The urban county executive shall give bond payable to the county in the amount of not less than $5,000. The director of finance shall give bond in the amount of not less than fifteen percent of the amount of money to be received by him annually, but he shall not be required to give a bond in excess of five million dollars except as hereinafter provided. If the urban county executive serves also as director of finance, he shall give bond to the full amount indicated above for the director of finance. The board may fix bonds in excess of these amounts and require bonds of other county officers in the board’s discretion, conditioned on the faithful discharge of their duties and the proper accounting for all funds coming into their possession.