Nope, your first year you usually get short-changed as the timing of expiration IS based on location (i.e. resident permits in certain areas of the city all expire at the same time). So, for instance, if in May you move into an area where the permits all expire in July, your first $15 only pays for those initial few months, then in July you have to spend another $15 for a new permit that will run through the following July.
no subject