Hard to answer your question without seeing what the written contract provides. Most written contracts have a clause saying the written contract trumps all earlier verbal or other communications between the parties (usually called the Merger or Integration clause). You might want to seek legal advice from an attorney who could review the written contract.
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Good evening. I agree with Dana. This is called the "parol evidence rule" and its a rule for interpreting written contracts. Generally courts will always assume that the terms in a contact will trump any prior oral agreements. After all, that's why the parties signed a written agreement, so goes the logic. You should review you documents with a lawyer and quickly figure out exactly what you signed and whether you must pay the full amount. Thanks for your question and good luck!