To determine the book value of a [tex]$\$[/tex]2500[tex]$ computer after 3 years using the MACRS rates provided, we'll follow these steps:
1. Identify the MACRS rates for each of the first three years:
- Year 1: \(20.0\% = 0.20\)
- Year 2: \(32.0\% = 0.32\)
- Year 3: \(19.2\% = 0.192\)
2. Calculate the depreciation for each of the three years:
- Depreciation for Year 1:
\[
\text{Depreciation Year 1} = \$[/tex]2500 \times 0.20 = \[tex]$500.00
\]
- Depreciation for Year 2:
\[
\text{Depreciation Year 2} = \$[/tex]2500 \times 0.32 = \[tex]$800.00
\]
- Depreciation for Year 3:
\[
\text{Depreciation Year 3} = \$[/tex]2500 \times 0.192 = \[tex]$480.00
\]
3. Calculate the accumulated depreciation over the first three years:
\[
\text{Accumulated Depreciation} = \$[/tex]500.00 + \[tex]$800.00 + \$[/tex]480.00 = \[tex]$1780.00
\]
4. Determine the book value after 3 years:
\[
\text{Book Value} = \$[/tex]2500 - \[tex]$1780.00 = \$[/tex]720.00
\]
Therefore, the book value of the computer after 3 years is [tex]\(\$720.00\)[/tex].
