The city treasurer shall, as soon as any assessment roll payable on the "bond installment plan" has been placed in his hands for collection, publish a notice in the official newspaper of the city for ten consecutive daily or two consecutive weekly issues, that such 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. Whenever the cost and expense of any improvement shall be payable by the mode of "payment by bonds" the whole or any portion of any assessment levied on account of such improvement may be paid without penalty or interest during the first thirty (30) days following the date of the first publication of a notice by the city treasurer that such assessment and assessment roll is in his hands for collection, and the unpaid balance, if any, may be paid in equal annual installments, the number of which shall equal the number of years which the bonds to pay for the improvement may run; or, the lien of any such assessment may be discharged at any time after the said thirty (30) days by paying the entire unpaid portion thereof with all penalty and costs attaching, together with all interest thereof to date of delinquency of the installment thereof next falling due. The first installment shall become due and payable during the thirty-day period succeeding a date one year after the date of first publication of such notice, and annually thereafter each succeeding installment shall become due and payable in like manner. If the whole or any portion of any assessment remain unpaid after the first thirty-day period herein provided for, interest upon the whole unpaid sum shall be charged at the rate fixed in the ordinance providing for such improvement, and each year thereafter one of said installments, together with interest due upon the whole of the unpaid balance shall be collected. Any installment not paid prior to the expiration of the thirty-day period during which such installment is due and payable, shall thereupon become delinquent. All delinquent installments shall be subject to a charge for interest at the bond rate and to an additional charge of five percent penalty levied upon both principal and interest due on such installment or installments, until certified to the county treasurer as hereinafter provided.