Suppose a company charges an annual premium of $140 for an insurance policy for minor injuries

Question

Suppose a company charges an annual premium of $140 for an insurance policy for minor injuries. 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

Based on the averages being out of 1000 policies. We assume that there are 1000 policies purchased in a year.

So the company gets (140x1000) $140,000 a year from policy holders.

They would spend (5x900) $4500 on out patient and (3x3000) $9,000 on over night patient per year.

This totals $13,500 a year paid out based on averages

So profit would be (140,000 - 13, 500) $126,500 a year on average for every 1000 policies sold.