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Question 1 (Multiple Choice, Worth 3 points)

The piecewise function represents the amount of taxes owed, [tex]f(x)[/tex], as a function of the taxable income, [tex]x[/tex]. Use the marginal tax rate chart or the piecewise function to answer the question.

Marginal Tax Rate Chart

\begin{tabular}{|c|c|}
\hline Tax Bracket & Marginal Tax Rate \\
\hline \[tex]$0 - \$[/tex]10,275 & 10\% \\
\hline \[tex]$10,276 - \$[/tex]41,175 & 12\% \\
\hline \[tex]$41,176 - \$[/tex]89,075 & 22\% \\
\hline \[tex]$89,076 - \$[/tex]170,050 & 24\% \\
\hline \[tex]$170,051 - \$[/tex]215,950 & 32\% \\
\hline \[tex]$215,951 - \$[/tex]539,900 & 35\% \\
\hline >\$539,901 & 37\% \\
\hline
\end{tabular}

Piecewise Function:
\[
f(x) = \left\{
\begin{array}{l l}
0.10x & \text{if } 0 \leq x \leq 10,275 \\
0.12x - 205.50 & \text{if } 10,276 \leq x \leq 41,175 \\
0.22x - 4,323.00 & \text{if } 41,176 \leq x \leq 89,075 \\
0.24x - 6,104.50 & \text{if } 89,076 \leq x \leq 170,050 \\
0.32x - 19,708.50 & \text{if } 170,051 \leq x \leq 215,950 \\
0.35x - 26,187.00 & \text{if } 215,951 \leq x \leq 539,900 \\
0.37x - 36,985.00 & \text{if } x \geq 539,901 \\
\end{array}
\right.
\]

Determine the effective tax rate for a taxable income of [tex]\$95,600[/tex]. Round the final answer to the nearest hundredth.

A. 17.00%
B. 17.61%
C. 22.70%
D. 24.00%



Answer :

GinnyAnswer
To determine the effective tax rate for a taxable income of [tex]$95,600, let's follow the steps to compute the tax owed and the effective tax rate. 1. Identify the Tax Bracket: - Taxable income: $[/tex]95,600
- From the given table, the [tex]$95,600 falls within the tax bracket of $[/tex]89,076 to [tex]$170,050 which has a marginal tax rate of 24%. 2. Calculate the Tax Owed: - The formula for this tax bracket is \(0.24x - 6104.50\). - Plugging in the taxable income: \[ Tax\ Owed = 0.24 \times 95,600 - 6,104.50 = 22,944 - 6,104.50 = 16,839.50 \] 3. Compute the Effective Tax Rate: - Effective Tax Rate \(= \left(\frac{Tax\ Owed}{Taxable\ Income}\right) \times 100\%\) - Using the values: \[ Effective Tax Rate = \left(\frac{16,839.50}{95,600}\right) \times 100\% \approx 17.61\% \] So, the effective tax rate for a taxable income of $[/tex]95,600 is approximately 17.61%, rounded to the nearest hundredth. Hence, the correct answer is:

- [tex]$17.61 \%$[/tex]

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