# Modeling Health Insurance – Project Under Development

This past May, I was faced with a problem regarding health insurance. My employer offers two different plans, the Basic Plus Plan and the Premier. In the past, I was insured under the Premier plan with no cost to me. However, this summer I added my wife and child to my health insurance. I was faced with a decision. Should I cover my family under the Premier plan or change to family coverage under the Basic Plus Plan?

The two plans are described in the summary plan (PDF). Examining the two plans you’ll see that there are several differences for family coverage.

• The out of pocket maximum for the Premier Plan is \$6000 per year versus \$12,000 per year for the Basic Plus Plan.
• The annual deductible for the Premier Plan is \$600 per family versus \$1200 per family for the Basic Plus Plan.
• In general, the Premier Plan covers 80% of medical charges and the Basic Plus Plan covers 60% of medical charges.

The plans differ in cost too. Family coverage under the Premier Plan is \$514 per month compared to \$46 per month under the Basic Plus Plan. There are other difference regarding in network and out of network, but these facts are what I used to make my coverage decision.

Under a number of assumptions (which I’ll detail in later posts), I came up with the following graph.

This graph shows the total annual cost for each plan as a function of the medical charges incurred by the insured. As you can see, each plan is described by a piecewise linear function. If my family incurs less than \$26,880 in medical charges during the year, the Basic Plus Plan is cheaper. For more than \$26,880 in medical charges, the Premier Plan is cheaper.

In this project, I want students to create a graph and accompanying mathematics for other insurance plans. Luckily, it is easy to get health insurance quotes online. Humana One will give you an instance quote when you click on the Get Quote link on their webpage. Although they ask for a lot of personal information, only the state, zip code and birthday information about the insured are required. For a family coverage of a 46 year old in Arizona, this PDF demonstrates that a number of plans are available with different levels of coverage, different out of pocket maximums, and different deductibles. Another great source for health insurance quotes from many different companies is eHealthInsurance. I want my students in College Algebra to enter in their pertinent information and compare two plans like I did in the graph above.

Over the next week, I’ll post the assignments I create to help point students in the proper direction as well as the project letter I come up with.