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Question 1 (Multiple Choice Worth 3 points)

(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
\end{tabular}

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

Determine the effective tax rate for a taxable income of \$63,425. Round the final answer to the nearest hundredth.
A. 10\%
B. 14.67\%



Answer :

GinnyAnswer
To determine the amount of taxes owed and subsequently the effective tax rate for a taxable income of [tex]$63,425, we will follow these steps: 1. Identify the appropriate tax bracket: - The income of $[/tex]63,425 falls within the bracket of [tex]$41,176 to $[/tex]89,075. According to the given tax piecewise function, the formula for this range is:
[tex]\[ f(x) = 0.22 x - 4,323.00 \][/tex]

2. Calculate the amount of taxes owed:
- Plugging [tex]$63,425 into the formula: \[ f(63425) = 0.22 \times 63425 - 4323.00 \] - Perform the multiplication: \[ 0.22 \times 63425 = 13,993.50 \] - Subtract $[/tex]4,323.00 from [tex]$13,993.50: \[ 13,993.50 - 4323.00 = 9670.50 \] 3. Calculate the effective tax rate: - The formula for the effective tax rate is: \[ \text{Effective Tax Rate} = \left(\frac{\text{Tax Owed}}{\text{Income}}\right) \times 100 \] - Plugging in the values: \[ \text{Effective Tax Rate} = \left(\frac{9670.50}{63425}\right) \times 100 \] - Perform the division: \[ \frac{9670.50}{63425} \approx 0.1524 \] - Convert to percentage by multiplying by 100: \[ 0.1524 \times 100 = 15.24\% \] - Rounding to the nearest hundredth gives: \[ 15.18\% \] Thus, the effective tax rate for a taxable income of $[/tex]63,425 is approximately [tex]\(15.18\%\)[/tex].