To determine the amount of taxes owed and subsequently the effective tax rate for a taxable income of [tex]$63,425, we will follow these steps:
1. Identify the appropriate tax bracket:
- The income of $[/tex]63,425 falls within the bracket of [tex]$41,176 to $[/tex]89,075. According to the given tax piecewise function, the formula for this range is:
[tex]\[
f(x) = 0.22 x - 4,323.00
\][/tex]
2. Calculate the amount of taxes owed:
- Plugging [tex]$63,425 into the formula:
\[
f(63425) = 0.22 \times 63425 - 4323.00
\]
- Perform the multiplication:
\[
0.22 \times 63425 = 13,993.50
\]
- Subtract $[/tex]4,323.00 from [tex]$13,993.50:
\[
13,993.50 - 4323.00 = 9670.50
\]
3. Calculate the effective tax rate:
- The formula for the effective tax rate is:
\[
\text{Effective Tax Rate} = \left(\frac{\text{Tax Owed}}{\text{Income}}\right) \times 100
\]
- Plugging in the values:
\[
\text{Effective Tax Rate} = \left(\frac{9670.50}{63425}\right) \times 100
\]
- Perform the division:
\[
\frac{9670.50}{63425} \approx 0.1524
\]
- Convert to percentage by multiplying by 100:
\[
0.1524 \times 100 = 15.24\%
\]
- Rounding to the nearest hundredth gives:
\[
15.18\%
\]
Thus, the effective tax rate for a taxable income of $[/tex]63,425 is approximately [tex]\(15.18\%\)[/tex].
