Earlier this week, a car rear-ended a CTA bus near the intersection of Western and Harrison in Chicago. Thirteen people were on board at the time of the CTA bus accident, a four reported injury at the time. Three of the injured bus passengers and one passenger from the car had to be transported by ambulance to area hospitals.The news story makes clear that there were at least 5 injured people, four of whom were hurt seriously enough to require hospital treatment. In accidents like this, it is almost common for people to start feeling the symptoms of neck and back injuries later that day or when they wake up the following day. In short, you can expect that there will be a number of claims made against the driver of the car that hit the bus.Every insurance policy has limits of liability. The Illinois state minimum liability insurance for autos is $20,000 per person and $40,000 per accident. That means that the most any one injured person can receive is $20,000, and the most that the insurance company for the at-fault driver will have to pay is a total of $40,000, regardless of the total number of people hurt.Accidents like this are a good reason why is is important for you to carry underinsured motorist coverage on your vehicle. Underinsured motorist coverage steps in and pays your damages from an Illinois car accident when the amount of your damages exceeds the amount of liability insurance available, up to your policy limits.In a case like this where there a multiple victims of a car accident, underinsured motorist coverage has special value. Let’s assume that each of the accident victims receives $8,000 from the at-fault driver’s insurance company, but has $15,000 in damages. In that case, their underinsured motorist coverage would step in and pay the additional $7,000 in damages.When there is not enough insurance coverage to go around after a car accident, underinsured motorist coverage provides special value to accident victims.