To determine the effective tax rate for a taxable income of \[tex]$23,470, we need to calculate the total tax owed based on the given marginal tax rates and then find the effective tax rate.
Step-by-Step Solution:
1. Identify the income ranges for each tax bracket and their corresponding marginal tax rates:
- \$[/tex]0 - \[tex]$10,275 at 10%
- \$[/tex]10,276 - \[tex]$41,175 at 12%
- \$[/tex]41,176 - \[tex]$89,075 at 22%
- \$[/tex]89,076 - \[tex]$170,050 at 24%
- \$[/tex]170,051 - \[tex]$215,950 at 32%
- \$[/tex]215,951 - \[tex]$539,900 at 35%
- Over \$[/tex]539,901 at 37%
2. Break down the income of \[tex]$23,470 into the relevant tax brackets:
- The first \$[/tex]10,275 is taxed at 10%.
- The next portion, from \[tex]$10,276 to \$[/tex]23,470, falls into the 12% bracket.
3. Calculate the tax for each portion of the income:
- For the first \[tex]$10,275 at 10%:
\[
\text{Tax for the first bracket} = 10,275 \times 0.10 = 1,027.50
\]
- For the income from \$[/tex]10,276 to \[tex]$23,470 (which is \$[/tex]13,195) at 12%:
[tex]\[
\text{Tax for the second bracket} = (23,470 - 10,275) \times 0.12 = 13,195 \times 0.12 = 1,583.40
\][/tex]
4. Sum the taxes for all brackets:
[tex]\[
\text{Total tax} = 1,027.50 + 1,583.40 = 2,610.90
\][/tex]
5. Calculate the effective tax rate:
[tex]\[
\text{Effective tax rate} = \left(\frac{\text{Total tax}}{\text{Total income}}\right) \times 100 = \left(\frac{2,610.90}{23,470}\right) \times 100 \approx 11.12\%
\][/tex]
6. Round to the nearest hundredth:
[tex]\[
\text{Effective tax rate} \approx 11.12\%
\][/tex]
Thus, the effective tax rate for a taxable income of \$23,470 is 11.12%.
