Question
Tue March 15, 2011 By: Khushboo Panwar

a piece of equipment cost a certain factory Rs600000 If it depreciates in value, 15% the first, 13.5% the next year,12% the third year and so on what will be its value at the end of the 10 years all % applying to the original cost?

Expert Reply
Wed March 16, 2011
Dear Student,
 
Here is the solution:
 
Let the cost of an equipment is Rs. 100.
Now the percentages of depreciation at the end of 1st, 2nd, 3rd years are 15, 13.5, 12, which are in A.P., with a = 15 and d = - 1.5.

Hence, percentage of depreciation in the tenth year = a + (10-1) d = 15 + 9 (-1.5) = 1.5
Also total value depreciated in 10 years = 15 + 13.5 + 12 + ... + 1.5 = 82.5

Hence, the value of equipment at the end of 10 years=100 - 82.5 = 17.5.
The total cost being Rs. 6,00,000/100  x  17.5 = Rs. 1,05,000.
Regards
Team Topperlearning.
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