Question

Suppose a company charges an annual premium of $110 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

$96.5

Explanation:

For each 1000 policies, we have:

5 cases that cost $900 each

3 cases that cost $3000 each

1000 - 5 - 3 = 992 cases that cost nothing.

So if the price of each policy is $110, the income for those 1000 policies is:

992 * 110 + 5 * (110 - 900) + 3 * (110 - 3000) = $96,500

To find the expected profit for one policy, we have:

$96,500 / 1000 = $96.5