When an election is made to deposit amounts reserved under RCW 60.28.010, in an interest bearing account in a bank, mutual savings bank, or savings and loan association, the contractor and the agency shall select an institution agreeable to both. Any bank selected must be a qualified public depository under RCW 39.58.010. Deposits in mutual savings banks are subject to RCW 32.12.100 and deposits in savings and loan associations to RCW 33.52.010.