Following the issuance of any refunding bonds pursuant to this article, the legislative body of the city shall provide for the payment of principal and interest thereon in the same manner and at the same times as it provides for payment of principal and interest on bonds issued pursuant to the act. The reassessments levied pursuant to this division shall be and constitute security for the payment of the refunding bonds in the same manner as the original unpaid assessments constituted security for the refunded bonds.