Suppose a company charges an annual premium of $120 for an insurance policy for minor injuries

Question

Actuarial studies show that in case of an injury claim, the company will pay out an average of $900 for outpatient care and an average of $3000 for an overnight stay in the hospital. They also determine that, on average, each year there are five claims made that result in outpatient care for every 1000 policies and three claims made that result in an overnight stay out of every 1000 policies. What is the expected annual profit of an insurance policy for the company?

Answer 1

 

expected loss   900(5/1000) + 3000(3/1000)

                       4500/1000 + 9000/1000

                        45/10 + 9

                        4.5 + 9

                        13.5

 

income - loss = profit

120 - 13.5 = profit

106.5 = profit     yet this is for only one policy

 

106.5(1000) = 106,500

 

The expected profit is $106,500.