Final answer:
In law, legal consideration refers to something of value exchanged in a contract, and application and initial premium are examples of this when forming an insurance contract.
Step-by-step explanation:
An example of legal consideration from the options provided is application and initial premium. In the context of law, consideration refers to something of value that is exchanged between parties in a contract. For instance, when an individual applies for an insurance policy, the initial premium paid is the consideration that makes the contract binding and legally enforceable. Politeness is not a legal consideration, legal purpose is the reason a contract is formed, and offer and acceptance are steps in forming a contract, but not consideration on their own.