Where the amount to be deposited exceeds the amount which all state depositories in the state are willing to accept on the terms specified in this chapter, the state treasurer may, with the consent of the investment board, deposit the excess in any one (1) or more banks or trust companies in the state designated by the director of the department of finance, or if there be no bank or trust company in the state satisfactory to the investment board which is willing to accept such excess on the terms and conditions specified by the board, then in a bank or banks designated by said board outside the state, having a paidup capital and unimpaired surplus of not less than $5,000,000, located in a reserve city, as designated by the United States comptroller of the currency, subject to such regulations, upon such conditions and with such security as the board may fix and determine, and except as in this section otherwise provided and in the special cases for which express statutory provision is made otherwise, the state treasurer shall not deposit the funds of the state in his custody in banks or trust companies located outside the state of Idaho.