It allows one party to "assume" the rights and responsibilities of the other party. The agreement means that the buyer or grantee in the deed takes the property, assuming the debt currently on the property.In an assumption, the buyer promises to pay the existing debt. This type of agreement transfers the obligations of one party under a contract to another party. It simply means that whomever gets awarded the house will assume the mortgage payments. Capitalized terms used and not otherwise defined in this Exhibit 4.13 will have the meanings assigned to those terms in the Purchase and Assumption Agreement.