- Identify the tax rate of \(6.2\%\) as the decimal \(0.062\).
- Recognize the wage cap of \(\$106,800\) as the maximum amount subject to this tax.
- Multiply the rate by the cap to find the maximum annual tax: \(0.062 \times \$106,800 = \$6,621.60\).
- Confirm the result against the given options, identifying the final answer as \(\boxed{\$6,621.60}\).
Explanation
- Analysis of the Problem
The problem asks us to determine the maximum annual Social Security tax given a specific tax rate and a cap on the income subject to that tax. We are provided with a Social Security tax rate of \(6.2\%\) and a maximum taxable income (wage cap) of \(\$106,800\). The tax is applied only to earnings up to this limit, meaning that once an individual's annual income reaches \(\$106,800\), no additional Social Security tax is withheld from their subsequent earnings for that year. To find the maximum tax, we need to apply the given percentage to the wage cap.
- Calculation of the Maximum Tax
To calculate the tax amount, we first convert the percentage into a decimal. A tax rate of \(6.2\%\) is equivalent to \(\frac{6.2}{100} = 0.062\). Next, we multiply this decimal rate by the maximum taxable wage of \(\$106,800\). The calculation is as follows: \(\text{Tax} = 0.062 \times \$106,800\). Performing this multiplication yields \(\$6,621.60\).
- Conclusion and Final Answer
Comparing our calculated value of \(\$6,621.60\) with the given options, we identify it as option c. Therefore, the maximum amount of Social Security tax that can be charged in a single year under these conditions is \(\$6,621.60\). The final answer is \(\boxed{\$6,621.60}\).
Examples
Understanding how tax caps work is essential for personal financial planning, such as budgeting for payroll deductions or calculating net income. For example, if you know that Social Security tax is only deducted from the first \(\$106,800\) you earn, you can anticipate an increase in your take-home pay once your cumulative earnings for the year exceed that amount. This is a common occurrence for high-income earners and helps in accurately projecting monthly cash flow.