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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?
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Solution
Given: A piece of equipment cost a certain factory is 600,000
To find: Value of the equipment at the end of 10 years
It depreciates 15%, 13.5%, 12% in 1st, 2nd, 3rd year and so on.
This means the price of the equipment is depreciating in an A.P.
A.P. will be 15, 13.5, 12,…………………………up to 10 terms
Hence a = 15, d = 13.5 – 15 = –1.5
Formula used:
`S_n = n/2 {2a +(n-1)d}`
where a is first term, d is common difference and n is number of terms in an A.P.
Therefore,
Total percentage of depreciation in 10 years,
`S_10 =10/2{2xx15+(10-1)xx-1.5}`
⇒ S10 = 5(30+9× -1.5)
⇒ S10 = 5(30 -13.5 )
⇒ S10 = 5(16.5)
⇒ S10 = 82.5
Value of the equipment at the end of 10 years,
`= (100-"Depreciation"%)/100 xx "cost of equipment"`
`=(100-82.5)/100 xx 600000`
`= 175/10 xx 6000`
=175 × 600
= 105000
Hence, value of equipment at the end of 10 years is Rs. 105000
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