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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."
Defined and addressed in the contract are the issues concerning the agreement. First and foremost, the rights and obligations of both parties must be defined in the written contract. Termination of contract and termination fees should also be included. Commonly, you will find the interest rates and other applicable fees included in the agreement.
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.
"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).