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?

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