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 $43,500.
Answer
Explanation:
Step1: Calculate annual depreciation
The initial value ($V_0$) is $51000$ and the final value ($V_f$) after 6 years is $42000$. The total depreciation ($D$) over 6 years is $D = V_0 - V_f=51000 - 42000 = 9000$. The annual depreciation ($a$) is $a=\frac{D}{6}=\frac{9000}{6}=1500$.
Step2: Calculate depreciation amount to reach target book - value
The initial value is $51000$ and the target book - value ($V_t$) is $43500$. The depreciation amount ($d$) to reach the target book - value is $d = 51000 - 43500=7500$.
Step3: Calculate number of years
Let the number of years be $n$. Since $d = a\times n$, then $n=\frac{d}{a}$. Substituting $d = 7500$ and $a = 1500$, we get $n=\frac{7500}{1500}=5$.
Answer:
5