Applied Math - Percentages - Insurance

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Introduction

Insurance plans often have percentages to calculate in order to determine what the individual owes and what the insurance company will pay.

First, a person usually has to meet a deductible. A deductible is amount of money a person has to pay for their expenses all on their own before the insurance company starts helping out. There are sometimes items that insurance companies will pay for a person without that person reaching their deductible, though (like a regular checkup to a primary care physician).

After a person’s medical expenses have passed the deductible, the insurance company starts paying some of the costs. Coinsurance is the percent of costs that you have to pay after the deductible. The insurance company pays the rest.

Below is an insurance plan offered to an individual in 2019:

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This individual gets to see their primary care doctor for $25 and get prescribed generic drugs for $10.

The insurance company pays the rest of the bill.

For other healthcare, though, they have to pay the entire bill themselves until they reach their deductible of $7,000.

After they pay the deductible, they pay 50% of both emergency room costs and costs for visiting a specialist.

Once they have paid $8,550 out of their own pocket, the insurance company pays the rest.

They have to pay $339.15 a month for the plan.

Example:

1.

A person has the following health insurance plan:

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The person has the following healthcare expenses for a year:

If there are no other healthcare expenses, what does the individual have to pay this year for healthcare costs?

The person has to pay all healthcare expenses until they have met the deductible.

Their total healthcare costs are the $3,000 deductible + $1,110 for their coinsurance portion of the emergency room, which is $4,110. If we add the cost of their $449.72 monthly premium, their total healthcare cost and health insurance cost for the year is \(\$4,110 + 12 \cdot \$449.72 = \$9,506.64\)



2.

Say the individual above had one additional visit to the specialist. The specialist performed an expensive procedure that cost $20,000. What are their total healthcare costs for the year, including the premium?

Before part 2, the individual had $4,110 in healthcare expenses. They have passed the deductible. The individual is responsible for 30% of the cost of the specialist after the deductible. Their share is \(0.30 \cdot \$20,000 = \$6,000\). Their total healthcare expenses are \(\$4,110 + \$6,000 = \$10,110\), but their out-of-pocket maximum is $7,500. That means They do not have to pay all of the $6,000 from their coinsurance. Once a person reaches their out-of-pocket maximum, the health insurance company pays everything else. This person has to pay $7,500 in healthcare expenses and the premium for the year.

Practice Problems

1. A person has the following health insurance plan:

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If there are no other healthcare expenses, what does the individual have to pay this year for health insurance and healthcare costs?



2. A person has the following health insurance plan:

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If there are no other healthcare expenses, what does the individual have to pay this year for health insurance and healthcare costs?

Theory Questions

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1. Compare the two plans above. Which plan would be best for a 21 year old individual with no previous health problems and who typically visits their primary doctor once a year? Why?



2. Compare the two plans above. Which plan would be best for a 57 year old individual who expects to have an expensive surgery in the coming year, who needs several prescription drugs, who has had a history of emergency care, and who visits their primary care doctor at least twice a year? Why?