Immediately after the expiration of the time fixed by his or her notice for payment of assessments without interest, the treasurer shall divide the several assessments which remain unpaid in whole or in part into ten equal amounts or installments, as near as may be, without fractional cents, and enter said installments upon the roll opposite the several assessments, numbering the same from one to ten successively. And thereafter said treasurer shall annually for ten years, before the time fixed by law for the collection of state and county taxes, add one of the said assessment installments with interest for one year from the expiration of the time for payment without interest, or of the anniversary thereof, at a rate determined by the board on the entire unpaid assessment, to the tax levied upon the property assessed, where said tax appears upon the county tax roll, and collect said installment and interest, without reduction of percentage for prepayment, at the same time and in the same manner as state and county taxes are collected. And after delinquency said installments and interest shall be subject to the same charges for increased interest and penalties as are other delinquent taxes. But no tax sale of lands assessed under this chapter shall discharge the same from the lien of any unpaid installments of the assessment against it until all installments and interest are fully paid.