a boat is purchased for $51,000 and has a resale value of $42,000 after a useful life of 6 years. using a…
a boat is purchased for $51,000 and has a resale value of $42,000 after a useful life of 6 years. using a book value depreciation chart, calculate the number of years until the book value of the boat is $46,500. ? years
Answer
Explanation:
Step1: Calculate annual depreciation
The initial value $P = 51000$, the salvage value $S=42000$ and the useful - life $n = 6$ years. The annual depreciation $d$ using straight - line depreciation formula $d=\frac{P - S}{n}$. $d=\frac{51000 - 42000}{6}=\frac{9000}{6}=1500$.
Step2: Calculate the depreciation amount from initial value to target book value
The initial value is $P = 51000$ and the target book value $B = 46500$. The depreciation amount $D$ is $D=P - B$. $D = 51000-46500 = 4500$.
Step3: Calculate the number of years
Let the number of years be $t$. Since $D = d\times t$, then $t=\frac{D}{d}$. $t=\frac{4500}{1500}=3$.
Answer:
3