A piece of equipment cost a certain factory Rs 600,000.

Question:

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?

Solution:

Cost of the piece of equipment at the end of the first year = Rs 600000 – 15% of 600000

= Rs 600000 – Rs 90000

= Rs 510000

Cost of the piece of equipment at the end of the second year = Rs 600000 – 13.5% of 600000

= Rs 600000 – Rs 81000

= Rs 519000

Cost of the piece of equipment at the end of the third year = Rs 600000 – 12% of Rs 600000

 = Rs 600000 – Rs 72000

= Rs 528000

The numbers 510000, 519000, 528000 are in an A.P. whose first term in 510000 and common difference is 9000.

∴ Cost of the piece of equipment at the end of 10 years = a + (10 – 1)d

= 510000 + 81000

 = Rs 591000

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