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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.
The loan agreements originated by commercial banks, savings banks, finance companies, insurance organizations, and investment banks are very different from each other and all feed a different purpose. "Commercial banks" and "Savings banks," because they accept deposits and benefit from FDIC insurance, generate loans that incorporate the concepts of the "public trust." Prior to interstate banking, that "public trust" was easily measured by State bank regulators who could see how local deposits were used to fund the working capital needs of local industry and businesses, and the benefits associated with those organization's employment.
"Insurance" organizations, who collect premiums for providing either life or property/casualty coverage, created their own types of loan agreements. "Banks" and "Insurance" organizations loan agreements and documentation standards evolved from their individual cultures and were governed by policies that somehow addressed each organizations liabilities (In the case of "banks," the liquidity needs of their depositors; in the case of insurance organizations, the liquidity needs associated with their expected "claims" payments).