In $2020,$ Van became responsible for providing his own health insurance. He obtained suitable coverage and paid annual premiums as shown in the following table. Compute Van$$s total premiums:

Van$$s Premiums

$2020$ $$4,479$

$20214,704$

$20224,824$

$20235,049$

Total

$

Except for an occasional minor illness requiring a doctor$$s attention, a drug prescription, and periodic, routine tests, Van enjoyed good health during those years. Because he had no reason to think that would change, by the end of $2022,$ Van was considering dropping his health insurance coverage. After all, he could think of a lot of other uses for the thousands of dollars he spent each year on increasing premiums. Van decided to pay premiums for another year but planned to take another look at his health care plan at the end of $2023.$

It Could Happen to You, It Could Happen to Me

In December $2023,$ Van accepted an invitation from friends to go snowboarding. Van did everything right: took a lesson, stayed on trails well within his skill level, and maintained an awareness of people and objects near him. Even though he thought it was a bit dorky to wear wrist guards and a helmet, his friends insisted that he take standard and reasonable safety measures.

Van was enjoying the day when, from out of nowhere $($actually$,$ the woods$),$ came an out of control skier who ran into Van. Van was injured and taken to the nearest hospital by ambulance.

Van$$s injuries included a broken wrist and elbow as well as cuts and bruises. Of biggest concern was the uncertainty of his head injury. Van spent a couple of days in intensive care. Fortunately, he didn$$t have a broken skull, but did have a concussion. Surgery was performed to repair the broken wrist and elbow. Since Van was in good health, his recovery was complete. Van returned to full function in about six months.

Soon after Van returned home, however, the medical bills for the ambulance, emergency room, intensive care, medications, doctors, tests, and other services arrived. Van also had to have physical therapy for his wrist and elbow. His total medical expenses were $$35,000.$ It was time to find out if all those premiums paid since $2020$ would pay off for just one, albeit dramatic, incident.

Overall, Van$$s insurance paid $80\%$ of the total medical expenses, thus making him responsible for

$1$

$\%$ of the expenses, or

$

$.$ Van$$s insurance paid

$

$.$

His out$-$of$-$pocket expenses for the accident of

$

plus the $2023$ insurance premiums of

$

totaled

$

$.$

If Van had canceled his health insurance at the end of $2022,$ his out$-$of$-$pocket expenses for the accident would have been

$

$.$ In this case, did Van benefit from having health insurance? $.$

What are reasonable morals of the story? Check all that apply.

Don$$t get sick.

Avoid engaging in physical activity.

It can be financially risky to go without health insurance.

Think long and hard about the best tradeoff of coverage and cost in a health care plan.

Never leave the house.

Some employers pay part or all of the health insurance premiums for employees who are enrolled in one of the company$$s sponsored plans. Assume that during the same time period that Van paid for his premiums in full that he had, instead, worked for a firm that paid $75\%$ of his premiums for the same coverage. Instead of paying premiums of

$

over the years, Van would have paid

$

and saved

$

$.$

In this case, Van$$s out$-$of$-$pocket expenses specific to his snowboarding accident would have been they actually were because $.$