1. **Problem Statement:** A machine costing 50000 depreciates at a constant rate of 8% per year. 2. **Formula for Depreciation at Constant Rate:** The book value after $n$ years is given by $$\text{Book Value}_n = \text{Cost} - n \times \text{Depreciation per year}$$ where depreciation per year = $8\%$ of the original cost. 3. **Calculate Depreciation per Year:** $$\text{Depreciation per year} = 0.08 \times 50000 = 4000$$ 4. **Book Value at the End of 7th Year:** $$\text{Book Value}_7 = 50000 - 7 \times 4000 = 50000 - 28000 = 22000$$ 5. **Book Value at the End of 8th Year:** $$\text{Book Value}_8 = 50000 - 8 \times 4000 = 50000 - 32000 = 18000$$ 6. **Depreciation Charge for the 8th Year:** Since depreciation is constant, $$\text{Depreciation for 8th year} = 4000$$ **Final Answers:** - Book value at end of 7th year: 22000 - Book value at end of 8th year: 18000 - Depreciation charge for 8th year: 4000