Consider the simplified example

In 2002 deaths from motor vehicle accidents occurred at a rate of 15.5 per 100,000 population. The probability of death from a motor vehicle accident in the next year is 15.5/100,000 = .000155. Suppose that you decide to sell insurance and offer to pay $10,000 if an insured person dies in a motor vehicle accident.

You plan to sell 1,000,000 policies. If you believe the rate of 15.5 deaths from motor vehicles per 100,000 population still holds today, you would expect to have to pay 155 claims on your 1,000,000 policies. You will need 155(10,000) = $1,550,000 to pay those claims. Since you have 1,000,000 policyholders, you can charge each one a premium of $1.55. The charge is small, but 1.55(1,000,000) = $1,550,000 gives you the money you will need to pay claims.

Q1: If your optimism was misplaced and you were only able to sell 500,000policies,how much would you need to charge for the policy?

a) 1.55

b)2.15

c)5.50

d) 1.96