Answered

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]$539,901 & 37\% \\
\hline
\end{tabular}

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

Determine the effective tax rate for a taxable income of \( \$[/tex]175,000 \). Round the final answer to the nearest hundredth.

A. [tex]\( 20.00\% \)[/tex]
B. [tex]\( 20.74\% \)[/tex]
C. [tex]\( 24.95\% \)[/tex]
D. [tex]\( 32.00\% \)[/tex]



Answer :

GinnyAnswer
Certainly! To determine the effective tax rate for a taxable income of [tex]$175,000, let's break down the solution step-by-step using the piecewise function provided. 1. Identify the appropriate tax bracket: - Since the taxable income is $[/tex]175,000, it falls within the range of [tex]$170,051 - $[/tex]215,950.
- According to the table, the marginal tax rate for this bracket is [tex]\( 32\% \)[/tex].

2. Using the piecewise function for the specified income:
- For the range [tex]\( 170,051 \leq x \leq 215,950 \)[/tex]:
[tex]\[ f(x) = 0.32x - 19,708.50 \][/tex]

3. Calculate the tax [tex]\( f(x) \)[/tex] for [tex]\( x = 175,000 \)[/tex]:
- Substitute [tex]\( x = 175,000 \)[/tex] into the piecewise function:
[tex]\[ f(175,000) = 0.32 \times 175,000 - 19,708.50 \][/tex]
- Perform the multiplication and subtraction:
[tex]\[ f(175,000) = 56,000 - 19,708.50 \][/tex]
[tex]\[ f(175,000) = 36,291.50 \][/tex]
- So, the total tax owed on [tex]$175,000 of taxable income is $[/tex]36,291.50.

4. Calculate the effective tax rate:
- The effective tax rate is the total tax divided by the taxable income, expressed as a percentage:
[tex]\[ \text{Effective Tax Rate} = \left( \frac{\text{Total Tax}}{\text{Taxable Income}} \right) \times 100 \][/tex]
- Substitute the values:
[tex]\[ \text{Effective Tax Rate} = \left( \frac{36,291.50}{175,000} \right) \times 100 \][/tex]
- Perform the division and then the multiplication:
[tex]\[ \text{Effective Tax Rate} \approx 20.738\% \][/tex]

5. Round the effective tax rate to the nearest hundredth:
- The effective tax rate rounded to the nearest hundredth is [tex]\( 20.74\% \)[/tex].

Therefore, the effective tax rate for a taxable income of $175,000 is 20.74\%.

So the correct answer is:
[tex]\[ \boxed{20.74\%} \][/tex]

Other Questions