QuestionJune 5, 2025

A printer is purchased for 1,600 and has a resale value of 300 after a useful life of 5 years . Using a book value depreciation chart calculate the number of years until the book value of the printer is 820 () years

A printer is purchased for 1,600 and has a resale value of 300 after a useful life of 5 years . Using a book value depreciation chart calculate the number of years until the book value of the printer is 820 () years
A printer is purchased for 1,600 and has
a resale value of 300 after a useful life
of 5 years . Using a book value
depreciation chart calculate the number
of years until the book value of the
printer is 820
() years

Solution
4.4(414 votes)

Answer

3 years Explanation 1. Calculate Annual Depreciation Use the formula for straight-line depreciation: **Depreciation = \frac{\text{Initial Cost} - \text{Resale Value}}{\text{Useful Life}}**. Here, it is \frac{1600 - 300}{5} = 260 per year. 2. Determine Book Value Equation The book value after ( n ) years is given by: **Book Value = \text{Initial Cost} - (\text{Depreciation} \times n)**. Substitute to get: 1600 - 260n. 3. Solve for Years Until Book Value is \820 Set the equation from Step 2 equal to 820: 1600 - 260n = 820. Solve for ( n ): \[ 1600 - 820 = 260n \] \[ 780 = 260n \] \[ n = \frac{780}{260} = 3 \]

Explanation

1. Calculate Annual Depreciation<br /> Use the formula for straight-line depreciation: **Depreciation = \frac{\text{Initial Cost} - \text{Resale Value}}{\text{Useful Life}}**. Here, it is $\frac{1600 - 300}{5} = 260$ per year.<br /><br />2. Determine Book Value Equation<br /> The book value after ( n ) years is given by: **Book Value = \text{Initial Cost} - (\text{Depreciation} \times n)**. Substitute to get: $1600 - 260n$.<br /><br />3. Solve for Years Until Book Value is \$820<br /> Set the equation from Step 2 equal to 820: $1600 - 260n = 820$. Solve for ( n ): <br />\[ 1600 - 820 = 260n \]<br />\[ 780 = 260n \]<br />\[ n = \frac{780}{260} = 3 \]
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