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?

Answer 1

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 1^st, 2^nd, 3^rd 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