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Be careful applying for private loans with banks. If your bank requires a co-borrower to sign on the agreement before the loan is sanctioned, make sure that your co-borrower has a good enough credit history. Not having a good credit history could jeopardize your chances of getting the private student loan that you would have otherwise got stand alone.
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.
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.
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."