To determine the effective tax rate for a taxable income of \[tex]$63,425 using the provided marginal tax rate chart and bracket formulas, follow these steps:
1. Determine the tax bracket of the given income (\$[/tex]63,425) using the tax bracket ranges:
- \[tex]$0 to \$[/tex]10,275: 10%
- \[tex]$10,276 to \$[/tex]41,175: 12%
- \[tex]$41,176 to \$[/tex]89,075: 22%
- \[tex]$89,076 to \$[/tex]170,050: 24%
- \[tex]$170,051 to \$[/tex]215,950: 32%
- \[tex]$215,951 to \$[/tex]539,900: 35%
- \[tex]$539,901 and above: 37%
\$[/tex]63,425 falls into the \[tex]$41,176 to \$[/tex]89,075 bracket, which has a marginal tax rate of 22%.
2. Use the piecewise function for the appropriate tax calculation:
- For \[tex]$41,176 to \$[/tex]89,075, the function is [tex]\(0.22x - 4,323.00\)[/tex].
3. Substitute \[tex]$63,425 for \(x\) in the formula:
\[
\text{tax} = 0.22 \times 63,425 - 4,323.00
\]
4. Calculate the tax:
\[
\text{tax} = 0.22 \times 63,425 - 4,323.00
\]
\[
\text{tax} = 13,953.50 - 4,323.00
\]
\[
\text{tax} = 9,630.50
\]
5. Compute the effective tax rate:
\[
\text{effective tax rate} = \left(\frac{\text{tax}}{\text{income}}\right) \times 100
\]
\[
\text{effective tax rate} = \left(\frac{9,630.50}{63,425}\right) \times 100
\]
\[
\text{effective tax rate} \approx 15.18\%
\]
Therefore, the effective tax rate for a taxable income of \$[/tex]63,425 is approximately [tex]\( \boxed{15.18\%} \)[/tex].
