To find the benefit rate for Maria, we need to calculate the total monetary value of all her benefits in relation to her salary. We will follow a step-by-step approach to do this:
1. Health Insurance Contribution:
Maria's health insurance totals [tex]$10,000$[/tex] annually, and her employer covers [tex]$70\%$[/tex] of this cost.
[tex]\[
\text{Employer's contribution to health insurance} = 10,000 \times 0.70 = \$7,000
\][/tex]
2. Paid Time Off (PTO) Calculation:
Maria receives 10 days of paid vacation. To find the monetary value of her PTO, we need to find her daily wage and multiply it by the number of PTO days.
[tex]\[
\text{Daily wage} = \frac{\$50,000}{365} \approx \$136.99
\][/tex]
[tex]\[
\text{Value of 10 PTO days} = 136.99 \times 10 = \$1,369.86
\][/tex]
3. Retirement Matching:
The employer matches [tex]$8\%$[/tex] of Maria's salary for retirement.
[tex]\[
\text{Employer's contribution to retirement} = 50,000 \times 0.08 = \$4,000
\][/tex]
4. FICA Contribution:
FICA taxes are [tex]$7.65\%$[/tex] of Maria's salary.
[tex]\[
\text{Employer's contribution to FICA} = 50,000 \times 0.0765 = \$3,825
\][/tex]
5. Total Benefits:
Add up all the contributions from the employer.
[tex]\[
\text{Total benefits} = 7,000 + 1,369.86 + 4,000 + 3,825 = \$16,194.86
\][/tex]
6. Benefit Rate Calculation:
To find the benefit rate, we compare the total benefits to Maria's salary and express it as a percentage.
[tex]\[
\text{Benefit rate} = \left( \frac{\$16,194.86}{\$50,000} \right) \times 100 \approx 32.39\%
\][/tex]
Rounding this to the nearest percentage point, we get:
[tex]\[
\text{Benefit rate} \approx 32\%
\][/tex]
So, the benefit rate for Maria is approximately [tex]\( \boxed{32\%} \)[/tex].
