A piece of equipment cost a certain factory 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?

Home » A piece of equipment cost a certain factory 600,000 . If it depreciates in value the first, the next year, the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?

A piece of equipment cost a certain factory 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?

A piece of equipment cost a certain factory 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?

Solution:

Given that a piece of equipment cost a certain factory is ₹ 600,000
We have to find the value of the equipment at the end of 10 years.
The price of equipment depreciates $15 \%, 13.5 \%, 12 \%$ in $1^{\text {st }}, 2^{\text {nd }}, 3^{\text {rd }}$ year and so on.
Therefore the A.P. will be $15,13.5,12, \ldots \ldots \ldots \ldots$ up to 10 terms
Here, $a=15, d=13.5-15=-1.5, n=10$
Using the formula,
$\begin{array}{l} S_{n}=n / 2[2 a+(n-1) d] \\ S_{10}=10 / 2[2(15)+(10-1)(-1.5)] \\ =5[30+9(-1.5)] \\ =5[30-13.5] \\ =5[16.5] \\ =82.5 \end{array}$
The value of equipment at the end of 10 years is $=[100-$ Depreciation $\%] / 100 \times$ cost
$\begin{array}{l} =[100-82.5] / 100 \times 600000 \\ =175 / 10 \times 6000 \\ =175 \times 600 \\ =105000 \end{array}$
As a result the value of equipment at the end of 10 years is ₹ 105000.