Question

Question 10

An insurance company initially is insuring a pool of 200 people, each of whom has a 5% chance of a $10,000 loss due to illness.

(III.) The insurer needs to charge a premium to each of the 200 people that is enough to fully cover the expected loss per person, plus an additional 8% “loading cost” to each person to cover all its operating expenses and generate a profit. How much does the premium per person have to be (in dollars)?

  

a. $540

   

b. $580

   

c. $625

   

d. $1,080

Question 12

An insurance company was initially insuring a pool of 200 people, each of whom has a 5% chance of a $10,000 loss due to illness.

In addition, a new, “high risk” group of 50 people is also being insured. Each of these 50 people has a 50% chance of the $10,000 loss.

(V.) Suppose the insurer must group everyone together into a single 250 person pool. If the insurer must now charge everyone the same premium, how much does it have to be (in dollars per person, including the 8% loading cost)?

  

a. $1,080

   

b. $1,400

   

c. $1,512

   

d. $5,940

Answer 1

Q10.

Number of members in the insuring pool = 200

Each person has a 5% chance of losing $10,000 due to illness

Expected value of loss per person = 0.05 * $10,000 = $500

Premium per person including an 8% loading cost on each person = (1+0.08) * $500 = 1.08 * $500 = $540

Ans: a. $540

Q12.

For the initial insurance pool of 200 persons with a 5% chance of losing $10,000 due to illness

The total expected value of loss for 200 persons = 0.05 * $10,000 * 200 = $100,000

For the insurance pool of 50 members with a 50% chance of losing $10,000 due to illness

The total expected value of loss for 50 members = 0.50 * $10,000 * 50 = $250,000

Total expected value of loss for 250 members including an 8% loading cost per person = (1+0.08) * ($100,000 + $250,000) = 1.08 * $350,000 = $378,000

Therefore, the premium per person = Total expected value for 250 members/250 = $378,000/250 = $1,512

Ans:  c. $1,512