To determine the effective tax rate for a taxable income of [tex]\( \$95,600 \)[/tex], we'll follow these steps:
1. Identify the Tax Bracket:
Given the taxable income [tex]\( \$95,600 \)[/tex], we need to determine which tax bracket it falls into. From the chart provided, [tex]\( \$95,600 \)[/tex] falls in the bracket:
[tex]\[
\$89,076 \leq x \leq \$170,050
\][/tex]
with a marginal tax rate of 24%.
2. Calculate the Taxes Owed:
Using the piecewise function defined for this bracket ([tex]\( 0.24x - 6104.50 \)[/tex]):
[tex]\[
f(x) = 0.24 \cdot 95,600 - 6104.50
\][/tex]
Calculate the taxes:
[tex]\[
f(95,600) = 0.24 \cdot 95,600 - 6104.50 = 22,944 - 6104.50 = 16,839.50
\][/tex]
So, the taxes owed are [tex]\( \$16,839.50 \)[/tex].
3. Calculate the Effective Tax Rate:
The effective tax rate is calculated as the total tax owed divided by the taxable income, then multiplied by 100 to convert it to a percentage:
[tex]\[
\text{Effective Tax Rate} = \left( \frac{\text{Tax Owed}}{\text{Taxable Income}} \right) \times 100
\][/tex]
Substituting the values:
[tex]\[
\text{Effective Tax Rate} = \left( \frac{16,839.50}{95,600} \right) \times 100 = 0.1761 \times 100 = 17.61\%
\][/tex]
Therefore, the effective tax rate for a taxable income of [tex]\( \$95,600 \)[/tex] is [tex]\( 17.61\% \)[/tex].
The correct answer is:
[tex]\[ 17.61\% \][/tex]
