Whenever the cost and expense of any improvement shall be payable by the mode of "immediate payment," the city treasurer shall, upon the receipt of such roll, publish a notice in the official paper of the city for ten consecutive daily or two consecutive weekly issues that the said roll is in his hands for collection and that any assessment thereon or any portion of any such assessment may be paid at any time within thirty (30) days from the date of the first publication of said notice, without penalty, interest or costs, and that unless payment be made within such time, such assessment or unpaid portion thereof will become delinquent. All such delinquent assessments shall be subject to a charge for interest at the rate of eight percent and to an additional charge of five percent penalty levied upon both principal and interest due until the same shall be certified to the county treasurer as hereinafter provided.