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Worked Examples · Example 29

Q.A machine costing ₹50,000 depreciates at a constant rate of 8%. What is the depreciation charge for the 8th year. If the estimated useful life of the machine is 10 years, determine its scrap value.

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Depreciating "at a constant rate of 8%" means the written-down-value (reducing-balance) method: each year's book value is 0.920.92 times the previous one. The 8th-year charge is 50000(0.92)7−50000(0.92)8=27892.33−25660.94=₹2231.3950000(0.92)^7-50000(0.92)^8=27892.33-25660.94=₹2231.39, and the scrap value after 10 years is 50000(0.92)10=₹21719.4250000(0.92)^{10}=₹21719.42.

Under the written-down-value method the book value after nn years is C(1−r)nC(1-r)^n, where C=₹50,000C=₹50{,}000 is the cost and r=0.08r=0.08 is the constant rate. The depreciation charged in any year is the fall in book value across that year.

  1. Book value at the end of the 7th year.

50000(1−0.08)7=50000(0.92)7=50000(0.5578466)=₹27892.33.50000(1-0.08)^7=50000(0.92)^7=50000(0.5578466)=₹27892.33.

  1. Book value at the end of the 8th year. 50000(0.92)8=50000(0.5132188)=₹25660.94.50000(0.92)^8=50000(0.5132188)=₹25660.94. …

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