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Loan agreements, like any contract, reflect an "offer," the "acceptance of the offer," "consideration," and can only involve situations that are "legal" (a term loan agreement involving heroin drug sales is not "legal"). Loan agreements are documented via their commitment letters, agreements that reflect the understandings reached between the involved parties, a promissory note, and a collateral agreement (such as a mortgage or a personal guarantee). Loan agreements offered by regulated banks are different from those that are offered by finance companies in that banks receive a "banking charter" granted as a privilege and involving the "public trust."
For commercial banks and large finance companies, "loan agreements" are usually not categorized although "loan portfolios" are often broadly characterized into "personal" and "commercial" loans while the "commercial" category is then subdivided into "industrial" and "commercial real estate" loans. "Industrial" loans are those that depend on the cashflow and creditworthiness of the company and the widgets or service that it sells. "Commercial real estate" loans are those that repay loans but that depend on the rental revenues paid by tenants who lease space, usually for extended times. More granular categorizations of loan portfolios exist but these are always variations around the larger themes.
Always obtain loan agreements in writing and read the fine print. One of the biggest mistakes borrowers make is entering into verbal agreements. If things go wrong there is no evidence to prove the case. Debtors should know the number of deferred payments, payment schedule, fees or penalties, and how the lender reports suspended payments to credit bureaus.
There are many financial institutions that offer private student loans with bad credit. The only fuss in the deal is the requirements of the financial institutions. Most entities that I know of providing this service would require a Co-borrower or a Co-Signer. This means as a student you and your parents would need to sign on the loan agreement agreeing to repay the loan.