Question

4. A machine depreciates by 40% in the first year, by 25% in the second year and by 10% per annum for the next three years. Each percentage being calculated on the diminishing value, what is the average percentage of depreciation for the entire period?​

Answer 1

Let's assume the original value of the machine is Rs. 100.
After the first year, the value of the machine depreciates by 40%, so its value becomes 60% of Rs. 100, or Rs. 60.
After the second year, the value of the machine depreciates by 25%, so its value becomes 75% of Rs. 60, or Rs. 45.
For the next three years, the value of the machine depreciates by 10% per annum, so its value becomes:
Year 3: 90% of Rs. 45, or Rs. 40.50
Year 4: 90% of Rs. 40.50, or Rs. 36.45
Year 5: 90% of Rs. 36.45, or Rs. 32.81
Therefore, the total depreciation over the five-year period is Rs. 100 - Rs. 32.81 = Rs. 67.19.
The average percentage of depreciation over the five-year period is:
(67.19 / 100) × 100 / 5 = 13.44%
Therefore, the average percentage of depreciation for the entire period is 13.44%