6
advanced-math

An investment doubles every 9 years. If you invest $3,000, what will it be worth after 27 years?

A

$24,000

B

$12,000

C

$6,000

D

$9,000

Correct Answer: A

Choice A is the correct answer. Apply the doubling pattern.

  1. Doubling periods: 279=3\frac{27}{9} = 3 periods.
  2. After each doubling: Multiply by 2.
  3. After 3 doublings: 3000×23=3000×8=24,0003000 \times 2^3 = 3000 \times 8 = 24,000.
  4. Formula: A(t)=3000(2)t/9A(t) = 3000(2)^{t/9}.

💡 Strategic Tip: 3 doublings = multiply by 23=82^3 = 8.

Choice B is incorrect because this is after 2 doublings (18 years). Choice C is incorrect because this is after only 1 doubling (9 years). Choice D is incorrect because this is the wrong calculation.