Answer :
To find the most economical way to purchase health insurance for the family, we'll compare the total cost of insuring the entire family (Patrick, Susie, and the twins) through each employer.
1. Insuring through Patrick's Employer:
- Patrick's own monthly insurance premium is fully covered by his employer.
- For each additional beneficiary (Susie and the twins), the cost is [tex]$280.
Calculate the monthly cost for additional beneficiaries:
- Additional beneficiaries: Susie and two twins = 3 beneficiaries.
- Cost per additional beneficiary = $[/tex]280.
- Total cost for additional beneficiaries = 3 * [tex]$280 = $[/tex]840.
The total monthly cost through Patrick's employer is:
- Patrick's premium = [tex]$0 (covered by employer).
- Total for additional beneficiaries = $[/tex]840.
- Total cost = [tex]$0 + $[/tex]840 = [tex]$840.
2. Insuring through Susie's Employer:
- Susie's monthly insurance premium is $[/tex]403, with her employer covering 63% of it.
Calculate Susie's personal premium cost:
- Employer contribution: 63% of [tex]$403 = 0.63 * $[/tex]403 = [tex]$253.89.
- Susie's cost after employer contribution: $[/tex]403 - [tex]$253.89 = $[/tex]149.11.
- Each additional beneficiary (Patrick and the twins) costs [tex]$310, with her employer covering 32% of it.
Calculate the monthly cost for additional beneficiaries:
- Cost per additional beneficiary = $[/tex]310.
- Number of additional beneficiaries: Patrick and two twins = 3.
- Total cost without employer contribution = 3 [tex]$310 = $[/tex]930.
- Employer covers 32% of [tex]$930 = 0.32 $[/tex]930 = [tex]$297.60.
- Remaining cost for additional beneficiaries = $[/tex]930 - [tex]$297.60 = $[/tex]632.40.
The total monthly cost through Susie's employer is:
- Susie's own cost = [tex]$149.11.
- Cost for additional beneficiaries = $[/tex]632.40.
- Total cost = [tex]$149.11 + $[/tex]632.40 = [tex]$781.51.
Conclusion:
The most economical option is insuring the family through Susie's employer, as the total monthly cost is approximately $[/tex]781.51, which is less than the $840 cost through Patrick's employer.
1. Insuring through Patrick's Employer:
- Patrick's own monthly insurance premium is fully covered by his employer.
- For each additional beneficiary (Susie and the twins), the cost is [tex]$280.
Calculate the monthly cost for additional beneficiaries:
- Additional beneficiaries: Susie and two twins = 3 beneficiaries.
- Cost per additional beneficiary = $[/tex]280.
- Total cost for additional beneficiaries = 3 * [tex]$280 = $[/tex]840.
The total monthly cost through Patrick's employer is:
- Patrick's premium = [tex]$0 (covered by employer).
- Total for additional beneficiaries = $[/tex]840.
- Total cost = [tex]$0 + $[/tex]840 = [tex]$840.
2. Insuring through Susie's Employer:
- Susie's monthly insurance premium is $[/tex]403, with her employer covering 63% of it.
Calculate Susie's personal premium cost:
- Employer contribution: 63% of [tex]$403 = 0.63 * $[/tex]403 = [tex]$253.89.
- Susie's cost after employer contribution: $[/tex]403 - [tex]$253.89 = $[/tex]149.11.
- Each additional beneficiary (Patrick and the twins) costs [tex]$310, with her employer covering 32% of it.
Calculate the monthly cost for additional beneficiaries:
- Cost per additional beneficiary = $[/tex]310.
- Number of additional beneficiaries: Patrick and two twins = 3.
- Total cost without employer contribution = 3 [tex]$310 = $[/tex]930.
- Employer covers 32% of [tex]$930 = 0.32 $[/tex]930 = [tex]$297.60.
- Remaining cost for additional beneficiaries = $[/tex]930 - [tex]$297.60 = $[/tex]632.40.
The total monthly cost through Susie's employer is:
- Susie's own cost = [tex]$149.11.
- Cost for additional beneficiaries = $[/tex]632.40.
- Total cost = [tex]$149.11 + $[/tex]632.40 = [tex]$781.51.
Conclusion:
The most economical option is insuring the family through Susie's employer, as the total monthly cost is approximately $[/tex]781.51, which is less than the $840 cost through Patrick's employer.
