To determine the benefit rate for Sofia, follow these steps:
1. Calculate the value of Paid Time Off (PTO):
- Sofia's annual salary is [tex]$70,000.
- She has 15 days of PTO.
- There are typically 52 weeks in a year and 5 workdays in a week.
- Therefore, the value of PTO is calculated based on the number of weeks: \( \frac{15 \text{ days}}{5 \text{ days per week}} = 3 \text{ weeks} \)
- The weekly salary is \( \frac{70000}{52} \).
- The value of the PTO in terms of salary is therefore \( 3 \times \left(\frac{70000}{52}\right) \approx 4038.46 \).
2. Calculate the Retirement Matching:
- Sofia's retirement matching benefit is 8% of her annual salary.
- \( 8\% \text{ of } 70000 = 0.08 \times 70000 = 5600 \).
3. Calculate the Health Insurance Subsidy:
- The employer covers 70% of the cost of the health insurance plan, which totals $[/tex]10,000.
- [tex]\( 70\% \text{ of } 10000 = 0.70 \times 10000 = 7000 \)[/tex].
4. Calculate the FICA contribution:
- The FICA contribution is 7.65% of her annual salary.
- [tex]\( 7.65\% \text{ of } 70000 = 0.0765 \times 70000 = 5355 \)[/tex].
5. Calculate the Total Value of Benefits:
- Sum up the values calculated from PTO, Retirement Matching, Health Insurance, and FICA.
- [tex]\( 4038.46 (PTO) + 5600 (Retirement) + 7000 (Health Insurance) + 5355 (FICA) = 21993.46 \)[/tex].
6. Calculate the Benefit Rate as a Percentage of the Annual Salary:
- The benefit rate is the ratio of the total value of benefits to the annual salary expressed as a percentage.
- [tex]\( \text{Benefit Rate} = \left( \frac{21993.46}{70000} \right) \times 100 \approx 31.42 \)[/tex].
7. Round to the Nearest Percentage Point:
- The benefit rate of 31.42% is rounded to 31%.
Therefore, the benefit rate, rounded to the nearest percentage point, is [tex]\( \boxed{31\%} \)[/tex].
