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?

#### Solution

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** .