Vacant elective offices in the city shall be filled by a majority vote of the whole council. The appointee’s term of office shall begin immediately after appointment and shall continue throughout the unexpired term of the predecessor . However, if an appointed councilmember’s term begins at least thirty (30) days prior to the last day for filing nominating petitions for the general election which comes in the middle of the predecessor’s unexpired term, the appointee’s term shall terminate at the end of such election year, and the vacancy shall then be filled at the mid-term general election for the balance of the original term, so that the system of overlapping four-year terms in each ward shall be preserved.