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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}{|l|l|}
\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
> \[tex]$539,901 & 37\% \\
\hline
\end{tabular}

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

Determine the effective tax rate for a taxable income of \( \$[/tex]95,600 \). 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]\( \$95,600 \)[/tex], we'll follow these steps:

1. Identify the Tax Bracket:
Given the taxable income [tex]\( \$95,600 \)[/tex], we need to determine which tax bracket it falls into. From the chart provided, [tex]\( \$95,600 \)[/tex] falls in the bracket:
[tex]\[ \$89,076 \leq x \leq \$170,050 \][/tex]
with a marginal tax rate of 24%.

2. Calculate the Taxes Owed:
Using the piecewise function defined for this bracket ([tex]\( 0.24x - 6104.50 \)[/tex]):
[tex]\[ f(x) = 0.24 \cdot 95,600 - 6104.50 \][/tex]
Calculate the taxes:
[tex]\[ f(95,600) = 0.24 \cdot 95,600 - 6104.50 = 22,944 - 6104.50 = 16,839.50 \][/tex]
So, the taxes owed are [tex]\( \$16,839.50 \)[/tex].

3. Calculate the Effective Tax Rate:
The effective tax rate is calculated as the total tax owed divided by the taxable income, then multiplied by 100 to convert it to a percentage:
[tex]\[ \text{Effective Tax Rate} = \left( \frac{\text{Tax Owed}}{\text{Taxable Income}} \right) \times 100 \][/tex]
Substituting the values:
[tex]\[ \text{Effective Tax Rate} = \left( \frac{16,839.50}{95,600} \right) \times 100 = 0.1761 \times 100 = 17.61\% \][/tex]

Therefore, the effective tax rate for a taxable income of [tex]\( \$95,600 \)[/tex] is [tex]\( 17.61\% \)[/tex].

The correct answer is:
[tex]\[ 17.61\% \][/tex]

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