a truck is purchased for $22,500 and has a resale value of $16,500 after a useful life of 5 years. using a…
a truck is purchased for $22,500 and has a resale value of $16,500 after a useful life of 5 years. using a book value depreciation chart, calculate the number of years until the book value of the truck is $18,900.\n? years
Answer
Explanation:
Step1: Calculate annual depreciation
The initial value $P = 22500$, the salvage value $S=16500$, and the useful - life $n = 5$ years. The annual depreciation $D$ is calculated using the straight - line depreciation formula $D=\frac{P - S}{n}$. $D=\frac{22500 - 16500}{5}=\frac{6000}{5}=1200$.
Step2: Set up an equation for book value
The book value $BV$ at year $t$ is given by the formula $BV=P - Dt$. We know $BV = 18900$, $P = 22500$, and $D = 1200$. Substitute these values into the formula: $18900=22500-1200t$.
Step3: Solve the equation for $t$
First, rearrange the equation: $1200t=22500 - 18900$. $1200t = 3600$. Then, divide both sides by 1200: $t=\frac{3600}{1200}=3$.
Answer:
3