Whenever the assessment for any such improvement shall be immediately payable, the owner of any such lot, tract, or parcel of land or other property so assessed may pay such entire assessment, or any part thereof, without interest, within thirty days after the notice of such assessment.

The city treasurer shall, as soon as the certified copy of the assessment roll has been placed in his or her hands for collection, publish a notice in the official newspaper of the city for two consecutive daily, or two consecutive weekly issues, and then by posting four notices thereof in public places along the line of the proposed improvement, that the said roll is in his or her hands for collection, and that any assessment thereon, or any part thereof, may be paid within thirty days from the date of the first publication or posting of said notice, without penalty, interest or costs, and if not so paid, the same shall thereupon become delinquent.