“No. That’s not normal practice from a lender like a bank or credit union, but it’s definitely something a dealer would do.
It sounds like you got taken by the dealer. Even a substantial drop in APR might not even save you $2,000 over the life of the loan, and many extended warranties are generally considered a waste of money because they cover so little.
If you didn’t sign the papers, walk away from this one, as it sounds a bit sketchy.
Instead, get pre approved from a lender, get the offer letter in hand, and use it to guide your decision-making on a new car.”