To determine the book value of a [tex]$3,000 computer after 3 years using the MACRS (Modified Accelerated Cost Recovery System) depreciation rates, we need to follow these steps:
### Step 1: Calculate the depreciation for the 1st year
The initial value of the computer is $[/tex]3,000.
The MACRS rate for the 1st year is 20.0%.
[tex]\[
\text{Depreciation for Year 1} = 3000 \times 0.20 = \$600.00
\][/tex]
[tex]\[
\text{Book Value after Year 1} = 3000 - 600 = \$2400.00
\][/tex]
### Step 2: Calculate the depreciation for the 2nd year
The book value at the start of the 2nd year is [tex]$2,400.
The MACRS rate for the 2nd year is 32.0%.
\[
\text{Depreciation for Year 2} = 2400 \times 0.32 = \$[/tex]768.00
\]
[tex]\[
\text{Book Value after Year 2} = 2400 - 768 = \$1632.00
\][/tex]
### Step 3: Calculate the depreciation for the 3rd year
The book value at the start of the 3rd year is [tex]$1,632.
The MACRS rate for the 3rd year is 19.2%.
\[
\text{Depreciation for Year 3} = 1632 \times 0.192 = \$[/tex]313.344
\]
[tex]\[
\text{Book Value after Year 3} = 1632 - 313.344 = \$1318.66
\][/tex]
### Final Answer
The book value of the [tex]$3,000 computer after 3 years is approximately \$[/tex]1,318.66, rounded to the nearest cent.
