If either party feels aggrieved by the judgment, he may appeal as in other civil actions. An appeal by the defendant shall stay the execution of any writ of restitution, so long as the defendant deposits with the clerk of the district court the amount of judgment and costs, or gives an appeal bond with surety therefor, and thereafter pays into court, on a monthly basis, an amount equal to the monthly rent called for by the rental agreement at the time the complaint was filed.