Question

It’s your turn to be the insurance company actuary! Try your hand at forecasting the future with these sample problems! Background: ABC Insurance Company insures 1,000 eighteen year old drivers. Assume 300 of the 1000 have accidents within a year. Assume the average repair cost for each accident is $500. Question 1: What is the minimum amount of premium that ABC should charge an 18-year-old for a 1-year car insurance policy? Should ABC Insurance company charge more than this premium? If so, why?

Answer 1

SOLUTION

At a minimum, the total premiums collected must equal the total cost of the accidents.

Estimated cost of the accidents:

300 × $500 = $150,000

Minimum premium for each driver:

$150,000 ÷ 1,000 = $150

Part b

Assume 400 of the drivers are males and 600 are females.

Assume 200 out of 300 of accidents will involve males, and the remaining 100 accidents will involve females.

Total males’ premium: 200 accidents × $500 per accident = $100,000

Each male’s premium:$100,000 ÷ 400 males = $250

Total females’ premium: 100 accidents × $500 per accident = $50,000

Each female’s premium: $50,000 ÷ 600 females = $83.33

As per the above example, insurance premium company can charge more than the premium identified in part a