Question 5 (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 [tex]$f$[/tex].

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}

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

Determine the effective tax rate for a taxable income of $\$[/tex]63,425$. Round the final answer to the nearest hundredth.

A. 10\%
B. 14.67\%

To determine the effective tax rate for a taxable income of [tex]$63,425, we need to follow these steps: 1. Identify the applicable tax bracket: From the given piecewise function and the tax bracket chart, we see that a taxable income of $[/tex]63,425 falls in the range of [tex]$41,176 - $[/tex]89,075.

2. Calculate the tax owed:
For the tax bracket [tex]$41,176 - $[/tex]89,075[tex]$, the tax formula is: \[ f(x) = 0.22x - 4,323.00 \] Substituting $[/tex]x = 63,425[tex]$: \[ f(63,425) = 0.22 \cdot 63,425 - 4,323.00 \] \[ = 13,953.50 - 4,323.00 \] \[ = 9,630.50 \] So, the tax owed is $[/tex]9,630.50.

3. Calculate the effective tax rate:
The effective tax rate is calculated by dividing the tax owed by the taxable income and then multiplying by 100 to get a percentage:
[tex]\[ \text{Effective Tax Rate} = \left(\frac{\text{Tax Owed}}{\text{Taxable Income}}\right) \times 100 \][/tex]
Substituting in the values:
[tex]\[ \text{Effective Tax Rate} = \left(\frac{9,630.50}{63,425}\right) \times 100 \][/tex]
[tex]\[ = \left(\frac{9,630.50}{63,425}\right) \times 100 \][/tex]
[tex]\[ \approx 15.18\% \][/tex]

Therefore, the effective tax rate for a taxable income of $63,425 is approximately 15.18%.