To determine the overall benefit rate Josie receives, we must compute the value of her different benefits based on her annual salary and given information. Here’s a step-by-step breakdown of our calculations:
1. Paid Time Off (PTO):
- Josie has 15 PTO days annually.
- First, we determine the number of workdays in a year. Typically, there are 52 weeks each year, and most full-time jobs consider a 5-day work week. Thus, there are [tex]\(52 \times 5 = 260\)[/tex] workdays annually.
- Next, we'll find the value of each PTO day. This is her annual salary divided by the number of workdays:
[tex]\[
\text{Daily Salary} = \frac{52000}{260} = 200 \text{ (dollars per day)}
\][/tex]
- Therefore, the total value of her PTO:
[tex]\[
\text{PTO Value} = 200 \times 15 = 3000 \text{ (dollars)}
\][/tex]
2. Retirement Matching:
- Josie's retirement matching benefit is 6% of her annual salary.
- We calculate this as:
[tex]\[
\text{Retirement Value} = 52000 \times 0.06 = 3120 \text{ (dollars)}
\][/tex]
3. Health Insurance:
- Josie's employer subsidizes 70% of her total health insurance cost, which amounts to $10,000.
- We calculate the value of this subsidy:
[tex]\[
\text{Health Insurance Value} = 10000 \times 0.70 = 7000 \text{ (dollars)}
\][/tex]
4. Total Benefit Value:
- To get the total value of Josie's benefits, we sum the values of her PTO, retirement matching, and health insurance:
[tex]\[
\text{Total Benefit Value} = 3000 + 3120 + 7000 = 13120 \text{ (dollars)}
\][/tex]
5. Benefit Rate:
- The benefit rate expresses this total benefit value as a percentage of her annual salary.
- We calculate the benefit rate by dividing the total benefit value by her annual salary and then multiplying by 100 to get a percentage:
[tex]\[
\text{Benefit Rate} = \left( \frac{13120}{52000} \right) \times 100 = 25.23 \%
\][/tex]
Therefore, Josie's benefit rate is approximately [tex]\( 25.23\% \)[/tex].
