a. Arielle is an office assistant at Richardson. She makes $47,700 per year. She has individual health care. Her yearly contribution is 5% of the total cost. How much does her employer contribute?
b. Catherine is a department manager at Richardson. Her annual salary is $68,300. She has family health care. Her employer contributes $935 per month towards her total coverage cost. What percent does Catherine contribute toward the total coverage?
The correct answer and explanation is:
Answers:
a. Arielle’s Employer Contribution:
Arielle contributes 5% of the total health care cost. That means the total cost of her health care plan is calculated as: Total Cost=5% of her salary5%=0.05×477000.05=47700\text{Total Cost} = \frac{5\% \text{ of her salary}}{5\%} = \frac{0.05 \times 47700}{0.05} = 47700
Since her employer covers the remaining 95%, the employer contribution is: Employer Contribution=95%×47700=45315\text{Employer Contribution} = 95\% \times 47700 = 45315
So, Arielle’s employer contributes $45,315 per year.
b. Catherine’s Contribution Percentage:
Catherine’s employer contributes $935 per month, which totals: Annual Employer Contribution=935×12=11220\text{Annual Employer Contribution} = 935 \times 12 = 11220
Let the total annual health care cost be Y. Catherine pays the remaining portion: Catherine’s Contribution=Y−11220\text{Catherine’s Contribution} = Y – 11220
The percentage Catherine contributes is: (Y−11220)Y×100\frac{(Y – 11220)}{Y} \times 100
Since we do not have the total cost (Y) explicitly, her percentage contribution depends on that value. If we had the total cost, we could calculate the exact percentage.
Explanation:
Arielle’s health care cost is calculated based on her own salary, where she contributes 5% and her employer covers the rest. Since her total health care cost matches her salary, her employer’s contribution is significant.
For Catherine, the employer contributes a fixed $935 per month ($11,220 annually). To determine her percentage, we need the total health care cost. Her contribution percentage depends on how much more than $11,220 the total cost is.
Would you like to specify a total cost for Catherine’s plan to get the exact percentage?