To determine Sofia's benefit rate, we need to calculate the value of each benefit she receives and compare that to her annual salary. Here’s a step-by-step breakdown of the solution:
1. Calculate the value of Sofia's Paid Time Off (PTO):
- Sofia earns [tex]$70,000 per year.
- She receives 15 days of PTO.
- Assuming there are 250 working days in a year, the value of one PTO day is:
\[
\frac{\$[/tex]70,000}{250} = \[tex]$280 \text{ per day}
\]
- Therefore, the value of 15 PTO days is:
\[
15 \times \$[/tex]280 = \[tex]$4,200
\]
2. Calculate the value of the Retirement Matching contribution:
- The retirement matching is 8% of her annual salary.
- Therefore, the retirement matching value is:
\[
0.08 \times \$[/tex]70,000 = \[tex]$5,600
\]
3. Calculate the value of the subsidized Health Insurance:
- The total cost of health insurance is $[/tex]10,000.
- Sofia's employer covers 70% of this cost.
- Therefore, the employer's contribution towards health insurance is:
[tex]\[
0.70 \times \$10,000 = \$7,000
\][/tex]
4. Add up the value of all benefits:
The total value of Sofia's benefits is:
[tex]\[
\$4,200 \text{ (PTO)} + \$5,600 \text{ (Retirement matching)} + \$7,000 \text{ (Health insurance)} = \$16,800
\][/tex]
5. Calculate the benefit rate as a percentage of Sofia's salary:
- The benefit rate is given by the total value of benefits divided by the annual salary, multiplied by 100:
[tex]\[
\frac{\$16,800}{\$70,000} \times 100 = 24\%
\][/tex]
Thus, Sofia's benefit rate is 24%, rounded to the nearest percentage point.
