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



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:


and so


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


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

#"Truck" color(white)(00000000000000000000)16,725#
#"Accumulated Depreciation" color(white)(000)color(red)(6,690)#
#"Net Value of Truck" color(white)(000000000)10,035#