To determine the book value of a \[tex]$4,000 computer after 3 years using the given MACRS (Modified Accelerated Cost Recovery System) rates, we will compute the depreciation for each year, and subsequently, the book value.
The initial cost of the computer is \$[/tex]4,000.
### Year 1:
The MACRS rate for the first year is 20%.
First-year depreciation amount:
[tex]\[
\text{Depreciation}_{\text{year 1}} = \text{Initial Cost} \times \text{MACRS Rate}_{\text{year 1}} = 4000 \times 0.20 = 800
\][/tex]
Book value after year 1:
[tex]\[
\text{Book Value}_{\text{year 1}} = \text{Initial Cost} - \text{Depreciation}_{\text{year 1}} = 4000 - 800 = 3200
\][/tex]
### Year 2:
The MACRS rate for the second year is 32%.
Second-year depreciation amount:
[tex]\[
\text{Depreciation}_{\text{year 2}} = \text{Initial Cost} \times \text{MACRS Rate}_{\text{year 2}} = 4000 \times 0.32 = 1280
\][/tex]
Book value after year 2:
[tex]\[
\text{Book Value}_{\text{year 2}} = \text{Book Value}_{\text{year 1}} - \text{Depreciation}_{\text{year 2}} = 3200 - 1280 = 1920
\][/tex]
### Year 3:
The MACRS rate for the third year is 19.2%.
Third-year depreciation amount:
[tex]\[
\text{Depreciation}_{\text{year 3}} = \text{Initial Cost} \times \text{MACRS Rate}_{\text{year 3}} = 4000 \times 0.192 = 768
\][/tex]
Book value after year 3:
[tex]\[
\text{Book Value}_{\text{year 3}} = \text{Book Value}_{\text{year 2}} - \text{Depreciation}_{\text{year 3}} = 1920 - 768 = 1152
\][/tex]
Therefore, the book value of the \[tex]$4,000 computer after 3 years is \$[/tex]1,152.00, rounded to the nearest cent.
