10
advanced-math

A vehicle depreciates 22% per year. If bought for $35,000, what's its value after 5 years?

A

$10,404.67

B

$15,000.00

C

$20,000.00

D

$12,500.00

Correct Answer: A

Choice A is the correct answer. Apply depreciation formula.

  1. Retention: Loses 22%, keeps 78% = 0.78 each year.
  2. Formula: V(t)=35000(0.78)tV(t) = 35000(0.78)^t where t=5t = 5.
  3. Calculate: V(5)=35000(0.78)5=35000(0.2973)10,405V(5) = 35000(0.78)^5 = 35000(0.2973) \approx 10,405.

💡 Strategic Tip: High depreciation rates lead to rapid value loss.

Choice B is incorrect because this underestimates the depreciation. Choice C is incorrect because this assumes much slower depreciation. Choice D is incorrect because the calculation is wrong.