8
advanced-math

A new phone loses 30% of its value each year. If it costs $1,200 new, what will it be worth after 3 years?

A

$411.60

B

$360.00

C

$840.00

D

$600.00

Correct Answer: A

Choice A is the correct answer. Apply depreciation formula.

  1. Retention: Loses 30%, keeps 70% = 0.70.
  2. Formula: V(t)=1200(0.70)tV(t) = 1200(0.70)^t where t=3t = 3.
  3. Calculate: V(3)=1200(0.70)3=1200(0.343)=411.60V(3) = 1200(0.70)^3 = 1200(0.343) = 411.60.

💡 Strategic Tip: Loses 30% means retention factor of 0.70.

Choice B is incorrect because this assumes 70% loss, not retention. Choice C is incorrect because this is the value after 1 year. Choice D is incorrect because this is the value after a 50% loss total.