Any town adopting a resolution for which provision is made in § 7-340 shall, at the next regular municipal election elect six electors of such town who shall constitute the board of finance, two of whom shall be elected to serve until the next such election, two to serve until the second such election from such date and two to serve until the third such election from such date. At each such election thereafter, the town shall elect, in the same manner as the town officers are elected, two electors of such town as members of such board of finance to serve for six years. Each member of the board of finance shall serve for the term for which he is elected and until his successor is elected and has qualified.