All banks, trust companies, savings banks, investment companies and other persons carrying on a banking business are authorized to give to the authority a good and sufficient undertaking with such sureties as are approved by the bank, to the effect that the bank or banking institution shall faithfully keep and pay over to the order of, or upon the warrant of, the authority or its authorized agent all those funds deposited with it by the bank and agreed interest under, or by reason of, this chapter at such times or upon such demands as may be agreed with the bank or in lieu of these sureties, deposit with the authority or its authorized agent or a trustee or for the holders of bonds, as collateral, those securities as the authority may approve. The deposits of the authority may be evidenced by an agreement in the form, and upon the terms and conditions, that may be agreed upon by the authority and the depository bank or banking institution.