Recently two types of insurance policy covering automobile liability have become available. With this kind of policy, the insured party receives a prepaid discount on the annual premium; however, he must make an additional payment to the insurer on first report of an accident.

We shall examine only one of these two types of policy, since the second is very similar to the first.

On stipulation of the contract, the insured party pays a premium equal to 78 percent of that currently in force for complete coverage, depending on the various limits. However, at the same time at which the insured reports his first accident in the course of the year (and only in this case), he must make an additional payment equal to 35 percent of the premium due in the case of complete coverage. This additional payment, considered as a deposit, is repaid to the insured party if the accident has no follow up within four months; however, it may be requested again by the insurer if the case is subsequently reopened and leads to payment of damages. This additional payment will thus become a part of the premium only in the case of payment of damages for the first accident reported.

In this way, the premium paid by the insured is equal to 78 percent or to 113 percent of the current premium, depending on whether or not the insured reports accidents.