Please show work and/or explain how you arrived at your answer (numerical answers with no explanation will not be given full credit).

Assume 100 people join an insurance pool (a group of people insured through community rating).Based on past 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 of insuredAnticipated Health Claims/year/person

10$600

10750

10900

101050

101200

101350

101500

101650

102250

104500

1.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?

2.Year 2:

The claims experience of the customers is found to be generally consistent with expectations of the insurance company (the table above). 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 in the second year now decide not to continue to buy insurance, how many will continue to be insured in the second year?

3.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 in the third year now decide not to continue to buy insurance, how many will continue to be insured in the third year?

4.Year 4:

What would be the premium in the fourth year? If those customers who had claims in the third year less than or equal to the premium now decide not to continue to buy insurance, how many will to continue to be insured in the fourth year?