Most insurance companies require you to inform them anytime there is an accident. Typically when someone backs into you, their insurance will pay for the damages. Here is what to expect when filing your claim.
If the policy was in your name when the accident occurred, the accident will show up on your claims history as an at-fault accident. The reason this shows up is your responsible for claims that are paid out on behalf of your policy.
When your insurance pays out on a claim, it can impact your rates for up to five years. Since he was at fault, they may not go up as much as they would if you were at fault. Here is more information on the insurance laws for Michigan.
Although you might not have to file a claim with your insurance company, you will probably have to report the accident to your insurance company. Most insurance companies outlined in their policies that all accidents need to be reported - regardless if a claim isn't filed.