Questions: 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 45,000. [?] years

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 45,000.
[?] years

Transcript text: 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 $\$ 45,000$. $[?]$ years

Solution

Solution Steps

Step 1: Determine the Annual Depreciation Rate

The annual depreciation rate is calculated using the formula $\frac{P - R}{L}$, where $P$ is the initial purchase price, $R$ is the resale value, and $L$ is the useful life. Substituting the given values, we get $\frac{51000 - 42000}{6} = 1500$.

Step 2: Calculate the Yearly Book Value and Count the Number of Years

Starting from the initial purchase price of $51000$, we subtract the annual depreciation of $1500$ for each year until the book value reaches or falls below the target book value of $45000$.