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Using the MACRS rates from the table, calculate the book value of a [tex]$3,000 computer after 3 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 = $[/tex][?]$
(Round to the nearest cent.)


Sagot :

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.