To find the benefit rate for Maria's employment package, let's go through the calculations step-by-step:
1. Calculate the value of PTO (Paid Time Off):
- Maria's annual salary is \[tex]$50,000.
- She gets 10 days of PTO.
- We assume a 5-day workweek over 52 weeks, which totals 260 workdays per year.
- Daily salary: \( \frac{\$[/tex]50,000}{260} \approx \[tex]$192.31 \)
- Value of PTO: \( 10 \text{ days} \times \$[/tex]192.31 \approx \[tex]$1923.08 \)
2. Calculate the retirement matching value:
- Maria's salary is \$[/tex]50,000.
- The retirement matching percentage is 8%.
- Retirement matching value: [tex]\( \$50,000 \times 0.08 = \$4,000 \)[/tex]
3. Calculate the health insurance subsidy value:
- Total health insurance cost is \[tex]$10,000.
- The employer subsidizes 70% of this cost.
- Health insurance subsidy value: \( \$[/tex]10,000 \times 0.70 = \[tex]$7,000 \)
4. Calculate the FICA contribution value:
- Maria's salary is \$[/tex]50,000.
- The FICA tax percentage is 7.65%.
- FICA contribution value: [tex]\( \$50,000 \times 0.0765 = \$3,825 \)[/tex]
5. Sum up all the benefits to find the total benefit value:
- Value of PTO: \[tex]$1,923.08
- Retirement matching value: \$[/tex]4,000
- Health insurance subsidy value: \[tex]$7,000
- FICA contribution value: \$[/tex]3,825
- Total benefits value: [tex]\( \$1,923.08 + \$4,000 + \$7,000 + \$3,825 \approx \$16,748.08 \)[/tex]
6. Calculate the benefit rate as a percentage of the salary:
- Maria's salary is \[tex]$50,000.
- Benefit rate: \( \left( \frac{\$[/tex]16,748.08}{\$50,000} \right) \times 100 \approx 33.50\% \)
7. Round to the nearest whole percentage point:
- Rounding 33.50% to the nearest whole percentage, we get 33%.
Therefore, the benefit rate is approximately 33%.
