The premium that the insurance company should charge each year to realize an average profit of $500 is $6,900.
First step is to calculated the expected amount to pay
Expected amount=Total loss +50% loss+25% loss
Expected amount=$200,000(0.002)(1)+$200,000(0.01)(0.5)+$200,000(0.1)(0.25)
Expected amount=$400+$1,000+$5,000
Expected amount=$6,400
Second step is to calculate the premium
Premium=Expected amount+ Average profit
Premium=$6,400+$500
Premium=$6,900
Inconclusion the premium that the insurance company should charge each year to realize an average profit of $500 is $6,900.
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