To determine the effective tax rate for a taxable income of [tex]$95,600, we will follow these steps:
1. Identify the Appropriate Tax Bracket: First, see which bracket $[/tex]95,600 falls into. According to the provided tax brackets, [tex]$95,600 falls in the range $[/tex]89,076 - [tex]$170,050$[/tex], which has a marginal tax rate of 24%.
2. Use the Piecewise Function: Since [tex]$95,600 is in the range $[/tex]89,076 - [tex]$170,050$[/tex], we will use the equation for this range:
[tex]\[
f(x) = 0.24x - 6,104.50
\][/tex]
3. Calculate the Taxes Owed: Substitute [tex]$95,600 for \( x \) in the piecewise function:
\[
f(95,600) = 0.24 \cdot 95,600 - 6,104.50
\]
4. Perform the Calculation:
\[
0.24 \cdot 95,600 = 22,944
\]
\[
22,944 - 6,104.50 = 16,839.50
\]
Therefore, the total taxes owed for a taxable income of $[/tex]95,600 is [tex]$16,839.50.
5. Calculate the Effective Tax Rate: The effective tax rate is the ratio of the taxes owed to the taxable income, expressed as a percentage. We calculate it using the formula:
\[
\text{Effective Tax Rate} = \left( \frac{\text{Taxes Owed}}{\text{Taxable Income}} \right) \times 100
\]
Substituting the values we have:
\[
\text{Effective Tax Rate} = \left( \frac{16,839.50}{95,600} \right) \times 100 \approx 17.61\%
\]
6. Round to the Nearest Hundredth: The effective tax rate, when rounded to the nearest hundredth, is \( 17.61\% \).
Thus, the effective tax rate for a taxable income of $[/tex]95,600 is [tex]\( 17.61\% \)[/tex].
