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(Federal Income Taxes and Piecewise Functions MC)

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
\${content-ask}gt;539,901 & 37\% \\
\hline
\end{tabular}

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

Determine the effective tax rate for a taxable income of \$95,600. Round the final answer to the nearest hundredth.
[tex]17.00\%[/tex]



Answer :

GinnyAnswer
To determine the effective tax rate for a taxable income of [tex]$95,600, we will follow these steps: 1. Identify the Appropriate Tax Bracket: First, see which bracket $[/tex]95,600 falls into. According to the provided tax brackets, [tex]$95,600 falls in the range $[/tex]89,076 - [tex]$170,050$[/tex], which has a marginal tax rate of 24%.

2. Use the Piecewise Function: Since [tex]$95,600 is in the range $[/tex]89,076 - [tex]$170,050$[/tex], we will use the equation for this range:
[tex]\[ f(x) = 0.24x - 6,104.50 \][/tex]

3. Calculate the Taxes Owed: Substitute [tex]$95,600 for \( x \) in the piecewise function: \[ f(95,600) = 0.24 \cdot 95,600 - 6,104.50 \] 4. Perform the Calculation: \[ 0.24 \cdot 95,600 = 22,944 \] \[ 22,944 - 6,104.50 = 16,839.50 \] Therefore, the total taxes owed for a taxable income of $[/tex]95,600 is [tex]$16,839.50. 5. Calculate the Effective Tax Rate: The effective tax rate is the ratio of the taxes owed to the taxable income, expressed as a percentage. We calculate it using the formula: \[ \text{Effective Tax Rate} = \left( \frac{\text{Taxes Owed}}{\text{Taxable Income}} \right) \times 100 \] Substituting the values we have: \[ \text{Effective Tax Rate} = \left( \frac{16,839.50}{95,600} \right) \times 100 \approx 17.61\% \] 6. Round to the Nearest Hundredth: The effective tax rate, when rounded to the nearest hundredth, is \( 17.61\% \). Thus, the effective tax rate for a taxable income of $[/tex]95,600 is [tex]\( 17.61\% \)[/tex].

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