Homework problems: Please show work and/or explain how you arrived at your answer (numerical answers with no explanation will not be given ill credit). Assume 100 people join an insurance pool (a group of people insured through community rating). Based on experience insuring people in this area and based on the age distribution, the insurance company expects a range of anticipated health insurance claims as shown in the table below. Number 9f instited Anti eipeted HeeltLi gleimetyeettpereen 10 $800 10 1000 10 1200 10 1400 10 1600 10 1800 10 2000 10 6000 A. Year 1: Customers will buy insurance if their anticipated health claims are greater than the premium. Let's say in the first year, all 100 people purchase the insurance plan. What is the highest premium the insurance company could have charged for all 100 people to have joined? B. Year 2: The claims experience of the customers is found to be generally consistent with expectations of the insurance company. What would be the premium in the second year? If those customers who had claims in the first year that were less than or equal to the premium now decide not to continue to buy insurance, how many will continue to be insured in the second year? C. Year 3: What would be the premium in the third year? If those customers who had claims in the second year less than or equal to the premium now decide not to continue to buy insurance, how many will continue to be insured in the third year