Let's break down the problem step by step to calculate the benefit rate for Josie.
1. Annual Salary:
- Josie's annual salary is [tex]\( \$52,000 \)[/tex].
2. Health Insurance Subsidy:
- Josie receives 70% of a [tex]$10,000 health insurance plan paid by her employer.
- Health insurance subsidy \( = 0.70 \times 10,000 = \$[/tex]7,000 \).
3. FICA (Federal Insurance Contributions Act):
- FICA is 7.65% of Josie's annual salary.
- FICA contributions [tex]\( = 0.0765 \times 52,000 = \$3,978 \)[/tex].
4. Retirement Matching:
- Josie’s employer matches 6% of her annual salary for retirement.
- Retirement matching [tex]\( = 0.06 \times 52,000 = \$3,120 \)[/tex].
5. Paid Time Off (PTO) Worth:
- Josie has 15 days of paid vacation.
- To find the worth of her PTO, we first need to calculate her daily salary.
- Assume 260 working days in a year.
- Daily salary [tex]\( = 52000 / 260 = \$200 \)[/tex].
- PTO worth [tex]\( = 15 \times 200 = \$3,000 \)[/tex].
6. Total Benefits Calculation:
- Total benefits [tex]\( = \text{Health Insurance Subsidy} + \text{FICA} + \text{Retirement Matching} + \text{PTO Worth} \)[/tex]
- Total benefits [tex]\( = 7,000 + 3,978 + 3,120 + 3,000 = \$17,098 \)[/tex].
7. Benefit Rate:
- Benefit rate [tex]\( = \left( \frac{\text{Total Benefits}}{\text{Annual Salary}} \right) \times 100 \)[/tex]
- Benefit rate [tex]\( = \left( \frac{17,098}{52,000} \right) \times 100 = 32.88076923076923 \)[/tex].
8. Round to the Nearest Percentage Point:
- Rounded benefit rate [tex]\( = 33\% \)[/tex].
Therefore, the benefit rate for Josie is [tex]\( 33\% \)[/tex].
