When sufficient money is in the funding fund to redeem one or more outstanding past due bonds, warrants, judgments, notes, or other evidences of indebtedness or to redeem one or more of the outstanding bonds, warrants, notes, or other evidences of indebtedness which are subject to call or payment before maturity, and which are proposed to be funded or refunded, the treasurer shall publish a notice that he is prepared to pay the bond, warrant, judgment, note, or other evidence of indebtedness (giving its number, if any). The notice shall be published once a week for two weeks in a newspaper of general circulation published in the city, if there is one. If the bond, warrant, judgment, note, or other evidence of indebtedness is not presented for redemption within thirty days after the first publication of the notice, the interest upon it ceases.