Contracts don’t need to be written down to be enforceable. (There are some exceptions to this rule – including contracts to buy and sell land and employment agreements – they do need to be in writing.) Most of us enter numerous contracts every week where we don’t write down the exact terms of our agreement. For example, every time you buy a bottle of milk from the dairy you are entering a legally enforceable contract.
In most cases, that’s fine. You get the milk you want. The dairy owner gets the money and everyone’s happy.