Question

Eros Industries bought a laser printer for $3400. It is expected to depreciate at a rate of 12% per year. What will the value of the printerbe in 6 years? Round to the nearest dollar.

Answer 1

The value of the printer at the 6th year will be $1,579 to the nearest dollar

Here, we want to calculate the value of a printer after some years given that it depreciates at a constant rate per year.

To be able to answer this, we need to set up an exponential equation that can represent the rate how the depreciation plays out per year.

Mathematically, we can have the depreciation equation as follows;

$A(t)=I(1-r)^t$

Where A(t) represents the value of the laser printer at a particular given year

I represents the initial cost of the printer which is the cost at which the printer was bought which is $3,400

r represents the depreciation percentage which is 12% (this is same as 12/100 = 0.12)

t is the particular year number we are trying to find the cost

From the question, we are trying to get the cost of the printer at the 6th year, this means the value of t at this point is t= 6

Now, plugging these values into the equation, we have;

$\begin{gathered} A(6)=3,400(1-0.12)^6 \\ \\ A(6)=3,400(0.88)^6 \\ \\ A(6)\text{ = 1,578.97} \end{gathered}$

The value of the printer at the 6th year will be $1,579 to the nearest dollar