contracts

I live in TN have recently inquired as to refinancing my lease car for a lesser payment. The company I am dealing with is in NY. They approved me for the refinance and quoted me the new payment over the phone. They then sent me all of the contract papers to sign with the agreed amount showing. After I had sent them a check for the specified amount and returned the forms signed, I called them because it had been over a week and I had heard nothing from them. It was then I was told that they had made an error and I was going to have to pay a higher rate. The next day I rec'd my copies of the original contract. Two days later, I rec'd the "updated" one showing my new payment along with my original check.
question: Since the original contract was agreed upon and signed and returned, can the company now force me to go with the new figure or are they bound by the original contract?

By its terms the contract probably has to be approved by the office in writing, and oral okays do not count. But if they pull a bait and switch, you can get out of the new deal.