Did you pay any money up front to your mortgage broker or bank? For example, have you already paid the 1 point that enabled you to buy down the rate? If so, then they may have a clause they made you sign which said if you back out of the deal the money you paid up front is non-refundable. It's not a common practice right now, but there are still those out there who do that. However, if the rate has already been locked then the loan officer should have been required to disclose to the bank what kind of property it is (one family or two family). If he locked it as a two family and the appraisal comes back as a one family then you will have a very strong case for not moving forward on the transaction - because the terms have now changed and as a result, the original commitment no longer stands. However, if no money was paid up front, there should not be any form of cancellation penalty for you backing out of the deal.