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 so on. What will be its value at the end of 10 years, all percentages applying to the original cost?

Asked by ponmani | 2nd Mar, 2011, 01:32: PM

Expert Answer:

Dear student,
 
Let the cost of an equipment be 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 (Sum of 10 terms of the AP)

Hence, the value of equipment at the end of 10 years=100 - 82.5 = 17.5.

Thus the required total value = Rs.  = Rs. 1,05,000.

We hope that clarifies your query.
 
Regards,
Team
TopperLearning

Answered by  | 2nd Mar, 2011, 05:04: PM

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