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Worked Examples · Example 25

Q.A manufacturer reckons that the value of a machine, which costs him ₹56200, will depreciate each year by 20%. Find the estimated value at the end of 3 years.

Sikkim CbseNCERTSubjective· 2mImportance★★★★★
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Depreciation at a fixed percentage per year is a G.P. with common ratio (1−rate)(1-\text{rate}); the value after 3 years is 56200(0.8)356200(0.8)^3.

[!FORMULA] Declining-balance depreciation: Vn=V0(1−r)nV_n=V_0(1-r)^n, where V0V_0 = initial cost, rr = annual depreciation rate, nn = number of years.

  1. V0=₹56200V_0=\text{₹}56200, r=20%=0.2r=20\%=0.2, so the retained fraction each year is 1−0.2=0.81-0.2=0.8.
  2. n=3n=3 years, so V3=56200×(0.8)3V_3=56200\times(0.8)^3. …

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