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Using the MACRS rates from the following table, what is the book value of a [tex]\$2,500[/tex] computer after 4 years?

\begin{tabular}{|c|r|}
\hline Year & MACRS Rate \\
\hline 1 & 20.0\% \\
\hline 2 & 32.0\% \\
\hline 3 & 19.2\% \\
\hline 4 & 11.52\% \\
\hline 5 & 11.52\% \\
\hline 6 & 5.76\% \\
\hline
\end{tabular}

Book Value [tex]=\$[?][/tex]

Round to the nearest cent.

Sagot :

GinnyAnsweridn
To determine the book value of the computer after 4 years using the MACRS (Modified Accelerated Cost Recovery System) rates, let's follow a detailed step-by-step approach:

### Initial Value and MACRS Rates
We start with an initial book value of the computer:
- Initial Value = \[tex]$2,500 The MACRS rates for each year are provided as follows: - Year 1: 20.0% - Year 2: 32.0% - Year 3: 19.2% - Year 4: 11.52% - Year 5: 11.52% - Year 6: 5.76% ### Step-by-Step Depreciation Calculation #### Year 1 Depreciation: - Depreciation for Year 1 = Initial Value * MACRS Rate for Year 1 - Depreciation for Year 1 = \$[/tex]2,500 20.0% = \[tex]$2,500 0.20 = \$[/tex]500

#### Year 2 Depreciation:
- Depreciation for Year 2 = Initial Value MACRS Rate for Year 2
- Depreciation for Year 2 = \[tex]$2,500 32.0% = \$[/tex]2,500 * 0.32 = \[tex]$800 #### Year 3 Depreciation: - Depreciation for Year 3 = Initial Value * MACRS Rate for Year 3 - Depreciation for Year 3 = \$[/tex]2,500 19.2% = \[tex]$2,500 0.192 = \$[/tex]480

#### Year 4 Depreciation:
- Depreciation for Year 4 = Initial Value MACRS Rate for Year 4
- Depreciation for Year 4 = \[tex]$2,500 11.52% = \$[/tex]2,500 * 0.1152 = \[tex]$288 ### Total Depreciation After 4 Years - Total Depreciation = Depreciation for Year 1 + Depreciation for Year 2 + Depreciation for Year 3 + Depreciation for Year 4 - Total Depreciation = \$[/tex]500 + \[tex]$800 + \$[/tex]480 + \[tex]$288 = \$[/tex]2,068

### Book Value After 4 Years
- Book Value = Initial Value - Total Depreciation
- Book Value = \[tex]$2,500 - \$[/tex]2,068 = \[tex]$432 ### Summary The book value of the computer after 4 years, rounded to the nearest cent, is: - Book Value = \$[/tex]432.00

Thus, the book value of the \[tex]$2,500 computer after 4 years is \$[/tex]432.00.
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