The answer will likely be determined by the language of the agreement. Oftentimes, particularly with used cars, the dealership allows you to drive the car off the lot subject to approval by financing. If this is the deal you have, then you will have to return the car or agree to the higher interest rate. However, if there is nothing conditional in the agreement, the dealer cannot unilaterally change the terms of the deal. You really need to have someone look at your agreement to be able to advise you properly.
You should carefully read (front and back) of each document that you signed during the deal. The contract will determine what the dealership can or cannot do under the contract (with few public policy exceptions). There is also likely an arbitration agreement that you signed. If you and the dealership cannot come to an agreement, and they insist on rescinding the contract, your case will likely be resolved in a binding arbitration. Best of luck.
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