If you want to make changes to your policy such as dropping your physical damage coverages of collision and comprehensive so that you only have the state required liability coverages you, the policyholder, would need to inform the insurer, your insurance company, of the change. Auto insurance coverages do not change automatically after a few years.
An insurance carrier does not make changes to your policy such as this without you requesting it. Also if you are still paying for the new car after a few years it is doubtful that you could lower your coverages from "full coverage" to basic liability. Your lien holder normally requires you to have the physical damage coverages on the vehicle since it their asset until you pay it off.
If you own the car in the free and clear then you can place only liability on it if you so desire but you would need to notify your insurance agent of the changes you would want to make on policy so that they could be done and your rates adjusted accordingly.
To determine the type of coverage you need try out our Insurance Coverage Calculator.
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