5
advanced-math

A laptop depreciates by 20% each year. After how many years will it be worth less than 50% of its original value?

A

4 years

B

3 years

C

2 years

D

5 years

Correct Answer: A

Choice A is the correct answer. Find when value drops below 50%.

  1. Retention: Keeps 80% each year, so V(t)=V0(0.8)tV(t) = V_0(0.8)^t.
  2. Test values:
    • Year 1: (0.8)1=0.80=80%(0.8)^1 = 0.80 = 80\%
    • Year 2: (0.8)2=0.64=64%(0.8)^2 = 0.64 = 64\%
    • Year 3: (0.8)3=0.512=51.2%(0.8)^3 = 0.512 = 51.2\% (still above 50%)
    • Year 4: (0.8)4=0.4096=40.96%(0.8)^4 = 0.4096 = 40.96\% (below 50%) ✓
  3. Answer: 4 years.

💡 Strategic Tip: Test successive years until value drops below the threshold.

Choice B is incorrect because after 3 years, value is still 51.2%. Choice C is incorrect because after 2 years, value is 64%. Choice D is incorrect because it drops below 50% before year 5.