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Exercise 7.7 · Q5

Q.A machine costing ₹5000 depreciates at a constant rate of 5%. What is the depreciation charge for the 5th year?

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"Depreciates at a constant rate of 5%" is the written-down-value method, so the 5th-year charge is the fall in book value from the end of year 4 to the end of year 5: 5000(0.95)4−5000(0.95)5=4072.53−3868.90≈₹203.635000(0.95)^4-5000(0.95)^5=4072.53-3868.90\approx ₹203.63 (the textbook answer key rounds this to ₹203.50).

Under the reducing-balance (written-down-value) method the book value after nn years is C(1−r)nC(1-r)^n, with C=₹5000C=₹5000 and r=0.05r=0.05. The depreciation for a given year is the amount by which the book value falls during that year.

  1. Book value at the end of year 4.

5000(0.95)4=5000(0.81450625)=₹4072.53.5000(0.95)^4=5000(0.81450625)=₹4072.53.

  1. Book value at the end of year 5. 5000(0.95)5=5000(0.7737809)=₹3868.90.5000(0.95)^5=5000(0.7737809)=₹3868.90. …

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