That topic that @favouritesio included does cover much of what you are asking about here, but just to be completely clear, the tiers (500, 1000, 2500, 5000, 10000) are the number of requests that you will be able to make per month. Your payment and requests reset will occur on the day that you are/were approved for a developer account.
Based on this, @favouritesio - your math is correct.
Please keep in mind that the Premium Full-Archive Search API will provide you a more complete set of results, has more advanced filtering operators, and provides more information with each Tweet than the standard search/tweets API.