Contracts can be formed in many ways. The classic is the written contract, a single document signed by both parties setting forth the terms of their agreement. However, oral (also called verbal) contracts are enforceable in most cases (there are a few special types that are not). In between the two are agreements shown by an exchange of correspondence. The key is that there must have been an offer--such as to loan money; acceptance of that offer; and some consideration (such as the exchange of money) to bind the contract. If there is, then it should be enforceable, and if you have emails or other correspondence and evidence, you can use that to prove the existence and terms of the agreement. One important point: the agreement that this money was a loan and not, say, a gift, must have been made up front, before the money changed hands. If you simply paid the money for your roommate under conditions that looks like it might have been a gift or might have been done for your own benefit with no expectation of repayment (e.g. to avoid eviction), you cannot after the fact change a unilateral payment into a loan.