4
advanced-math

An antique increases in value by 12% per year. If currently worth $5,000, what will it be worth in 10 years?

A

$15,529.24

B

$11,000.00

C

$20,000.00

D

$6,000.00

Correct Answer: A

Choice A is the correct answer. Apply exponential appreciation.

  1. Formula: V(t)=5000(1.12)tV(t) = 5000(1.12)^t where t=10t = 10.
  2. Calculate: V(10)=5000(1.12)10=5000(3.10585)15,529.24V(10) = 5000(1.12)^{10} = 5000(3.10585) \approx 15,529.24.
  3. Result: Value ≈ $15,529.24.

💡 Strategic Tip: 12% growth means multiplying by 1.12 each year.

Choice B is incorrect because this assumes simple interest (5000 + 6000). Choice C is incorrect because this growth is too high. Choice D is incorrect because this is only 1 year of growth.