This type of agreement transfers the obligations of one party under a contract to another party. It allows one party to "assume" the rights and responsibilities of the other party.Lender is willing to consent to the Transfer and agree to the Assumption, subject to the terms and conditions set forth in this Assumption Agreement. I. Mortgage assumption allows a buyer to take on the original loan balance at the original terms, but it doesn't account for any home equity the seller has built. Loan assumption is when you take over full responsibility of the mortgage loan.