Hitting a boulder in your neighbor's yard will fall under your physical damage coverage, most likely the collision portion. You can make a claim with your insurance agent and a claims adjuster should contact you about getting the damages looked at by him or her or at a repair shop.

Since you are using your physical damage coverage of your auto policy, you will owe the deductible which you chose for this coverage when setting up your policy. The remainder of the damages should then be taken care of by the insurance carrier.

Since you are making a claim against your own policy it could affect your rates. If the damages are not that sustainable and you have a clean claims and driving history besides this one incident then your rates will not likely be "drastically" increased.

The amount of your car insurance premium and any rate increases will be determined by your insurance company and their rating system. To find out about the insurer's rating system request information from your agent or you may also contact your state's insurance regulator since rates must be filed with this state agency.