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Sagot :
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].
[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].
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