A piece of equipment cost a certain factory Rs.600,000. If it depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and soon. What will be its value at the end of 10 years, all percentages applying to the original cost?
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The value of equipment at end of 10 yrs is Rs. 10,5000
Cost of equipment = Rs.. 6,00,000 (Given)
Depreciation in first year 15%, (Given)
Depreciation in second year 13.5% (Given)
Depreciation in third year 12% (Given)
Let the cost of equipment be = Rs. 100.
AP = 15, 13.5,12, where a=15 and d = 12 - 13.5 = -1.5.
Therefore,
percentage of depreciation in tenth year
= a + (10-1) d
= 15 + 9 (-1.5)
= 1.5
Total value depreciated in 10 years = 15 + 13.5 + 12 + ... + 1.5
= 82.5 (Sum of 10 terms of AP)
Thus, the value of equipment at the end of 10 years
= 100 - 82.5
= 17.5
Value of equipment - 17.5/100 × 600,000.
= 105000.
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