Where the willingness of the petitioner to pay all of the total cost is stated in the petition, the engineer shall compute the actual total cost as soon as the improvement is completed and the account called for in section nine of this article is furnished to him and, where more than one petitioner filed the petition, the engineer shall assess the amount owed by each petitioner according to the method indicated in the petition as prescribed in section four of this article: Provided, That if the actual total cost exceeds $1,000, the municipality shall be responsible for such excess over $1,000, and if the actual total cost is less than $1,000 but exceeds the estimated total cost by more than ten percent of the latter, the municipality shall be responsible for such excess over one hundred ten percent of the estimated total cost.
The engineer shall certify his determination of charges to the governing body, and, after adopting the same by ordinance or resolution, the governing body shall notify the petitioner of the assessment list by mailing a written copy thereof to the petitioner at the proper address, determined as aforesaid.