7
advanced-math

A car depreciates at 15% per year. If purchased for $25,000, what is its value after 4 years?

A

$13,050.06

B

$10,000

C

$15,000

D

$20,000

Correct Answer: A

Choice A is the correct answer. Use exponential decay for depreciation.

  1. Retention Rate: If it loses 15%, it keeps 85% = 0.85.
  2. Formula: V(t)=25000(0.85)tV(t) = 25000(0.85)^t where t=4t = 4.
  3. Calculate: V(4)=25000(0.85)4=25000(0.52200625)13,050.06V(4) = 25000(0.85)^4 = 25000(0.52200625) \approx 13,050.06.

💡 Strategic Tip: Depreciation of 15% means retention factor of 0.85.

Choice B is incorrect because this assumes too much depreciation. Choice C is incorrect because this assumes only 1-2 years of depreciation. Choice D is incorrect because this assumes only 1 year of depreciation.