Two health insurance plans are offered to employees of a company. Plan 1 has a $400 deductible and then pays 65% of the rest of the cost versus plan 2 that has a $1000 deductible and then pays 75% of the rest of the cost. What would annual medical costs have to be for plan 2 to be the least expensive?

Question

Two health insurance plans are offered to employees of a company. Plan 1 has a $400 deductible and then pays 65% of the rest of the cost versus plan 2 that has a $1000 deductible and then pays 75% of the rest of the cost. What would annual medical costs have to be for plan 2 to be the least expensive?

Answer 1

well, just compare the two plans for how much it costs the patient:

400 + 0.35(x-400) > 1000 + 0.25(x-1000)

Answer 2

To determine the annual medical costs for plan 2 to be the least expensive, we need to compare the costs of both plans for different levels of medical expenses.

First, let's calculate the cost for plan 1. The cost for plan 1 can be calculated using the formula:

Cost1 = Deductible + (1 - Coverage) * Medical expenses

In this case, the deductible for plan 1 is $400, and the coverage is 65% (or 0.65). We need to find the point at which the cost for plan 1 exceeds the cost for plan 2.

Now, let's calculate the cost for plan 2 using the same formula:

Cost2 = Deductible + (1 - Coverage) * Medical expenses

In this case, the deductible for plan 2 is $1000, and the coverage is 75% (or 0.75). We need to find the point at which the cost for plan 2 becomes the least expensive option.

To compare the costs of both plans, we set the cost of plan 1 equal to the cost of plan 2:

Deductible1 + (1 - Coverage1) * Medical expenses = Deductible2 + (1 - Coverage2) * Medical expenses

Simplifying the equation:

Deductible1 - Deductible2 = (1 - Coverage2) * Medical expenses - (1 - Coverage1) * Medical expenses

Deductible1 - Deductible 2 = Medical expenses * (1 - Coverage2 - 1 + Coverage1)

Deductible1 - Deductible2 = Medical expenses * (Coverage1 - Coverage2)

Now we can calculate the medical expenses at which plan 2 becomes the least expensive:

Medical expenses = (Deductible1 - Deductible2) / (Coverage1 - Coverage2)

Substituting the provided values:

Medical expenses = ($400 - $1000) / (0.65 - 0.75)

Medical expenses = -$600 / (-0.1)

Medical expenses = $6000

Therefore, the annual medical costs would have to be $6000 for plan 2 to be the least expensive option.