Answered

Carol uses this graduated tax schedule to determine how much income tax she owes.




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		\$64,250\$4,386.25 plus 25\% of the amount over 31,850

\$64,250		\$97,925\$12,486.25 plus 28\% of the amount over 64,250

\$97,925		\$174,850\$21,915.25 plus 33\% of the amount over 97,925

\$174,850		no limit\$47,300.50 plus 35\% of the amount over 174,850






If Carol's taxable income is \$89,786, how much income tax does she owe, to the nearest dollar?


A\$25,140
B\$12,654
C\$19,636
D\$37,626

Verified Answer :

  • Determine the appropriate tax bracket for Carol's income of \(\$89,786\), which is \(\$64,250 < \text{income} \leq \$97,925\).
  • Calculate the excess income above the threshold: \(\$89,786 - \$64,250 = \$25,536\).
  • Apply the tax rate for the bracket to the excess and add the base tax: \(\$12,486.25 + (\$25,536 \times 0.28) = \$19,636.33\).
  • Round the result to the nearest dollar, arriving at the final answer of \(\boxed{\$19,636}\), which is option c.

Explanation

  1. Identifying the Tax Bracket

To determine Carol's total income tax, we must identify which tax bracket her income of \(\$89,786\) falls into based on the provided table. The table indicates that an income over \(\$64,250\) but not over \(\$97,925\) is taxed according to the rule: \(\$12,486.25\) plus \(28\%\) of the amount exceeding \(\$64,250\).

  1. Calculating the Taxable Excess Amount

Next, we calculate the portion of Carol's income that is subject to the \(28\%\) tax rate by subtracting the lower limit of the bracket from her total income:
\[\$89,786 - \$64,250 = \$25,536\]
This is the amount of income that exceeds the \(\$64,250\) threshold.

  1. Calculating the Total Tax Owed

We then calculate the tax on this excess amount by multiplying \(\$25,536\) by \(28\%\):
\[\$25,536 \times 0.28 = \$7,150.08\]
Adding this amount to the base tax provided for this bracket gives the total tax owed:
\[\$12,486.25 + \$7,150.08 = \$19,636.33\]

  1. Conclusion and Selection of the Correct Option

Finally, rounding the calculated total tax of \(\$19,636.33\) to the nearest dollar results in \(\$19,636\). Comparing this result with the given choices, we find it corresponds to option c. Thus, the total tax Carol owes is \(\$19,636\).

Examples

Understanding graduated tax systems is crucial for personal financial management and budgeting. For example, if you are planning your future career and potential salary, knowing how tax brackets work helps you estimate your "take-home" pay. By applying these calculations, you can determine how much of your gross income will actually be available for savings, living expenses, or investments, allowing for more accurate financial planning.