Suppose a company charges an annual premium of $100
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 $400
for outpatient care and an average of $4000
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?
To calculate the expected annual profit for the insurance policy, you need to consider the total premium revenue and the total claim payouts.
First, let's calculate the total premium revenue:
Since the annual premium for each policy is $100, and there are 1000 policies, the total premium revenue is:
Total premium revenue = Annual premium per policy * Number of policies
= $100 * 1000
= $100,000
Next, let's calculate the total claim payouts for outpatient care and overnight stays:
Number of claims for outpatient care = (Number of outpatient claims per 1000 policies) * (Number of policies / 1000)
= 5 * (1000/1000)
= 5
Number of claims for overnight stays = (Number of overnight claims per 1000 policies) * (Number of policies / 1000)
= 3 * (1000/1000)
= 3
Average claim payout for outpatient care = $400
Average claim payout for overnight stay = $4000
Total claim payout for outpatient care = Number of claims * Average claim payout for outpatient care
= 5 * $400
= $2000
Total claim payout for overnight stays = Number of claims * Average claim payout for overnight stay
= 3 * $4000
= $12,000
Finally, let's calculate the expected annual profit:
Expected annual profit = Total premium revenue - Total claim payouts
= $100,000 - ($2000 + $12,000)
= $100,000 - $14,000
= $86,000
Therefore, the expected annual profit of the insurance policy for the company is $86,000.