Question

A piece of equipment cost a certain factory Rs 60,000. 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

In the given problem,

Cost of the equipment = Rs 600,000

It depreciates by 15% in the first year. So,

Depreciation in 1 year

= 600000 − 495000

= 105000

= 90000

It depreciates by 13.5% of the original cost in the 2 year. So,

Depreciation in 2 year  `= (13.5)/100 (600000) = 81000`

Further, it depreciates by 12% of the original cost in the 3 year. So,

Depreciation in 3 year  `= 12/100 (600000)=72000` 

 

So, the depreciation in value of the equipment forms an A.P. with first term as 90000 and common difference as −9000.

So, the total depreciation in value in 10 years can be calculated by using the formula for the sum of n terms of an A.P.

`S_n = n/2 [2a + (n-1) d]`

We get,

`S_n = 10/2 [2(90000) +(10-1)(-9000)]`

      `=10/2 [180000 + (9)(-9000)]`

      `=5(180000 - 81000)`  

     ` = 5(99000)`

       = 495000

So, the total depreciation in the value after 10 years is Rs 495000.

Therefore, the value of equipment = 600000 − 495000 = 105000 

So, the value of the equipment after 10 years is Rs 105,000.