Determine the effective tax rate for a taxable income of \[tex]$63,425. Round the final answer to the nearest hundredth.

Marginal Tax Rate Chart
\begin{tabular}{|l|l|}
\hline
Tax Bracket & Marginal Tax Rate \\
\hline
\$[/tex]0-\[tex]$10,275 & 10\% \\
\hline
\$[/tex]10,276-\[tex]$41,175 & 12\% \\
\hline
\$[/tex]41,176-\[tex]$89,075 & 22\% \\
\hline
\$[/tex]89,076-\[tex]$170,050 & 24\% \\
\hline
\$[/tex]170,051-\[tex]$215,950 & 32\% \\
\hline
\$[/tex]215,951-\[tex]$539,900 & 35\% \\
\hline
\$[/tex]>539,901 & 37\% \\
\hline
\end{tabular}

Piecewise Function
[tex]\[ f(x)=\left\{
\begin{array}{ll}
0.10x & \text{if } 0 \leq x \leq 10,275 \\
0.12x - 205.50 & \text{if } 10,276 \leq x \leq 41,175 \\
0.22x - 4,323.00 & \text{if } 41,176 \leq x \leq 89,075 \\
0.24x - 6,104.50 & \text{if } 89,076 \leq x \leq 170,050 \\
0.32x - 19,708.50 & \text{if } 170,051 \leq x \leq 215,950 \\
0.35x - 26,187.00 & \text{if } 215,951 \leq x \leq 539,900 \\
0.37x - 36,985.00 & \text{if } x \geq 539,901
\end{array}\right.
\][/tex]

Options:
A. 10\%
B. 14.67\%
C. 15.18\%
D. 22\%



Answer :

To determine the effective tax rate for a taxable income of [tex]$63,425, we need to follow a structured approach using the given piecewise function and tax brackets. 1. Identify which tax bracket the income falls into: - The income of $[/tex]63,425 falls into the third bracket: [tex]\( \$41,176 \leq x \leq \$89,075 \)[/tex], which means the tax rate is [tex]\( 22\% \)[/tex].

2. Apply the corresponding piecewise function:
- For income in the range of [tex]\( \$41,176 \)[/tex] to [tex]\( \$89,075 \)[/tex], the tax owed can be calculated using the formula:
[tex]\[ f(x) = 0.22x - 4,323.00 \][/tex]

3. Calculate the tax owed:
- Substitute [tex]\( x = \$63,425 \)[/tex] into the piecewise function:
[tex]\[ f(63,425) = 0.22 \times 63,425 - 4,323.00 \][/tex]

4. Compute the tax value:
[tex]\[ f(63,425) = 0.22 \times 63,425 = 13,953.50 \][/tex]
[tex]\[ f(63,425) - 4,323.00 = 13,953.50 - 4,323.00 = 9,630.50 \][/tex]

So, the tax owed for an income of [tex]$63,425 is $[/tex]9,630.50.

5. Determine the effective tax rate:
- The effective tax rate is calculated by dividing the total tax by the total income and then multiplying by 100 to get a percentage:
[tex]\[ \text{Effective Tax Rate} = \left( \frac{\text{Tax}}{\text{Income}} \right) \times 100 \][/tex]
- Substitute the values into the formula:
[tex]\[ \text{Effective Tax Rate} = \left( \frac{9,630.50}{63,425} \right) \times 100 \][/tex]

6. Compute the effective tax rate:
- Perform the division:
[tex]\[ \frac{9,630.50}{63,425} \approx 0.1518 \][/tex]
- Convert to a percentage:
[tex]\[ 0.1518 \times 100 = 15.18\% \][/tex]

Therefore, the effective tax rate for a taxable income of $63,425 is [tex]\( 15.18\% \)[/tex].

The correct answer is [tex]\( 15.18\% \)[/tex].