After you file a claim for a car accident, your insurance premium will most likely go up, unless your policy includes accident forgiveness. Accident forgiveness does not mean that all costs associated with an accident are forgiven, but that an accident will not be factored in when the insurance company calculates your premium. If you do not have accident forgiveness, your premium may increase by as much as 70 percent, though the national average is 45 percent, according to Forbes.