Upon the written application, under oath, to the director, or the director’s designee, by depositors representing five percent (5%) of the deposits of any financial institution, as shown by the last published return of the financial institution, or upon the written application to the director, or the director’s designee, of persons holding at least twenty-five percent (25%) of the outstanding capital stock of any regulated institution, or upon the written application to the director, or the director’s designee, of at least one third (?) in number of the board of directors or trustees of any regulated institution, setting forth their interest and the reasons for making an examination, and requesting him or her to examine the regulated institution, the director, or the director’s designee, may make or cause to be made a full investigation or examination of its affairs as provided by law.