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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:

\begin{tabular}{|l|l|}
\hline
\multicolumn{1}{|c|}{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]$ \ \textgreater \ 539,901 & 37\% \\
\hline
\end{tabular}

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

Determine the effective tax rate for a taxable income of \$[/tex]192,700. Round the final answer to the nearest hundredth.

A. 32.00\%

B. 21.77\%

C. 24.00\%

D. 18.57\%



Answer :

GinnyAnswer
To determine the amount of taxes owed and the effective tax rate for a taxable income of [tex]$192,700, we need to follow the steps outlined below: 1. Identify the correct tax bracket for $[/tex]192,700:
Based on the tax bracket chart:
- [tex]$0 - $[/tex]10,275 at 10%
- [tex]$10,276 - $[/tex]41,175 at 12%
- [tex]$41,176 - $[/tex]89,075 at 22%
- [tex]$89,076 - $[/tex]170,050 at 24%
- [tex]$170,051 - $[/tex]215,950 at 32%
- [tex]$215,951 - $[/tex]539,900 at 35%
- [tex]${data-answer}gt;539,901 at 37% The taxable income of $[/tex]192,700 falls within the [tex]$170,051 to $[/tex]215,950 bracket, taxed at 32%.

2. Use the piecewise function for the correct bracket:
For the bracket [tex]$170,051 to $[/tex]215,950, the tax owed formula is:
[tex]\[ f(x) = 0.32x - 19708.50 \][/tex]
Plugging in [tex]$192,700 for $[/tex]x[tex]$ yields: \[ f(192700) = 0.32 \times 192700 - 19708.50 \] 3. Calculate the tax owed: \[ f(192700) = 0.32 \times 192700 - 19708.50 = 61664 - 19708.50 = 41955.5 \] Thus, the tax owed on a taxable income of $[/tex]192,700 is [tex]$41,955.50. 4. Calculate the effective tax rate: The effective tax rate is calculated as the percentage of the income that is paid in taxes. \[ \text{Effective Tax Rate} = \left( \frac{\text{Tax Owed}}{\text{Taxable Income}} \right) \times 100 \] Substituting the known values: \[ \text{Effective Tax Rate} = \left( \frac{41955.5}{192700} \right) \times 100 \approx 21.77\% \] The effective tax rate should be rounded to the nearest hundredth, which is $[/tex]21.77\%[tex]$. Conclusion: The effective tax rate for a taxable income of $[/tex]192,700 is [tex]$\boxed{21.77\%}$[/tex].

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