a scooter is purchased for $4,000 and has a resale value of $200 after a useful life of 5 years. using a…
a scooter is purchased for $4,000 and has a resale value of $200 after a useful life of 5 years. using a book value depreciation chart, calculate the number of years until the book value of the scooter is $2,480. ? years
Answer
Explanation:
Step1: Calculate annual depreciation
The initial cost $C = 4000$, the salvage value $S=200$, and the useful - life $n = 5$ years. The annual depreciation $D$ using the straight - line depreciation formula $D=\frac{C - S}{n}$. $D=\frac{4000 - 200}{5}=\frac{3800}{5}=760$.
Step2: Set up an equation for book value
The book value $BV$ at the end of year $t$ is given by $BV = C−Dt$. We know $BV = 2480$, $C = 4000$, and $D = 760$. Substitute these values into the equation: $2480=4000−760t$.
Step3: Solve the equation for $t$
First, rearrange the equation: $760t=4000 - 2480$. $760t = 1520$. Then, divide both sides by 760: $t=\frac{1520}{760}=2$.
Answer:
2