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Jim and Stephanie just got married and are thinking about changing their health care insurance plans to be more affordable. Currently, both Jim and Stephanie are insured through their own employers. Jim's employer pays 42\% of his \$378 monthly premium. His insurance plan will also pay for 23\% of the \$345 premium for additional beneficiaries. Stephanie's employer pays 35\% of her \$298 monthly premium but offers to pay an extra 10\% of her premium for each beneficiary Stephanie adds to her plan. Her employer would then pay 30\% of the \$349 premium for each additional beneficiary.



\multicolumn{3}{|c|}{Insurance}

\multicolumn{2}{|c|}{Jim's Employer}

Beneficiary		Monthly PremiumEmployer Contribution

Jim		\$37842\%

Additional (each)		\$34523\%


\multicolumn{3}{|c|}{Stephanie's Employer}

Beneficiary		Monthly PremiumEmployer Contribution

Stephanie		\$19835\% (+10\% for each additional beneficiary)

Additional (each)		\$34930\%

Verified Answer :

  • Jim as primary: \(\$219.24 \text{ (Jim)} + \$265.65 \text{ (Stephanie)} = \$484.89\).
  • Stephanie as primary: \(\$108.90 \text{ (Stephanie)} + \$244.30 \text{ (Jim)} = \$353.20\).
  • Comparing the two, Stephanie as the primary holder is more cost-effective.
  • The cheapest monthly cost for the couple is \(\boxed{\$353.20}\).

Explanation

  1. Calculating Individual Premiums and Employer Contributions

To determine the most cost-effective health insurance plan for Jim and Stephanie, we evaluate two scenarios: one where Jim is the primary holder adding Stephanie as a beneficiary, and one where Stephanie is the primary holder adding Jim as a beneficiary.

For Jim's insurance:

  • The base premium is \(\$378\), and his employer covers \(42\%\).
  • The cost to Jim is \(\$378 \times (1 - 0.42) = \$\$378 \times 0.58 = \$219.24\).
  • If he adds a beneficiary, the employer covers \(23\%\) of the \(\$345\) premium.
  • The cost for the beneficiary is \(\$345 \times (1 - 0.23) = \$345 \times 0.77 = \$265.65\).

For Stephanie's insurance:

  • The base premium is \(\$198\), and her employer covers \(35\%\).
  • When she adds a beneficiary, her employer increases coverage for her premium by \(10\%\) (to a total of \(35\% + 10\% = 45\%\)) and covers \(30\%\) of the beneficiary's \(\$349\) premium.
  • The cost to Stephanie for her own premium is \(\$198 \times (1 - 0.45) = \$198 \times 0.55 = \$108.90\).
  • The cost for the beneficiary is \(\$349 \times (1 - 0.30) = \$349 \times 0.70 = \$244.30\).
  1. Calculating Total Monthly Costs for Both Scenarios

Now we calculate the total monthly cost for each scenario.

Scenario 1: Jim is the primary, and Stephanie is the beneficiary.

  • Total cost = (Jim's cost) + (Stephanie's beneficiary cost)
  • Total cost = \(\$219.24 + \$265.65 = \$484.89\).

Scenario 2: Stephanie is the primary, and Jim is the beneficiary.

  • Total cost = (Stephanie's cost) + (Jim's beneficiary cost)
  • Total cost = \(\$108.90 + \$244.30 = \$353.20\).
  1. Conclusion and Comparison

Comparing the two scenarios, the total monthly cost of \(\$484.89\) for Scenario 1 is significantly higher than the total monthly cost of \(\$353.20\) for Scenario 2. Therefore, the more affordable plan is for Stephanie to be the primary insurance holder and to add Jim as a beneficiary.

The monthly costs for the two scenarios are \(\$484.89\) and \(\$353.20\), respectively. The cheapest monthly cost is \(\boxed{\$353.20}\).

Examples

In real-life scenarios, comparing insurance plans between partners is a standard practice for household budgeting. By calculating the net cost—which accounts for both the base premiums and employer subsidies—couples can significantly optimize their monthly expenditures. This approach, similar to evaluating offers for bundled services or utility contracts, ensures that a family makes informed financial decisions rather than choosing plans based solely on surface-level information.

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