approx 2.105 (over 2)
  4. Answer: About 10-11 years, so "About 10 years".

💡 Strategic Tip: Rule of 72: doubling time ≈ 72710\frac{72}{7} \approx 10 years.

Choice B is incorrect because doubling happens sooner. Choice C is incorrect because this is the interest rate, not doubling time. Choice D is incorrect because doubling occurs much earlier.