If you financed the new car by means of a lease or loan than it would appear the dealership was telling you that you needed to obtain full coverage on your vehicle which would cost more than your current insurance policy of just Liability coverage.

The auto insurance coverage that lien holders require on a car is not only Liability but physical damages of Collision and Comprehensive which is referred to as full coverage.  These extra coverages will be needed to be added to your car insurance coverage if all you placed on your vehicle is Liability or if you say traded in a vehicle with only Liability and want the insurance to cover this new vehicle.  A lien holder wants their vehicle better protected and so requires coverages that cover the vehicle, not just Liability that does not cover the car, their asset, in any way.

The dealership may require that you show proof of full coverage auto insurance on a financed vehicle before you drive it off so that you not only are complying with the state minimum Liability requirements but also your lien holders insurance mandate.

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