- Calculate the employee's cost for a primary beneficiary as \(\$149.11\) and for an additional member as \(\$210.80\).
- Compare the cost of insuring the entire family under one employer (\(\$781.51\)) versus splitting the family into two primary insurance groups (\(\$719.82\)).
- Identify that scenario (c) allows for two primary beneficiary rates, which reduces the total cost due to higher employer contributions.
- The lowest cost strategy is option C: \(\boxed{C}\).
Explanation
- Analyzing the Cost Structure
To determine the most cost-effective insurance strategy for the family (Patrick, Susie, and two twins, totaling 4 members), we must analyze the cost structure provided. The insurance plan classifies participants into a 'primary beneficiary' (Susie) and 'additional' members. The employee's monthly cost is calculated as the portion of the premium not covered by the employer.
- Primary beneficiary cost: \(\$403 \times (1 - 0.63) = \$403 \times 0.37 = \$149.11\).
- Additional member cost: \(\$310 \times (1 - 0.32) = \$310 \times 0.68 = \$210.80\).
- Comparing Insurance Scenarios
We evaluate two primary ways to structure the family's coverage.
- Scenario (b): Entire family under one employer. Here, one person is the primary beneficiary and three are additional members.
Total Cost = \(1 \times \$149.11 + 3 \times \$210.80 = \$149.11 + \$632.40 = \$781.51\).
- Scenario (c): Splitting the family. Here, each employer covers one primary beneficiary. One employer covers Patrick (as a primary beneficiary), and the other employer covers Susie (as a primary beneficiary) along with the two twins as additional members.
Total Cost = (Patrick's cost as primary) + (Susie's cost as primary + 2 twins' cost as additional)
Total Cost = \(\$149.11 + (\$149.11 + 2 \times \$210.80) = \$149.11 + \$570.71 = \$719.82\).
- Conclusion
Comparing the calculated costs:
- Scenario (b) total: \(\$781.51\)
- Scenario (c) total: \(\$719.82\)
By splitting the family members across two employers, each family unit can take advantage of the 'primary beneficiary' rate, which has a significantly higher employer contribution (63%) compared to the 'additional' member rate (32%). Thus, scenario (c) results in the lowest monthly cost for the family. The best answer is C. \(\boxed{C}\).
Examples
Insurance companies often offer lower rates or higher subsidies for the primary account holder to encourage individuals to enroll themselves and their families. This problem illustrates the concept of "optimal resource allocation." Just as splitting family members into separate primary accounts can reduce total insurance costs, businesses or individuals often optimize their expenses by distributing assets or liabilities across different categories to take advantage of specific tax benefits, subsidies, or rate brackets. This approach is fundamental in financial planning, logistics, and supply chain management to maximize savings and efficiency.