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?
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 $=\frac{13.5}{100}(600000)=81000$
Further, it depreciates by 12% of the original cost in the 3 year. So,
Depreciation in 3 year $=\frac{12}{100}(600000)=72000$
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,
$S_{n}=\frac{n}{2}[2 a+(n-1) d]$
We get,
$S_{n}=\frac{10}{2}[2(90000)+(10-1)(-9000)]$
$=\frac{10}{2}[180000+(9)(-9000)]$
$=5(180000-81000)$
$=5(99000)$
$=495000$
So, the total depreciation in the value after 10 years is Rs 495000.
Therefore, the value of equipment 
So, the value of the equipment after 10 years is
.