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Q.The value of a car depreciates by 12.5% every year. By what percent will the value of the car decrease after 3 years and after 5 years ?

CBSECBSE Class XII Board 2024Subjective· 3mImportance★★★★★
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A depreciation of 12.5% per year means a retention factor of 0.8750.875; over nn years the value becomes (0.875)n(0.875)^n of the original, so the fall is [1−(0.875)n]×100%\big[1-(0.875)^n\big]\times100\%.

Reducing-balance depreciation: value after nn years =V0(1−r)n=V_0(1-r)^n, where rr is the annual depreciation rate. Total percentage decrease =[1−(1−r)n]×100%=\big[1-(1-r)^n\big]\times 100\%.

  1. Here r=12.5%=0.125r=12.5\%=0.125, so the retention factor is 1−r=0.8751-r=0.875.
  2. After 3 years: retained fraction =(0.875)3=0.669921875.=(0.875)^3=0.669921875.
  3. Decrease =1−0.669921875=0.330078125≈33.01%.=1-0.669921875=0.330078125\approx 33.01\%. …

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