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In certain cases where you have repaid some installments of a previous student loan independently, you would be given the authority of branching away the Co-borrower. This is known as Co-Borrower Release and by doing so, you ensure that the loan repayment is entirely yours. This also puts you in a position where you are not hit by the Credit History of your Co-Borrower. Both of you are separate entities speaking from the loan perspective and you would hence need to take charge of repaying your loan off.
A loan agreement is a contract between a borrower and a lender which regulates the mutual promises made by each party. There are many types of loan agreements, including "facilities agreements," "revolvers," "term loans," "working capital loans." Loan agreements are documented via a compilation of the various mutual promises made by the involved parties.
Prior to entering into a loan agreement, the "borrower" first makes representations about his affairs surrounding his character, creditworthiness, cashflow, and any collateral that he may have available to pledge as security for a loan. These representations are taken into consideration and the lender then determines under what conditions (terms), if any, they are prepared to advance money.
The first thing that should be checked while signing the agreement is the interest rate as it may create stress on you while repaying the loan amount. With the current income level, you should be able to validate whether you can afford to repay the loan at the interest mentioned in the loan agreement.