All warrants issued under RCW 91.08.550 may be presented by the holders thereof to the county treasurer, who shall pay them or endorse thereon the date of presentation for payment and if the same are not paid, and the reason for their nonpayment; and no warrant shall draw interest until it is so presented and endorsed by the county treasurer. It shall be the duty of the treasurer from time to time, when he or she has sufficient funds in his or her hands for the purpose, to give notice to warrant holders to present their warrants for payment; such notice to be given by advertisement in the county newspaper. And thirty days after the first publication of said notice the warrants called shall cease to bear interest. Said notice shall be published once each week for two weeks consecutively, and such warrants shall be called and paid in the order of their endorsement.