Mortgage
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A mortgage is granting of a lien on real property, such as a home, by a debtor (borrower) to his creditor (lender), such that the property is security for the repayment on a loan. Once the loan is paid, the mortgage should be discharged.
Hypothecation refers to the right that a creditor has to liquidate goods, securities, or other assets, if you fail to service a loan.
A sub-prime mortgage is one where the credit-worthiness of the borrower or his ability to repay the loan is questionable.