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Mary pays income tax according to the graduated schedule shown below.




If taxable income is over-		But not over- -The tax is:

\$0		\$7,82510\% of the amount over \$0

\$7,825		\$31,850\$782.50 plus 15\% of the amount over 7,825

\$31,850		\$77,100\$4,386.25 plus 25\% of the amount over 31,850

\$77,100		\$160,850\$15,698.75 plus 28\% of the amount over 77,100

\$160,850		\$349,700\$39,148.75 plus 33\% of the amount over 160,850

\$349,700		no limit\$101.469.25 plus 35\% of the amount over 349,700






If Mary's taxable income is $\$ 68,562$, how much income tax does she owe, rounded to the nearest dollar?


A\$13,564
B\$17,140
C\$ 21,527
D\$12,349

Verified Answer :

  • Identify the applicable tax bracket for an income of \(\$68,562\), which is \(\$4,386.25 + 0.25 \times (\text{Income} - \$31,850)\).
  • Subtract the bracket threshold from the total income: \(\$68,562 - \$31,850 = \$36,712\).
  • Apply the tax rate to the difference: \(0.25 \times \$36,712 = \$9,178\).
  • Sum the base tax and the calculated portion: \(\$4,386.25 + \$9,178 = \$13,564.25\), rounding to \(\boxed{\text{a. } \$13,564}\).

Explanation

  1. Identifying the Tax Bracket

To determine the income tax Mary owes, we must identify her applicable tax bracket based on her taxable income of \(\$68,562\). Examining the provided tax schedule, we see that an income of \(\$68,562\) falls into the range where income is over \(\$31,850\) but not over \(\$77,100\). In this range, the tax is calculated as \(\$4,386.25\) plus \(25\%\) of the amount that exceeds \(\$31,850\).

  1. Calculating the Tax Amount

First, we find the portion of Mary's income that is subject to the \(25\%\) tax rate:
\[\$68,562 - \$31,850 = \$36,712\]
Next, we calculate \(25\%\) of this amount:
\[0.25 \times \$36,712 = \$9,178\]
Finally, we add the base tax amount of \(\$4,386.25\) to this result to find the total tax:
\[\text{Total Tax} = \$4,386.25 + \$9,178 = \$13,564.25\]
Rounding \(\$13,564.25\) to the nearest dollar gives us \(\$13,564\). Comparing this to the provided options, it corresponds to option (a).

Examples

Understanding progressive tax brackets is essential for personal finance management. For example, if you are planning your budget, knowing how your income is taxed allows you to accurately estimate your net (take-home) pay. This is a practical application of linear functions and percentage calculations, ensuring you are prepared for tax obligations at different income levels.

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