To determine how much income tax Carol owes with a taxable income of $89,786, we use the given graduated tax schedule. Let's go through the detailed step-by-step calculations:
1. Identifying the Correct Tax Bracket:
Carol's taxable income is $89,786. We need to find which bracket this income falls into:
[tex]\[
\text{Brackets and rates:}
\begin{align*}
0 \, \text{to} \, \$7,825 & \quad 10\% \\
\[tex]$7,825 \, \text{to} \, \$[/tex]31,850 & \quad \[tex]$782.50 + 15\% \, \text{over} \, \$[/tex]7,825 \\
\[tex]$31,850 \, \text{to} \, \$[/tex]64,250 & \quad \[tex]$4,386.25 + 25\% \, \text{over} \, \$[/tex]31,850 \\
\[tex]$64,250 \, \text{to} \, \$[/tex]97,925 & \quad \[tex]$12,486.25 + 28\% \, \text{over} \, \$[/tex]64,250 \\
\[tex]$97,925 \, \text{to} \, \$[/tex]174,850 & \quad \[tex]$21,915.25 + 33\% \, \text{over} \, \$[/tex]97,925 \\
\[tex]$174,850+ & \quad \$[/tex]47,300.50 + 35\% \, \text{over} \, \$174,850 \\
\end{align*}
\][/tex]
Since [tex]$89,786$[/tex] falls into the bracket \[tex]$64,250 to \$[/tex]97,925, we will use the corresponding formula for that range:
2. Calculating the Base Tax:
The fixed tax amount for income up to \[tex]$64,250 is \$[/tex]12,486.25.
3. Calculating the Additional Tax:
- Subtract the lower limit of the bracket (\[tex]$64,250) from Carol's income (\$[/tex]89,786):
[tex]\[
89,786 - 64,250 = 25,536
\][/tex]
- Calculate 28% of the additional amount over \$64,250:
[tex]\[
25,536 \times 0.28 = 7,150.08
\][/tex]
4. Adding the Fixed Amount to the Additional Tax:
- Add the fixed base tax (\[tex]$12,486.25) to the calculated additional tax (\$[/tex]7,150.08):
[tex]\[
12,486.25 + 7,150.08 = 19,636.33
\][/tex]
5. Rounding to the Nearest Dollar:
- The calculated total tax amount is \[tex]$19,636.33. Rounding this to the nearest dollar gives us \$[/tex]19,636.
Therefore, Carol owes $19,636 in income tax.
The correct answer is:
c. \$19,636
