After acquiring jurisdiction to proceed with the improvement, the city council shall levy the assessment for the portion or percentage required to pay for the improvement for the period of time beginning with the date of commencement of the improvement fixed by the city council and ending, as determined by and at the discretion of the city council either with the close of one 12-month period thereafter or with the close of the current or of the following fiscal year, upon all the respective lots or parcels of land in the assessment district. Thereafter during the period of time provided in the resolution of intention, the city council shall, on or before the beginning of the next succeeding 12-month period or the following fiscal year, levy in like manner and on the same lots or parcels of land the assessment for the portion or percentage required to pay for such improvement for such year, and said board, commission, or officer of the city authorized therefor shall, on or before 60 days prior to the commencement of each such period make and file with the city council a report in writing.