For tax and accounting purposes businesses often have to depreciate equipment values over time. One method of depreciation is the straight-line method. Three years ago Hilde Construction purchased a bulldozer for $51,500. Using the straight-line method, the bulldozer has now depreciated to a value of $43,200. If V equals the value at the end of year t, write a linear equation expressing the value of the bulldozer over time. How many years from the purchase date will the value equal $0?
V(t) = 51500 - (51500-43200)/3 t
Now just find t when V=0.
To write a linear equation expressing the value of the bulldozer over time using the straight-line method, we can use the formula:
V = C - (C / n) * t
Where:
V is the value at the end of year t
C is the initial cost (purchase price) of the bulldozer
n is the useful life of the bulldozer in years
t is the number of years since the purchase date
We are given:
C = $51,500
V = $43,200
Substituting these values into the formula, we get:
$43,200 = $51,500 - ($51,500 / n) * t
To find n, the useful life of the bulldozer in years, we can set up the equation using the given information after the bulldozer has depreciated to $0:
$0 = $51,500 - ($51,500 / n) * t
Solving this equation will give us the number of years from the purchase date when the value will equal $0.
To find the linear equation expressing the value of the bulldozer over time using the straight-line method of depreciation, we need to determine the rate at which the bulldozer's value is decreasing each year.
The formula for straight-line depreciation is:
Depreciation Expense = (Initial Value - Residual Value) / Useful Life
In this case, Hilde Construction purchased the bulldozer for $51,500 and it has depreciated to a value of $43,200 over a period of three years.
Using the formula, we can calculate the annual depreciation expense as follows:
Depreciation Expense = ($51,500 - $43,200) / 3
= $8,300 / 3
= $2,766.67
Now that we know the annual depreciation expense, we can write the linear equation expressing the value of the bulldozer over time. Since the value at the end of year t (V) is decreasing by $2,766.67 each year, the equation can be written as:
V = $51,500 - ($2,766.67 * t)
Where t represents the number of years since the purchase date.
To find out how many years from the purchase date will the value equal $0, we can set V to 0 in the equation and solve for t:
0 = $51,500 - ($2,766.67 * t)
Solving for t:
$2,766.67 * t = $51,500
t = $51,500 / $2,766.67
t ≈ 18.63
Therefore, approximately 18.63 years after the purchase date, the value of the bulldozer will equal $0 according to the straight-line depreciation method.