# Imelda bought a truck for her business and depreciated it over 5 years using the straight-line method. If its value 2 years later was $10,035, how much did she pay for it? ##### 1 Answer $T = 10 , 035 \times \frac{5}{3} = 16 , 725$#### Explanation: An accounting/depreciation question: Depreciation seeks to assign the expense of buying an asset, such as a truck, to the time period when it's being used. And so the full cost of the truck doesn't get expensed in the year it's purchased - instead the expense is spread out over a number of years. The straight-line method of depreciation takes the cost of the asset, divides it evenly for a set number of year, and then each year that amount of the cost is expensed. The value of the asset is then expressed as the Cost-Accumulated Depreciation. In this case, we have a truck, $T$, whose value we don't know, but whose value at the end of year 2 is$10,035. What is the value of $T$?

There are three years of life left on the truck, so we can say:

$\frac{3}{5} T = 10 , 035$

and so

$T = 10 , 035 \times \frac{5}{3} = 16 , 725$

which means that the accumulated depreciation at the end of year two is:

#16725-10035=6690

We can express the value of the truck at the end of year two as:

$\text{Truck} \textcolor{w h i t e}{00000000000000000000} 16 , 725$
$\text{Accumulated Depreciation} \textcolor{w h i t e}{000} \textcolor{red}{6 , 690}$
$\text{Net Value of Truck} \textcolor{w h i t e}{000000000} 10 , 035$