To find the book value of a [tex]$2,500 computer after 3 years using the MACRS rates, follow these steps:
1. Initial Value:
\[
\text{Initial Value} = \$[/tex]2,500
\]
2. MACRS Rates:
[tex]\[
\text{Year 1} = 20.0\%
\][/tex]
[tex]\[
\text{Year 2} = 32.0\%
\][/tex]
[tex]\[
\text{Year 3} = 19.2\%
\][/tex]
3. Calculate depreciation for each year:
- Year 1:
[tex]\[
\text{Depreciation}_{\text{Year 1}} = \$2,500 \times 0.20 = \$500
\][/tex]
- Year 2:
[tex]\[
\text{Remaining Value after Year 1} = \$2,500 - \$500 = \$2,000
\][/tex]
[tex]\[
\text{Depreciation}_{\text{Year 2}} = \$2,000 \times 0.32 = \$640
\][/tex]
- Year 3:
[tex]\[
\text{Remaining Value after Year 2} = \$2,000 - \$640 = \$1,360
\][/tex]
[tex]\[
\text{Depreciation}_{\text{Year 3}} = \$1,360 \times 0.192 = \$261.12
\][/tex]
4. Total depreciation over 3 years:
[tex]\[
\text{Total Depreciation} = \$500 + \$640 + \$261.12 = \$1,401.12
\][/tex]
5. Calculate book value after 3 years:
[tex]\[
\text{Book Value} = \$2,500 - \$1,401.12 = \$1,098.88
\][/tex]
Result:
After 3 years, the book value of the computer is:
[tex]\[
\boxed{\$1,098.88}
\][/tex]
