Document:

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                                                                    Exhibit 4.31

                    PREFERRED SECURITIES GUARANTEE AGREEMENT

                              BANK ONE CAPITAL II

                           Dated as of August 8, 2000
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                                TABLE OF CONTENTS

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ARTICLE I      DEFINITIONS AND INTERPRETATION

     SECTION 1.1    Definitions and Interpretation.......................................  2

ARTICLE II     TRUST INDENTURE ACT

     SECTION 2.1    Trust Indenture Act; Application.....................................  5
     SECTION 2.2    Lists of Holders of Securities.......................................  5
     SECTION 2.3    Reports by the Preferred Guarantee Trustee...........................  6
     SECTION 2.4    Periodic Reports to Preferred Guarantee Trustee......................  6
     SECTION 2.5    Evidence of Compliance with Conditions Precedent.....................  6
     SECTION 2.6    Events of Default; Waiver............................................  6
     SECTION 2.7    Event of Default; Notice.............................................  6
     SECTION 2.8    Conflicting Interests................................................  7

ARTICLE III    POWERS, DUTIES AND RIGHTS OF PREFERRED GUARANTEE TRUSTEE

     SECTION 3.1    Powers and Duties of the Preferred Guarantee Trustee.................  7
     SECTION 3.2    Certain Rights of Preferred Guarantee Trustee........................  9
     SECTION 3.3    Not Responsible for Recitals or Issuance of
                    Preferred Securities Guarantee....................................... 11

ARTICLE IV     PREFERRED GUARANTEE TRUSTEE

     SECTION 4.1    Preferred Guarantee Trustee; Eligibility............................. 11
     SECTION 4.2    Appointment, Removal and Resignation of Preferred Guarantee Trustee.. 12

ARTICLE V      GUARANTEE

     SECTION 5.1    Guarantee............................................................ 13
     SECTION 5.2    Waiver of Notice and Demand.......................................... 13
     SECTION 5.3    Obligations Not Affected............................................. 13
     SECTION 5.4    Rights of Holders.................................................... 14
     SECTION 5.5    Guarantee of Payment................................................. 15
     SECTION 5.6    Subrogation.......................................................... 15
     SECTION 5.7    Independent Obligations.............................................. 16

ARTICLE VI     LIMITATION OF TRANSACTIONS, SUBORDINATION

     SECTION 6.1    Limitation of Transactions........................................... 16
     SECTION 6.2    Subordination........................................................ 16
     SECTION 6.3    Pari Passu Guarantees................................................ 16

ARTICLE VII    TERMINATION

     SECTION 7.1    Termination.......................................................... 17
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ARTICLE VIII   INDEMNIFICATION

     SECTION 8.1    Exculpation.......................................................... 17
     SECTION 8.2    Indemnification...................................................... 18
     SECTION 8.3    Compensation and Reimbursement....................................... 18

ARTICLE IX     MISCELLANEOUS

     SECTION 9.1    Successors and Assigns............................................... 19
     SECTION 9.2    Amendments........................................................... 19
     SECTION 9.3    Notices.............................................................. 19
     SECTION 9.4    Benefit.............................................................. 20
     SECTION 9.5    Governing Law........................................................ 20
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                   PREFERRED SECURITIES GUARANTEE AGREEMENT

                  This GUARANTEE AGREEMENT (the "Preferred Securities
Guarantee"), dated as of August 8, 2000, is executed and delivered by BANK ONE
CORPORATION, a Delaware corporation (the "Guarantor"), and The Chase Manhattan
Bank, as trustee (the "Preferred Guarantee Trustee"), for the benefit of the
Holders (as defined herein) from time to time of the Preferred Securities (as
defined herein) of BANK ONE Capital II, a Delaware statutory business trust (the
"Issuer").

                  WHEREAS, pursuant to an Amended and Restated Declaration of
Trust (the "Declaration"), dated as of August 8, 2000, among the trustees of the
Issuer named therein, the Guarantor, as sponsor, and the holders from time to
time of undivided beneficial interests in the assets of the Issuer, the Issuer
is issuing on the date hereof 11,200,000 preferred securities, having an
aggregate liquidation amount of $280,000,000, designated the 8.500% Preferred
Securities (the "Preferred Securities") (including exercise of the underwriters'
over-allotment option);

                  WHEREAS, as incentive for the Holders to purchase the
Preferred Securities, the Guarantor desires irrevocably and unconditionally to
agree, to the extent set forth in this Preferred Securities Guarantee, to pay to
the Holders of the Preferred Securities the Guarantee Payments (as defined
herein) and to make certain other payments on the terms and conditions set forth
herein.

                  WHEREAS, the Guarantor is also executing and delivering a
guarantee agreement (the "Common Securities Guarantee") in substantially
identical terms to this Preferred Securities Guarantee for the benefit of the
holders of the Common Securities (as defined herein), except that if an Event of
Default (as defined in the Indenture), has occurred and is continuing, the
rights of holders of the Common Securities to receive Guarantee Payments under
the Common Securities Guarantee are subordinated to the rights of Holders of
Preferred Securities to receive Guarantee Payments under this Preferred
Securities Guarantee.

                  NOW, THEREFORE, in consideration of the purchase by each
Holder of Preferred Securities, which purchase the Guarantor hereby agrees shall
benefit the Guarantor, the Guarantor executes and delivers this Preferred
Securities Guarantee for the benefit of the Holders.
<PAGE>

                                   ARTICLE I
                        DEFINITIONS AND INTERPRETATION

SECTION 1.1 Definitions and Interpretation
            ------------------------------

                  In this Preferred Securities Guarantee, unless the context
otherwise requires:

                  (1)      Capitalized terms used in this Preferred Securities
     Guarantee but not defined in the preamble above have the respective
     meanings assigned to them in this Section 1.1 or in the Declaration, as the
     case may be;

                  (2)      a term defined anywhere in this Preferred Securities
     Guarantee has the same meaning throughout;

                  (3)      all references to "the Preferred Securities
     Guarantee" or "this Preferred Securities Guarantee" are to this Preferred
     Securities Guarantee as modified, supplemented or amended from time to
     time;

                  (4)      all references in this Preferred Securities Guarantee
     to Articles and Sections are to Articles and Sections of this Preferred
     Securities Guarantee, unless otherwise specified;

                  (5)      a term defined in the Trust Indenture Act has the
     same meaning when used in this Preferred Securities Guarantee, unless
     otherwise defined in this Preferred Securities Guarantee or unless the
     context otherwise requires; and

                  (6)      a reference to the singular includes the plural and
     vice versa.

                  "Affiliate" has the same meaning as given to that term in Rule
                   ---------
405 of the Securities Act of 1933, as amended, or any successor rule thereunder.

                  "Business Day" means a day other than (a) a Saturday or
                   ------------
Sunday, (b) a day on which banking institutions in The City of New York or the
City of Chicago are authorized or required by law or executive order to remain
closed, or (c) a day on which the Institutional Trustee's Corporate Trust Office
or the Corporate Trust Office of the Debenture Trustee is closed for business.

                  "Common Securities" means the securities representing common
                   -----------------
undivided beneficial interests in the assets of the Issuer.

                  "Corporate Trust Office" means (i) when used with respect to
                   ----------------------
the Preferred Guarantee Trustee, the principal corporate office of the Preferred
Guarantee Trustee located in New York, New York which on the date of this
Trustee Agreement is 450 West 33rd Street, New York, New York 10001 - Attention:
Capital Markets Fiduciary Services, (ii) when used with
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respect to the Debenture Trustee, its Principal Corporate Trust Office as
defined in the Indenture, and (iii) when used with respect to the Institutional
Trustee, its Corporate Trust Office as defined in the Declaration.

                  "Covered Person" means any Holder or beneficial owner of
                   --------------
Preferred Securities.

                  "Debentures" means the series of junior subordinated debt
                   ----------
securities of the Guarantor designated the Floating Rate Junior Subordinated
Deferrable Interest Debentures due August 15, 2030, held by the Institutional
Trustee (as defined in the Declaration) of the Issuer.

                  "Event of Default" means a default by the Guarantor on any of
                   ----------------
its payment or other obligations under this Preferred Securities Guarantee.

                  "Guarantee Payments" means the following payments or
                   ------------------
distributions, without duplication, with respect to the Preferred Securities, to
the extent not paid or made by the Issuer: (i) any accrued and unpaid
Distributions (as defined in the Declaration) that are required to be paid on
such Preferred Securities to the extent the Issuer shall have funds available
therefor, (ii) the redemption price, including all accrued and unpaid
Distributions to the date of redemption (the "Redemption Price") to the extent
the Issuer has funds available therefor, with respect to any Preferred
Securities called for redemption by the Issuer, and (iii) upon a voluntary or
involuntary dissolution, winding-up or termination of the Issuer (other than in
connection with the distribution of Debentures to the Holders in exchange for
Preferred Securities as provided in the Declaration), the lesser of (a) the
aggregate of the liquidation amount and all accrued and unpaid Distributions on
the Preferred Securities to the date of payment, to the extent the Issuer shall
have funds available therefor, and (b) the amount of assets of the Issuer
remaining available for distribution to Holders in liquidation of the Issuer (in
either case, the "Liquidation Distribution"). If an event of default under the
 Indenture has occurred and is continuing, the rights of holders of the Common
Securities to receive payments under the Common Securities Guarantee Agreement
are subordinated to the rights of Holders of Preferred Securities to receive
Guarantee Payments.

                  "Holder" shall mean any holder, as registered on the books and
                   ------
records of the Issuer of any Preferred Securities; provided, however, that, in
determining whether the holders of the requisite percentage of Preferred
Securities have given any request, notice, consent or waiver hereunder, "Holder"
shall not include the Guarantor or any Affiliate of the Guarantor.

                  "Indemnified Person" means the Preferred Guarantee Trustee,
                   ------------------
any Affiliate of the Preferred Guarantee Trustee, or any officers, directors,
shareholders, members, partners, employees, representatives, nominees,
custodians or agents of the Preferred Guarantee Trustee.

                  "Indenture" means the Indenture dated as of January 1, 1997,
                   ---------
among the Guarantor (the "Debenture Issuer") and The Chase Manhattan Bank, as
trustee, and any indenture supplemental thereto pursuant to which certain
subordinated debt securities of the Debenture Issuer are to be issued to the
Institutional Trustee of the Issuer.
<PAGE>

                  "Majority in liquidation amount of the Securities" means,
                   ------------------------------------------------
except as provided by the Trust Indenture Act, a vote by Holder(s) of Preferred
Securities, voting separately as a class, of more than 50% of the liquidation
amount (including the stated amount that would be paid on redemption,
liquidation or otherwise, plus accrued and unpaid Distributions to the date upon
which the voting percentages are determined) of all Preferred Securities.

                  "Officers' Certificate" means, with respect to any Person, a
                   ---------------------
certificate signed by two Authorized Officers of such Person. Any Officers'
Certificate delivered with respect to compliance with a condition or covenant
provided for in this Preferred Securities Guarantee (other than pursuant to
Section 314(a)(4) of the Trust Indenture Act) shall include:

                  (7)      a statement that each officer signing the Officers'
     Certificate has read the covenant or condition and the definition relating
     thereto;

                  (8)      a brief statement of the nature and scope of the
     examination or investigation undertaken by each officer in rendering the
     Officers' Certificate;

                  (9)      a statement that each such officer has made such
     examination or investigation as, in such officer's opinion, is necessary to
     enable such officer to express an informed opinion as to whether or not
     such covenant or condition has been complied with; and

                  (10)     a statement as to whether, in the opinion of each
     such officer, such condition or covenant has been complied with.

                  "Person" means a legal person, including any individual,
                   ------
corporation, estate, partnership, joint venture, association, joint stock
company, limited liability company, trust, unincorporated association, or
government or any agency or political subdivision thereof, or any other entity
of whatever nature.

                  "Preferred Guarantee Trustee" means The Chase Manhattan Bank,
                   ---------------------------
until a Successor Preferred Guarantee Trustee has been appointed and has
accepted such appointment pursuant to the terms of this Preferred Securities
Guarantee and thereafter means each such Successor Preferred Guarantee Trustee.

                  "Responsible Officer" means, when used with respect to the
                   -------------------
Preferred Guarantee Trustee, any officer assigned to the Corporate Trust Office
of the Preferred Guarantee Trustee, including any managing director, vice
president, assistant vice president, senior trust officer, trust officer,
assistant treasurer, assistant secretary or any other officer of the Preferred
Guarantee Trustee, customarily performing functions similar to those performed
by any of the above designated officers, and also, with respect to a particular
corporate trust matter, any other officer, to whom such matter is referred
because of such officer's knowledge of and familiarity with the particular
subject.
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                  "Successor Preferred Guarantee Trustee" means a successor
                   -------------------------------------
Preferred Guarantee Trustee possessing the qualifications to act as Preferred
Guarantee Trustee under Section 4.1.

                  "Trust Indenture Act" means the Trust Indenture Act of 1939,
                   -------------------
as amended.

                  "Trust Securities" means the Common Securities and the
                   ----------------
Preferred Securities.

                                  ARTICLE II
                              TRUST INDENTURE ACT

SECTION 2.1 Trust Indenture Act; Application
            --------------------------------

                  (1)      This Preferred Securities Guarantee is subject to the
     provisions of the Trust Indenture Act that are required to be part of this
     Preferred Securities Guarantee and shall, to the extent applicable, be
     governed by such provisions; and

                  (2)      if and to the extent that any provision of this
     Preferred Securities Guarantee limits, qualifies or conflicts with the
     duties imposed by Section 310 to 317, inclusive, of the Trust Indenture
     Act, such imposed duties shall control.

SECTION 2.2 Lists of Holders of Securities
            ------------------------------

                  (1)      The Guarantor shall provide the Preferred Guarantee
     Trustee with a list, in such form as the Preferred Guarantee Trustee may
     reasonably require, of the names and addresses of the Holders ("List of
     Holders"), (i) within 14 days after each record date for payment of
     Distributions (as defined in the Declaration) as of such record date, and
     (ii) at any other time within 30 days of receipt by the Guarantor of a
     written request for a List of Holders as of a date no more than 14 days
     before such List of Holders is given to the Preferred Guarantee Trustee
     provided, that the Guarantor shall not be obligated to provide such List of
     Holders at any time the List of Holders does not differ from the most
     recent List of Holders given to the Preferred Guarantee Trustee by the
     Guarantor. The Preferred Guarantee Trustee may destroy any List of Holders
     previously given to it on receipt of a new List of Holders.

                  (2)      The Preferred Guarantee Trustee shall comply with its
     obligations under Sections 311(a), 311(b) and Section 312(b) of the Trust
     Indenture Act.

SECTION 2.3 Reports by the Preferred Guarantee Trustee
            ------------------------------------------

                  Within 60 days after November 15 of each year commencing in
2000, the Preferred Guarantee Trustee shall provide to the Holders such reports
as are required by Section 313(a) of the Trust Indenture Act, if any, in the
form and in the manner provided by Section 313 of the Trust Indenture Act. The
Preferred Guarantee Trustee shall also comply with the other requirements of
Section 313 of the Trust Indenture Act.
<PAGE>

SECTION 2.4 Periodic Reports to Preferred Guarantee Trustee
            -----------------------------------------------

                  The Guarantor shall provide to the Preferred Guarantee Trustee
such documents, reports and information as required by Section 314 (if any) and
the compliance certificate required by Section 314(a)(4) of the Trust Indenture
Act in the form, in the manner and at the times required by Section 314(a)(4) of
the Trust Indenture Act, provided that such compliance certificate shall be
delivered on or before 120 days after the end of each fiscal year of the
Guarantor.

SECTION 2.5 Evidence of Compliance with Conditions Precedent
            ------------------------------------------------

                  The Guarantor shall provide to the Preferred Guarantee Trustee
such evidence of compliance with any conditions precedent, if any, provided for
in this Preferred Securities Guarantee that relate to any of the matters set
forth in Section 314(c) of the Trust Indenture Act. Any certificate or opinion
required to be given by an officer pursuant to Section 314(c)(1) may be given in
the form of an Officers' Certificate.

SECTION 2.6 Events of Default; Waiver
            -------------------------

                  The Holders of a Majority in liquidation amount of Preferred
Securities may, by vote, on behalf of the Holders of all of the Preferred
Securities, waive any past Event of Default and its consequences. Upon such
waiver, any such Event of Default shall cease to exist, and any Event of Default
arising therefrom shall be deemed to have been cured, for every purpose of this
Preferred Securities Guarantee, but no such waiver shall extend to any
subsequent or other default or Event of Default or impair any right consequent
thereon.

SECTION 2.7 Event of Default; Notice
            ------------------------

                  (1)      The Preferred Guarantee Trustee shall, within 90 days
     after the occurrence of an Event of Default, transmit by mail, first class
     postage prepaid, to the Holders, notices of all Events of Default actually
     known to a Responsible Officer of the Preferred Guarantee Trustee, unless
     such defaults have been cured before the giving of such notice, provided,
     that, the Preferred Guarantee Trustee shall be protected in withholding
     such notice if and so long as a Responsible Officer of the Preferred
     Guarantee Trustee in good faith determines that the withholding of such
     notice is in the interests of the Holders of the Preferred Securities.

                  (2)      The Preferred Guarantee Trustee shall not be deemed
     to have knowledge of any Event of Default unless the Preferred Guarantee
     Trustee shall have received written notice thereof from the Guarantor or a
     Holder, or a Responsible Officer of the Preferred Guarantee Trustee charged
     with the administration of the Declaration shall have obtained actual
     knowledge thereof.
<PAGE>

SECTION 2.8 Conflicting Interests
            ---------------------

                  The Declaration shall be deemed to be specifically described
in this Preferred Securities Guarantee for the purposes of clause (i) of the
first proviso contained in Section 310(b) of the Trust Indenture Act.

                                  ARTICLE III
                         POWERS, DUTIES AND RIGHTS OF
                          PREFERRED GUARANTEE TRUSTEE

SECTION 3.1  Powers and Duties of the Preferred Guarantee Trustee
             ----------------------------------------------------

                  (1)      This Preferred Securities Guarantee shall be held by
     the Preferred Guarantee Trustee for the benefit of the Holders, and the
     Preferred Guarantee Trustee shall not transfer this Preferred Securities
     Guarantee to any Person except a Holder exercising his or her rights
     pursuant to Section 5.4(c) or to a Successor Preferred Guarantee Trustee on
     acceptance by such Successor Preferred Guarantee Trustee of its appointment
     to act as Successor Preferred Guarantee Trustee. The right, title and
     interest of the Preferred Guarantee Trustee shall automatically vest in any
     Successor Preferred Guarantee Trustee, and such vesting and cessation of
     title shall be effective whether or not conveyancing documents have been
     executed and delivered pursuant to the appointment of such Successor
     Preferred Guarantee Trustee.

                  (2)      If an Event of Default actually known to a
     Responsible Officer of the Preferred Guarantee Trustee has occurred and is
     continuing, the Preferred Guarantee Trustee shall enforce this Preferred
     Securities Guarantee for the benefit of the Holders.

                  (3)      The Preferred Guarantee Trustee, before the
     occurrence of any Event of Default and after the curing of all Events of
     Default that may have occurred, shall undertake to perform only such duties
     as are specifically set forth in this Preferred Securities Guarantee, and
     no implied covenants shall be read into this Preferred Securities Guarantee
     against the Preferred Guarantee Trustee. In case an Event of Default has
     occurred (that has not been cured or waived pursuant to Section 2.6) and is
     actually known to a Responsible Officer of the Preferred Guarantee Trustee,
     the Preferred Guarantee Trustee shall exercise such of the rights and
     powers vested in it by this Preferred Securities Guarantee, and use the
     same degree of care and skill in its exercise thereof, as a prudent person
     would exercise or use under the circumstances in the conduct of his or her
     own affairs.
<PAGE>

                  (4)      No provision of this Preferred Securities Guarantee
     shall be construed to relieve the Preferred Guarantee Trustee from
     liability for its own negligent action, its own negligent failure to act,
     or its own willful misconduct, except that:

                           (1)      prior to the occurrence of any Event of
                  Default and after the curing or waiving of all such Events of
                  Default that may have occurred:

                                    (1)     the duties and obligations of the
                           Preferred Guarantee Trustee shall be determined
                           solely by the express provisions of this Preferred
                           Securities Guarantee, and the Preferred Guarantee
                           Trustee shall not be liable except for the
                           performance of such duties and obligations as are
                           specifically set forth in this Preferred Securities
                           Guarantee, and no implied covenants or obligations
                           shall be read into this Preferred Securities
                           Guarantee against the Preferred Guarantee Trustee;
                           and

                                    (2)     in the absence of bad faith on the
                           part of the Preferred Guarantee Trustee, the
                           Preferred Guarantee Trustee may conclusively rely, as
                           to the truth of the statements and the correctness of
                           the opinions expressed therein, upon any certificates
                           or opinions furnished to the Preferred Guarantee
                           Trustee and conforming to the requirements of this
                           Preferred Securities Guarantee; but in the case of
                           any such certificates or opinions that by any
                           provision hereof are specifically required to be
                           furnished to the Preferred Guarantee Trustee, the
                           Preferred Guarantee Trustee shall be under a duty to
                           examine the same to determine whether or not they
                           conform to the requirements of this Preferred
                           Securities Guarantee;

                           (2)      the Preferred Guarantee Trustee shall not be
                    liable for any error of judgment made in good faith by a
                    Responsible Officer of the Preferred Guarantee Trustee,
                    unless it shall be proved that the Preferred Guarantee
                    Trustee was negligent in ascertaining the pertinent facts
                    upon which such judgment was made;

                           (3)      the Preferred Guarantee Trustee shall not be
                    liable with respect to any action taken or omitted to be
                    taken by it in good faith in accordance with the direction
                    of the Holders of not less than a Majority in liquidation
                    amount of the Preferred Securities relating to the time,
                    method and place of conducting any proceeding for any remedy
                    available to the Preferred Guarantee Trustee, or exercising
                    any trust or power conferred upon the Preferred Guarantee
                    Trustee under this Preferred Securities Guarantee; and

                           (4)      no provision of this Preferred Securities
                    Guarantee shall require the Preferred Guarantee Trustee to
                    expend or risk its own funds or otherwise incur personal
                    financial liability in the performance of any of its duties
                    or in the exercise of any of its rights or powers, if the
                    Preferred Guarantee Trustee shall
<PAGE>

             have reasonable grounds for believing that the repayment of such
             funds or liability is not reasonably assured to it under the terms
             of this Preferred Securities Guarantee or indemnity, reasonably
             satisfactory to the Preferred Guarantee Trustee, against such risk
             or liability is not reasonably assured to it.

SECTION 3.2  Certain Rights of Preferred Guarantee Trustee
             ---------------------------------------------

             (1)      Subject to the provisions of Section 3.1:

                      (1)      The Preferred Guarantee Trustee may conclusively
             rely, and shall be fully protected in acting or refraining from
             acting upon, any resolution, certificate, statement, instrument,
             opinion, report, notice, request, direction, consent, order, bond,
             debenture, note, other evidence of indebtedness or other paper or
             document believed by it to be genuine and to have been signed, sent
             or presented by the proper party or parties.

                      (2)      Any direction or act of the Guarantor
             contemplated by this Preferred Securities Guarantee shall be
             sufficiently evidenced by an Officers' Certificate.

                      (3)      Whenever, in the administration of this Preferred
             Securities Guarantee, the Preferred Guarantee Trustee shall deem it
             desirable that a matter be proved or established before taking,
             suffering or omitting any action hereunder, the Preferred Guarantee
             Trustee (unless other evidence is herein specifically prescribed)
             may, in the absence of bad faith on its part, request and
             conclusively rely upon an Officers' Certificate which, upon receipt
             of such request, shall be promptly delivered by the Guarantor.

                      (4)      The Preferred Guarantee Trustee shall have no
             duty to see to any recording, filing or registration of any
             instrument (or any rerecording, refiling or registration thereof).

                      (5)      The Preferred Guarantee Trustee may consult with
             counsel of its selection, and the advice or opinion of such counsel
             with respect to legal matters shall be full and complete
             authorization and protection in respect of any action taken,
             suffered or omitted by it hereunder in good faith and in accordance
             with such advice or opinion. Such counsel may be counsel to the
             Guarantor or any of its Affiliates and may include any of its
             employees. The Preferred Guarantee Trustee shall have the right at
             any time to seek instructions concerning the administration of this
             Preferred Securities Guarantee from any court of competent
             jurisdiction.

                      (6)      The Preferred Guarantee Trustee shall be under no
             obligation to exercise any of the rights or powers vested in it by
             this Preferred Securities
<PAGE>

             Guarantee at the request or direction of any Holder, unless such
             Holder shall have provided to the Preferred Guarantee Trustee such
             security and indemnity, reasonably satisfactory to the Preferred
             Guarantee Trustee, against the costs, expenses (including
             attorneys' fees and expenses and the expenses of the Preferred
             Guarantee Trustee's agents, nominees or custodians) and liabilities
             that might be incurred by it in complying with such request or
             direction, including such reasonable advances as may be requested
             by the Preferred Guarantee Trustee; provided that, nothing
             contained in this Section 3.2(a)(vi) shall be taken to relieve the
             Preferred Guarantee Trustee, upon the occurrence of an Event of
             Default, of its obligation to exercise the rights and powers vested
             in it by this Preferred Securities Guarantee.

                           (7)      The Preferred Guarantee Trustee shall not be
             bound to make any investigation into the facts or matters stated in
             any resolution, certificate, statement, instrument, opinion,
             report, notice, request, direction, consent, order, bond,
             debenture, note, other evidence of indebtedness or other paper or
             document, but the Preferred Guarantee Trustee, in its discretion,
             may make such further inquiry or investigation into such facts or
             matters as it may see fit.

                           (8)      The Preferred Guarantee Trustee may execute
             any of the trusts or powers hereunder or perform any duties
             hereunder either directly or by or through agents, nominees,
             custodians or attorneys, and the Preferred Guarantee Trustee shall
             not be responsible for any misconduct or negligence on the part of
             any agent or attorney appointed with due care by it hereunder.

                           (9)      Any action taken by the Preferred Guarantee
             Trustee or its agents hereunder shall bind the Holders, and the
             signature of the Preferred Guarantee Trustee or its agents alone
             shall be sufficient and effective to perform any such action. No
             third party shall be required to inquire as to the authority of the
             Preferred Guarantee Trustee to so act or as to its compliance with
             any of the terms and provisions of this Preferred Securities
             Guarantee, both of which shall be conclusively evidenced by the
             Preferred Guarantee Trustee's or its agent's taking such action.

                           (10)     Whenever in the administration of this
             Preferred Securities Guarantee the Preferred Guarantee Trustee
             shall deem it desirable to receive instructions with respect to
             enforcing any remedy or right or taking any other action hereunder,
             the Preferred Guarantee Trustee (i) may request instructions from
             the Holders of a Majority in liquidation amount of the Preferred
             Securities, (ii) may refrain from enforcing such remedy or right or
             taking such other action until such instructions are received, and
             (iii) shall be protected in conclusively relying on or acting in
             accordance with such instructions.
<PAGE>

               (11) The Preferred Guarantee Trustee shall not be liable for any
          action taken, suffered or omitted to be taken by it in good faith and
          reasonably believed by it to be authorized or within the discretion or
          rights or powers conferred upon it by this Preferred Securities
          Guarantee.

          (2) No provision of this Preferred Securities Guarantee shall be
     deemed to impose any duty or obligation on the Preferred Guarantee Trustee
     to perform any act or acts or exercise any right, power, duty or obligation
     conferred or imposed on it in any jurisdiction in which it shall be
     illegal, or in which the Preferred Guarantee Trustee shall be unqualified
     or incompetent in accordance with applicable law, to perform any such act
     or acts or to exercise any such right, power, duty or obligation.  No
     permissive power or authority available to the Preferred Guarantee Trustee
     shall be construed to be a duty.

SECTION 3.3    Not Responsible for Recitals or Issuance of Preferred Securities
               ----------------------------------------------------------------
Guarantee
---------

          The recitals contained in this Preferred Securities Guarantee shall be
taken as the statements of the Guarantor, and the Preferred Guarantee Trustee
does not assume any responsibility for their correctness.  The Preferred
Guarantee Trustee makes no representation as to the validity or sufficiency of
this Preferred Securities Guarantee.

                                   ARTICLE IV
                          PREFERRED GUARANTEE TRUSTEE

SECTION 4.1    Preferred Guarantee Trustee; Eligibility
               ----------------------------------------

          (1) There shall at all times be a Preferred Guarantee Trustee which
shall:

               (1) not be an Affiliate of the Guarantor; and

               (2) be a corporation organized and doing business under the laws
          of the United States of America or any State or Territory thereof or
          of the District of Columbia, or a corporation or Person permitted by
          the Securities and Exchange Commission to act as an institutional
          trustee under the Trust Indenture Act, authorized under such laws to
          exercise corporate trust powers, having a combined capital and surplus
          of at least fifty million U.S. dollars ($50,000,000), and subject to
          supervision or examination by Federal, State, Territorial or District
          of Columbia authority.  If such corporation publishes reports of
          condition at least annually, pursuant to law or to the requirements of
          the supervising or examining authority referred to above, then, for
          the purposes of this Section 4.1(a)(ii), the combined capital and
          surplus of such corporation shall be deemed to be its combined capital
          and surplus as set forth in its most recent report of condition so
          published.
<PAGE>

          (2) If at any time the Preferred Guarantee Trustee shall cease to be
     eligible to so act under Section 4.1(a), the Preferred Guarantee Trustee
     shall immediately resign in the manner and with the effect set out in
     Section 4.2(c).

          (3) If the Preferred Guarantee Trustee has or shall acquire any
     "conflicting interest" within the meaning of Section 310(b) of the Trust
     Indenture Act, the Preferred Guarantee Trustee and Guarantor shall in all
     respects comply with the provisions of Section 310(b) of the Trust
     Indenture Act, subject to the penultimate paragraph thereof.  To the extent
     permitted by the Trust Indenture Act, the Preferred Guarantee Trustee shall
     not be deemed to have a conflicting interest with respect to the Preferred
     Securities Guarantee by virtue of being trustee under the Indentures
     originally dated as of November 15, 1996 and January 1, 1997, between the
     Company and the Preferred Guarantee Trustee or by virtue of being (i) a
     trustee on the Series A Declaration, the Series B Declaration, the 1997
     Declaration or the 1999 Declaration (each as defined in the Declaration),
     (ii) a trustee on the Series A Guarantee, the Series B Guarantee, the 1997
     Guarantee or the 1999 Guarantee (each as defined in the Declaration), or
     (iii) a trustee on the Declaration.

SECTION 4.2    Appointment, Removal and Resignation of Preferred Guarantee
               -----------------------------------------------------------
Trustee
-------

          (1) Subject to Section 4.2(b), the Preferred Guarantee Trustee may be
     appointed or removed without cause at any time by the Guarantor except
     during an Event of Default.

          (2) The Preferred Guarantee Trustee shall not be removed in accordance
     with Section 4.2(a) until a Successor Preferred Guarantee Trustee has been
     appointed and has accepted such appointment by written instrument executed
     by such Successor Preferred Guarantee Trustee and delivered to the
     Guarantor.

          (3) The Preferred Guarantee Trustee appointed to office shall hold
     office until a Successor Preferred Guarantee Trustee shall have been
     appointed or until its removal or resignation.  The Preferred Guarantee
     Trustee may resign from office (without need for prior or subsequent
     accounting) by an instrument in writing executed by the Preferred Guarantee
     Trustee and delivered to the Guarantor, which resignation shall not take
     effect until a Successor Preferred Guarantee Trustee has been appointed and
     has accepted such appointment by instrument in writing executed by such
     Successor Preferred Guarantee Trustee and delivered to the Guarantor and
     the resigning Preferred Guarantee Trustee.

          (4) If no Successor Preferred Guarantee Trustee shall have been
     appointed and accepted appointment as provided in this Section 4.2 within
     60 days after delivery of an instrument of removal or resignation, the
     Preferred Guarantee Trustee resigning or being removed may petition any
     court of competent jurisdiction for appointment of a Successor Preferred
     Guarantee Trustee.  Such court may thereupon, after prescribing such
     notice, if any, as it may deem proper, appoint a Successor Preferred
     Guarantee Trustee.
<PAGE>

          (5) No Preferred Guarantee Trustee shall be liable for the acts or
     omissions to act of any Successor Preferred Guarantee Trustee.

          (6) Upon termination of this Preferred Securities Guarantee or removal
     or resignation of the Preferred Guarantee Trustee pursuant to this Section
     4.2, the Guarantor shall pay to the Preferred Guarantee Trustee all amounts
     due to the Preferred Guarantee Trustee accrued to the date of such
     termination, removal or resignation.

                                   ARTICLE V
                                   GUARANTEE

SECTION 5.1    Guarantee
               ---------

          The Guarantor irrevocably and unconditionally agrees to pay in full to
the Holders the Guarantee Payments (without duplication of amounts theretofore
paid by the Issuer), as and when due, regardless of any defense, right of set-
off or counterclaim that the Issuer may have or assert.  The Guarantor's
obligation to make a Guarantee Payment may be satisfied by direct payment of the
required amounts by the Guarantor to the Holders or by causing the Issuer to pay
such amounts to the Holders.

SECTION 5.2    Waiver of Notice and Demand
               ---------------------------

          The Guarantor hereby waives notice of acceptance of this Preferred
Securities Guarantee and of any liability to which it applies or may apply,
presentment, demand for payment, any right to require a proceeding first against
the Issuer or any other Person before proceeding against the Guarantor, protest,
notice of nonpayment, notice of dishonor, notice of redemption and all other
notices and demands.

SECTION 5.3    Obligations Not Affected
               ------------------------

          The obligations, covenants, agreements and duties of the Guarantor
under this Preferred Securities Guarantee shall in no way be affected or
impaired by reason of the happening from time to time of any of the following:

          (1) the release or waiver, by operation of law or otherwise, of the
     performance or observance by the Issuer of any express or implied
     agreement, covenant, term or condition relating to the Preferred Securities
     to be performed or observed by the Issuer;

          (2) the extension of time for the payment by the Issuer of all or any
     portion of the Distributions, Redemption Price, Liquidation Distribution or
     any other sums payable under the terms of the Preferred Securities or the
     extension of time for the performance of any other obligation under,
     arising out of, or in connection with, the Preferred Securities
<PAGE>

     (other than an extension of time for payment of Distributions, Redemption
     Price, Liquidation Distribution or other sum payable that results from the
     extension of any interest payment period on the Debentures or any extension
     of the maturity date of the Debentures permitted by the Indenture);

          (3) any failure, omission, delay or lack of diligence on the part of
     the Holders to enforce, assert or exercise any right, privilege, power or
     remedy conferred on the Holders pursuant to the terms of the Preferred
     Securities, or any action on the part of the Issuer granting indulgence or
     extension of any kind;

          (4) the voluntary or involuntary liquidation, dissolution, sale of any
     collateral, receivership, insolvency, bankruptcy, assignment for the
     benefit of creditors, reorganization, arrangement, composition or
     readjustment of debt of, or other similar proceedings affecting, the Issuer
     or any of the assets of the Issuer;

          (5) any invalidity of, or defect or deficiency in, the Preferred
     Securities;

          (6) the settlement or compromise of any obligation guaranteed hereby
     or hereby incurred; or

          (7) any other circumstance whatsoever that might otherwise constitute
     a legal or equitable discharge or defense of a guarantor, it being the
     intent of this Section 5.3 that the obligations of the Guarantor hereunder
     shall be absolute and unconditional under any and all circumstances.

          There shall be no obligation of the Holders to give notice to, or
obtain consent of, the Guarantor with respect to the happening of any of the
foregoing.

SECTION 5.4    Rights of Holders
               -----------------

          (1) The Issuer expressly acknowledges that (i) this Preferred
     Securities Guarantee will be deposited with the Preferred Guarantee Trustee
     to be held for the benefit of the Holders and (ii) the Preferred Guarantee
     Trustee has the right to enforce this Preferred Securities Guarantee on
     behalf of the Holders.

          (2) The Holders of a Majority in liquidation amount of the Preferred
     Securities have the right to direct the time, method and place of
     conducting of any proceeding for any remedy available to the Preferred
     Guarantee Trustee in respect of this Preferred Securities Guarantee or
     exercising any trust or power conferred upon the Preferred Guarantee
     Trustee under this Preferred Securities Guarantee; provided, however, that,
     subject to Section 3.1, the Preferred Guarantee Trustee shall have the
     right to decline to follow any such direction if the Preferred Guarantee
     Trustee shall determine that the action so directed would be unjustly
     prejudicial to the Holders not taking part in such direction or if the
     Preferred Guarantee Trustee being advised by counsel determines that the
     action or proceeding so directed may not lawfully be taken or if the
     Preferred
<PAGE>

     Guarantee Trustee in good faith by its board of directors or trustees,
     executive committee, or a trust committee of directors or trustees and/or
     Responsible Officers shall determine that the action or proceeding so
     directed would involve the Preferred Guarantee Trustee in personal
     liability.

          (3) If the Preferred Guarantee Trustee fails to enforce such Preferred
     Securities Guarantee, any Holder may institute a legal proceeding directly
     against the Guarantor to enforce the Preferred Guarantee Trustee's rights
     under this Preferred Securities Guarantee, without first instituting a
     legal proceeding against the Issuer, the Preferred Guarantee Trustee or any
     other person or entity.  The Guarantor waives any right or remedy to
     require that any action be brought first against the Issuer or any other
     person or entity before proceeding directly against the Guarantor.

SECTION 5.5    Guarantee of Payment
               --------------------

          This Preferred Securities Guarantee creates a guarantee of payment and
not of collection.

SECTION 5.6    Subrogation
               -----------

          The Guarantor shall be subrogated to all (if any) rights of the
Holders against the Issuer in respect of any amounts paid to such Holders by the
Guarantor under this Preferred Securities Guarantee; provided, however, that the
Guarantor shall not (except to the extent required by mandatory provisions of
law) be entitled to enforce or exercise any right that it may acquire by way of
subrogation or any indemnity, reimbursement or other agreement, in all cases as
a result of payment under this Preferred Securities Guarantee, if, at the time
of any such payment, any amounts are due and unpaid under this Preferred
Securities Guarantee.  If any amount shall be paid to the Guarantor in violation
of the preceding sentence, the Guarantor agrees to hold such amount in trust for
the Holders and to pay over such amount to the Holders.

SECTION 5.7    Independent Obligations
               -----------------------

          The Guarantor acknowledges that its obligations hereunder are
independent of the obligations of the Issuer with respect to the Preferred
Securities, and that the Guarantor shall be liable as principal and as debtor
hereunder to make Guarantee Payments pursuant to the terms of this Preferred
Securities Guarantee notwithstanding the occurrence of any event referred to in
subsections (a) through (g), inclusive, of Section 5.3 hereof.

                                   ARTICLE VI
                   LIMITATION OF TRANSACTIONS, SUBORDINATION

SECTION 6.1    Limitation of Transactions
               --------------------------
<PAGE>

          So long as any Preferred Securities remain outstanding, if there shall
have occurred an Event of Default, then the Guarantor shall not and it shall not
permit any subsidiary to, (a) declare or pay any dividends or distributions on,
or redeem, purchase, acquire or make a liquidation payment with respect to, any
shares of the Guarantor's capital stock, or (b) make any payment of principal of
or interest or premium, if any, on or repay, repurchase or redeem any debt
securities of the Guarantor that rank pari passu in all respects with or junior
in interest to the Debentures or make any guarantee payments with respect to any
guarantee by the Guarantor of debt securities of any subsidiary of the Guarantor
if such guarantee ranks pari passu with or junior in interest to the Debentures
(other than (a) dividends or distributions in common stock of the Guarantor, (b)
any declaration of a dividend in connection with the implementation of a Rights
Plan (as defined in the Indenture), or the issuance of stock under any such
Rights Plan in the future, or the redemption or repurchase of any such rights
pursuant thereto, (c) payments under this Preferred Securities Guarantee, (d)
purchases of common stock related to the issuance of common stock or rights
under any of the Guarantor's benefit plans for its directors, officers or
employees and (e) obligations under any dividend reinvestment and stock purchase
plan).

SECTION 6.2    Subordination.
               --------------

          The obligations of the Guarantor under this Preferred Securities
Guarantee will constitute unsecured obligations of the Guarantor and will rank
subordinate and junior in right of payments to the Senior Indebtedness and
General Obligations (each as defined in the Indenture) to the extent and in the
manner set forth in the Indenture.  The obligations of the Guarantor under this
Preferred Securities Guarantee do not constitute Senior Indebtedness or General
Obligations.

SECTION 6.3    Pari Passu Guarantees
               ---------------------

          The obligations of the Guarantor under this Preferred Securities
Guarantee shall rank pari passu with the obligations of the Guarantor under (i)
any similar Bank One Guarantee (as defined in the Indenture) issued by the
Guarantor on behalf of the holders of preferred or capital securities issued by
any Bank One Capital Trust (as defined in the Indenture) and (ii) the Series A
Guarantee, the Series B Guarantee, the 1997 Guarantee and the 1999 Guarantee.

                                  ARTICLE VII
                                  TERMINATION

SECTION 7.1    Termination
               -----------
<PAGE>

          This Preferred Securities Guarantee shall terminate upon (i) full
payment of the Redemption Price of all Preferred Securities, (ii) upon the
distribution of the Debentures to the Holders of all of the Preferred Securities
or (iii) upon full payment of the amounts payable in accordance with the
Declaration upon liquidation of the Issuer.  Notwithstanding the foregoing, this
Preferred Securities Guarantee will continue to be effective or will be
reinstated, as the case may be, if at any time any Holder must restore payment
of any sums paid under the Preferred Securities or under this Preferred
Securities Guarantee.

                                  ARTICLE VIII
                                INDEMNIFICATION

SECTION 8.1    Exculpation
               -----------

          (1) No Indemnified Person shall be liable, responsible or accountable
     in damages or otherwise to the Guarantor or any Covered Person for any
     loss, damage or claim incurred by reason of any act or omission performed
     or omitted by such Indemnified Person in good faith in accordance with this
     Preferred Securities Guarantee and in a manner that such Indemnified Person
     reasonably believed to be within the scope of the authority conferred on
     such Indemnified Person by this Preferred Securities Guarantee or by law,
     except that an Indemnified Person shall be liable for any such loss, damage
     or claim incurred by reason of such Indemnified Person's negligence or
     willful misconduct with respect to such acts or omissions.

          (2) An Indemnified Person shall be fully protected in relying in good
     faith upon the records of the Guarantor and upon such information,
     opinions, reports or statements presented to the Guarantor by any Person as
     to matters the Indemnified Person reasonably believes are within such other
     Person's professional or expert competence, including information,
     opinions, reports or statements as to the value and amount of the assets,
     liabilities, profits, losses or any other facts pertinent to the existence
     and amount of assets from which Distributions to Holders might properly be
     paid.

SECTION 8.2    Indemnification
               ---------------

          The Guarantor agrees to indemnify each Indemnified Person for, and to
hold each Indemnified Person harmless against, any and all loss, liability,
damage, claim or expense incurred without negligence or bad faith on its part,
arising out of or in connection with the acceptance or administration of the
trust or trusts hereunder, including the costs and expenses (including
reasonable legal fees and expenses) of defending itself against, or
investigating, any claim or liability in connection with the exercise or
performance of any of its powers or duties hereunder.  The obligation to
indemnify as set forth in this Section 8.2 shall survive the termination of this
Preferred Securities Guarantee or the earlier resignation or removal of the
Preferred Guarantee Trustee.
<PAGE>

SECTION 8.3    Compensation and Reimbursement
               ------------------------------

          The Guarantor agrees:

          (1) to pay to the Preferred Guarantee Trustee from time to time
reasonable compensation for all services rendered by it hereunder in such
amounts as the Guarantor and the Preferred Guarantee Trustee shall agree from
time to time (which compensation shall not be limited by any provision of law in
regard to the compensation of a trustee of an express trust); and

          (2) to reimburse the Preferred Guarantee Trustee upon its request for
all reasonable expenses, disbursements and advances incurred or made by the
Preferred Guarantee Trustee in accordance with any provision of this Preferred
Securities Guarantee (including the reasonable compensation and the expenses and
disbursements or its agents and counsel), except any such expense, disbursement
or advance as may be attributable to its negligence or bad faith.

          The obligations of the Guarantor under this Section 8.3 shall survive
the termination of this Preferred Securities Guarantee or the earlier
resignation or removal of the Preferred Guarantee Trustee.

          To secure the Guarantor's payment obligations in this Section and in
Section 8.2, the Guarantor and the Holders agree that the Preferred Guarantee
Trustee shall have a lien prior to the Preferred Securities on all money or
property held or collection by the Guarantee Trustee.  Such lien shall survive
the termination of this Preferred Securities Guarantee.

                                   ARTICLE IX
                                 MISCELLANEOUS

SECTION 9.1    Successors and Assigns
               ----------------------

          All guarantees and agreements contained in this Preferred Securities
Guarantee shall bind the successors, assigns, receivers, trustees and
representatives of the Guarantor and shall inure to the benefit of the Holders
of the Preferred Securities then outstanding.

SECTION 9.2    Amendments
               ----------
<PAGE>

          Except with respect to any changes that do not adversely affect the
rights of Holders (in which case no consent of Holders will be required), this
Preferred Securities Guarantee may only be amended with the prior approval of
the Holders of at least a Majority in liquidation amount (including the stated
amount that would be paid on redemption, liquidation or otherwise, plus accrued
and unpaid Distributions to the date upon which the voting percentages are
determined) of all the outstanding Preferred Securities.  The provisions of the
Declaration with respect to consents to amendments thereof (whether at a meeting
or otherwise) of Holders of the Securities shall apply to the giving of such
approval.

SECTION 9.3    Notices
               -------

          All notices provided for in this Preferred Securities Guarantee shall
be in writing, duly signed by the party giving such notice, and shall be
delivered, telecopied or mailed by first class mail, as follows:

          (1) If given to the Preferred Guarantee Trustee, at the Preferred
     Guarantee Trustee's mailing address set forth below (or such other address
     as the Preferred Guarantee Trustee may give notice of to the Holders and
     the Guarantor):

               The Chase Manhattan Bank
               450 West 33rd Street
               New York, New York  10001
               Attention:  Capital Markets Fiduciary Services
               Telecopy:   (212) 946-8159/8160

          (2) If given to the Guarantor, at the Guarantor's mailing address set
     forth below (or such other address as the Guarantor may give notice of to
     the Holders and the Preferred Guarantee Trustee):

               BANK ONE CORPORATION
               1 Bank One Plaza
               Chicago, Illinois  60670
               Attention:  Treasurer
               Telecopy:   (312) 732-3366

          (3) If given to any Holder, at the address set forth on the books and
     records of the Issuer.

          All such notices shall be deemed to have been given when received in
person, telecopied with receipt confirmed, or mailed by first class mail,
postage prepaid except that if a notice or other document is refused delivery or
cannot be delivered because of a changed address of which no notice was given,
such notice or other document shall be deemed to have been delivered on the date
of such refusal or inability to deliver.
<PAGE>

SECTION 9.4    Benefit
               -------

          This Preferred Securities Guarantee is solely for the benefit of the
Holders and, subject to Section 3.1(a), is not separately transferable from the
Preferred Securities.

SECTION 9.5    Governing Law
               -------------

          THIS PREFERRED SECURITIES GUARANTEE SHALL BE GOVERNED BY, AND
CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.
<PAGE>

          THIS PREFERRED SECURITIES GUARANTEE is executed as of the day and year
first above written.

                                   BANK ONE CORPORATION,
                                    as Guarantor

                                   By:__________________________________
                                      Name:  Charles W. Scharf
                                      Title: Executive Vice President and Chief
                                             Financial Officer

                                   THE CHASE MANHATTAN BANK,
                                   as Preferred Guarantee Trustee

                                   By:__________________________________
                                      Name:
                                      Title:<PAGE>
                                                                    Exhibit 10.5

                             MANAGEMENT AGREEMENT

                                    BETWEEN

                         USA OFFSHORE MANAGEMENT, LTD.

                                      AND

                        AMERINST INSURANCE COMPANY, LTD.

     THIS AGREEMENT is made and entered into this 2nd day of December, 1999,
between USA OFFSHORE MANAGEMENT, LTD., a Bermuda corporation with its principal
office in Hamilton, Bermuda (hereinafter referred to as "MANAGER"), and AmerInst
Insurance Company, Ltd. (on behalf of itself and related companies, AmerInst
Mezco, Ltd, AmerInst Insurance Group, Ltd. and AmerInst Investment Company,
Ltd.), a Bermuda corporation with its principal office in Hamilton, Bermuda
(hereinafter referred to as "COMPANY").

                              W I T N E S S E T H

     WHEREAS, MANAGER is a company engaged in managing and administering
insurance companies pursuant to section 10 of the Bermuda Insurance Act of 1978;
and

     WHEREAS, COMPANY desires to employ MANAGER serve as its Principal
Representative and to perform management and administration services in
connection with the operation of COMPANY, which is a Bermuda corporation
established pursuant to the Bermuda Insurance Act of 1978, and MANAGER is
willing to perform such services subject to the terms and conditions hereinafter
set forth; and

     WHEREAS, MANAGER represents and COMPANY believes that MANAGER has the
facilities and personnel in Bermuda to render the necessary management services
to COMPANY.
<PAGE>

     NOW, THEREFORE, in consideration of the mutual agreements herein contained,
the sufficiency of which is hereby acknowledged, and in consideration of the
performance by each of the parties hereto of the terms and agreements hereof, it
is agreed that:

                                   ARTICLE I
                                   ---------

                           Appointment and Authority
                           -------------------------

     1.1  The COMPANY hereby appoints MANAGER as its Principal Representative
(for the purposes described in this AGREEMENT) and hereby authorizes and directs
MANAGER to provide COMPANY management services hereof; MANAGER accepts such
appointment and undertakes and agrees to provide COMPANY with the services and
assistance herein provided upon the terms and conditions and for the
compensation herein specified.

     1.2  COMPANY retains all authority to perform on its own behalf such
          actions as it deems necessary to carry out the business of insurance.

                                   ARTICLE II
                                   ----------

                               Service of Manager
                               ------------------

     2.1  COMPANY, upon consultation with MANAGER, shall establish broad
principles to be applied by MANAGER in the performance of its duties under this
AGREEMENT.

     2.2  MANAGER, in the performance of its duties, agrees to do and perform
all acts reasonably as part of such management as customarily understood in the
insurance and reinsurance industry.

     2.3  Without limiting the generality of the foregoing, MANAGER specifically
agrees to perform the following services:

               (a) Maintain a home office and principal place of business in
          Bermuda for COMPANY during the term of this AGREEMENT and, if desired,
          recommend a person(s) who is a resident of Bermuda to serve as a
          director and/or officer.

          (b) Establish and maintain an accounting system appropriate to
          COMPANY'S operations and provide all accounting services required for
          purposes of
<PAGE>

          management and compliance with all requirements of Bermuda regulatory
          authorities (exclusive of audit and reserve certification services).
          In addition, MANAGER will duly perform all the duties and discharge
          all the responsibilities required of it as the COMPANY's Principal
          Representative by the Insurance Act 1978 and its Related Regulations
          and use its best endeavors to ensure that the Company is at all times
          in compliance with all statutes (including subordinate legislation and
          governmental or ministerial orders and decrees) in force from time to
          time regulating the activities of, or otherwise applicable to,
          insurers carrying on business in or from Bermuda.

          (c) Prepare financial statements at specified intervals and in the
          form requested by COMPANY as detailed in the attached Recordkeeping
          Addendum.

          (d) Submit on a timely basis to regulatory authorities such reports
          and other information as may be required by law, including statutory
          quarterly and annual statements and all returns for premium and other
          taxes required by the Bermuda tax authorities.

          (e) Render periodic advice, at such intervals and with such frequency
          as COMPANY may reasonably specify, as to the amount of reserves and
          other funds available for investment from time to time by COMPANY.

          (f) Perform certain insurance functions on behalf of COMPANY as
          outlined in the attached Insurance Addendum.

          (g) Perform certain shareholder relations functions on behalf of
          COMPANY as outlined in the attached Shareholder Relations addendum.

          (h) Maintain records of any funds due COMPANY and pay accounts payable
          owed by COMPANY of which MANAGER could reasonably be expected to have
          knowledge and which are required by the management duties assumed
          under this AGREEMENT including fees and charges of accountants,
          actuaries, lawyers and consultants.  MANAGER shall use diligence in
          the collection of accounts but shall be responsible to COMPANY only
          for funds which have been collected.  MANAGER shall not bear
          responsibility to pursue the collection of accounts through the use of
          court or other legal processes.
<PAGE>

          Specifically, MANAGER shall collect, receive and deposit all funds,
          including money and checks for premium on insurance, endorse "for
          deposit only" all checks payable to COMPANY, deposit such funds within
          fifteen (15) days of receipt only in checking and bank accounts in
          banks that are members of the Federal Reserve System or a Bermuda bank
          designated by the Board of COMPANY and abide in the respective
          accounts by the minimum and maximum amounts established by the Board;
          Manager shall hold all funds received by it in connection with this
          AGREEMENT as a fiduciary of COMPANY and segregated from its other
          funds and assets in compliance with all applicable laws and shall
          under no circumstances make any personal use of such funds.  Interest
          or revenue produced from such deposits shall inure to the benefit of
          COMPANY.

          (i) Assist COMPANY'S auditors in the audit of COMPANY'S books and
          records.

     2.4  COMPANY agrees to comply promptly with any request for instructions or
information which MANAGER may make in order to efficiently perform the
management duties under this AGREEMENT.  MANAGER shall bear no liability for its
failure to act or for its reasonable independent actions in connection with
COMPANY'S business in the absence of a timely response to any such request.

                                  ARTICLE III
                                  -----------

                              Manager Compensation
                              --------------------

     3.1  COMPANY hereby agrees to pay MANAGER as full compensation for all
services performed under this AGREEMENT the amount set forth in the Management
Fee Addendum at the intervals so specified. This amount is based on the
activities contemplated and responsibilities designated at the time of the
signing of this AGREEMENT. Changes in the operation or requirements of COMPANY
which change the services required of the MANAGER will be subject to review as
warranted with appropriate adjustment of the management fee, as mutually agreed.

     3.2  Promptly upon demand, COMPANY agrees to reimburse MANAGER for expenses
incurred directly on behalf of COMPANY, which are outside the ordinary course of
<PAGE>

providing the management services detailed in Article II.  These include, but
are not limited to, travel costs, COMPANY stationery, filing fees, premium
taxes, long distance telephone expenses, express delivery expense and like
matters.

                                   ARTICLE IV
                                   ----------

                              Term and Termination
                              --------------------

     4.1  This AGREEMENT shall be for the period commencing on the incorporation
of COMPANY through December 31, 2000, and shall automatically be renewed
annually thereafter for successive one-year periods.  However, either party may
terminate this Agreement without cause at any time after the first year by
giving the other party written notice of intention to terminate this Agreement,
and such notice shall be given not more than ninety (90) days, but not less than
sixty (60) days prior to the effective date of termination.

     4.2  Notwithstanding anything to the contrary herein, either party hereto
may terminate this AGREEMENT if the other party fails to perform or observe, or
commits a breach of, any provision of this AGREEMENT or is in violation of the
laws and regulations of Bermuda, and fails to cure or remedy such failure,
breach or violation within thirty (30) days following the delivery to such party
of a written notice specifying the alleged failure, breach or violation; such
termination to be effective upon the expiration of such thirty (30) day period.

     4.3  MANAGER agrees to cooperate with and assist COMPANY in the termination
of this AGREEMENT in all reasonable respects with regard to any matters arising
or occurring during the period this AGREEMENT is in force. COMPANY agrees to
reimburse MANAGER for all costs incurred by MANAGER with respect to the
cooperation and assistance provided by MANAGER pursuant to this Section 4.3.

     4.4  All books of account, insurance policies, reinsurance agreements, bank
statements and checks, loss information, minutes, correspondence and other
documentation maintained and held by MANAGER on behalf of and relating to the
affairs of COMPANY shall remain the sole and exclusive property of COMPANY and
shall be delivered promptly to COMPANY or its agent designated in writing
following any termination of this AGREEMENT by either party.
<PAGE>

                                   ARTICLE V
                                   ---------

                  Manager Responsibility; Limitations Thereon
                  -------------------------------------------

     5.1  MANAGER will use its best efforts and judgment to the end that the
services covered by this AGREEMENT shall at all times be performed in accordance
with such methods and in such manner as will comply with all laws and statutes
relating thereto and with all provisions of pertinent contracts and agreements
to the extent that COMPANY specifically notifies MANAGER of such provisions.
MANAGER does not hereby represent that it can or will render legal advice to
COMPANY or (except as otherwise expressly provided herein) that it will bear the
responsibility for COMPANY'S compliance with applicable legal requirements.
Rather, MANAGER will make reasonable efforts to conform its services to such
legal and contractual requirements as are made known to it.

     5.2  MANAGER shall indemnify and hold harmless COMPANY from and against any
liability, claims and expenses resulting from conduct of MANAGER.  However,
liability of MANAGER for any loss, injury or damages sustained by COMPANY as a
result of any act or omission of MANAGER shall not exceed an amount equal to the
annual fee actually received by MANAGER under and by virtue of this AGREEMENT,
except in cases where such loss, injury or damages result from the willful
misconduct, gross negligence or fraud of MANAGER.

     5.3  COMPANY shall defend and indemnify MANAGER and hold it harmless from
and against any and all liability, costs and expenses (including attorneys'
fees) arising out of or in any way relating to its management of COMPANY, except
liability which is a direct result of MANAGER'S gross negligence, willful or
wanton misconduct or fraud.

     5.4  MANAGER does not act as an insurer for any insured of COMPANY.  This
AGREEMENT shall not be construed as an insurance policy or any contract or
agreement of indemnity; it being understood that MANAGER is in no event under
the terms of this AGREEMENT financially responsible or liable for the payment or
satisfaction of claims, lawsuits or any cause of action against COMPANY or any
insured of COMPANY. The payment by MANAGER of any funds for the satisfaction of
any claim, lawsuit, or cause of action against COMPANY or any insured of COMPANY
shall not be considered an undertaking by MANAGER to be responsible financially
or liable for any present or future claims.

     5.5  MANAGER shall have no authority to hold itself out as an agent of
COMPANY for any other purpose than specifically prescribed in this AGREEMENT; to
waive any forfeiture; or to collect any premium except those for which policies
have been issued or valid receipts which have been sent for collection, or to
bind COMPANY in any way except as herein expressly stated.
<PAGE>

     5.6  MANAGER agrees that no forms, binders, pamphlets, booklets or any
other printed matter using COMPANY'S name shall be used, issued or circulated
unless authorized by COMPANY'S Board.

     5.7  Other than as provided by this AGREEMENT, the MANAGER is forbidden to
incur any indebtedness on behalf of the COMPANY whatsoever without first
obtaining the written consent of the Board of Directors of the COMPANY.

                                   ARTICLE VI
                                   ----------

                                Confidentiality
                                ---------------

     6.1  MANAGER shall not (except in the exercise of duties hereunder or as
required by law) disclose an information relating to the affairs of COMPANY to
any person not authorized by COMPANY to receive such information and MANAGER
will use its best efforts to prevent any such disclosure by its employees and
agents.

     6.2  All books and records of COMPANY shall be open to inspection only by
directors, officers and employees of MANAGER and by COMPANY'S officers,
directors and designated employees, in person or by agent or attorney, upon
written demand, at any reasonable time or times.

                                  ARTICLE VII
                                  -----------

                                 Miscellaneous
                                 -------------

     7.1  The failure of either party at any time to require the other party's
performance of any provision hereof shall not be construed as a waiver of any
continuing or succeeding breach of such provision, a waiver or modification of
the provision itself, or a waiver or modification of any other right under this
AGREEMENT.

     7.2  This AGREEMENT is governed by the laws of Bermuda.

     7.3  MANAGER shall at all times act as an independent contractor of
COMPANY, and in no event shall employees of MANAGER be considered employees of
COMPANY.

     7.4  This AGREEMENT (with all its addenda) constitutes the entire agreement
between the parties hereto concerning the subject matter addressed herein, and
supersedes all previous agreements or undertakings, whether oral or written.
This AGREEMENT may only be
<PAGE>

amended or modified in writing.

     7.5  Neither this AGREEMENT nor any right created hereunder may be assigned
by either party without the express written consent of the other.

     7.6  This AGREEMENT is binding upon the parties hereto, their successors
and assigns.

     7.7  Headings herein are for convenience of reference only and are not
intended for use in the interpretation of this AGREEMENT.

     7.8  No management personnel or other employees of the COMPANY are to
perform management functions and receive any remuneration therefore, through
this or any other management or service contract, in addition to compensation by
way of salary received directly from the COMPANY for their services.
<PAGE>

     IN WITNESS WHEREOF, the parties have caused this AGREEMENT to be executed
by their duly authorized representatives the day and year first mentioned above.

WITNESS:                            USA OFFSHORE MANAGEMENT, LTD.

/s/ Richard Lowther             By: /s/ Andrew Sargeant
-----------------------            -------------------------------
                                    Its duly authorized agent

WITNESS:                            AMERINST INSURANCE
                                    COMPANY, LTD.

/s/ Richard Lowther             By: /s/ Ronald Katch
-----------------------            ------------------------------
                                    Its duly authorized agent
<PAGE>

                             ADDENDA TO AGREEMENT

                                    BETWEEN

                        AMERINST INSURANCE COMPANY, LTD.

                                      AND

                         USA OFFSHORE MANAGEMENT, LTD.

INSURANCE ADDENDUM
------------------

MANAGER will:
-------------

(1)  Maintain and update all reinsurance policies, endorsements, binders, cover
     notes, and other evidence of insurance or reinsurance.

(2)  Issue Certificates of Insurance and act as COMPANY's registered agent for
     services of process.

(3)  Cooperate with authorized COMPANY employees, consultants, actuaries,
     auditors, claims personnel and attorneys on a day-to-day basis to ensure
     the efficient operation of the COMPANY.  The MANAGER also agrees to extend
     full cooperation to all regulatory and COMPANY officials during any and all
     audits or examinations.

RECORDKEEPING ADDENDUM
----------------------

MANAGER will:
-------------

(1)  Provide all routine accounting services to establish and maintain books of
     account, including, but not limited to, accounting for reinsurance,
     maintenance of underwriting statistics, invoicing, disbursements, cash and
     investment records and a general ledger.

(2)  Maintain true, accurate and complete records and accounts of all
     transactions arising out of this AGREEMENT, including, but not limited to,
     claims and losses, and financial matters.  Said records and accounts shall
     be maintained at all times in such a manner and form as may be agreed to by
     the Board of Directors of the COMPANY and in accordance with generally
     accepted accounting and insurance practices.

(3)  Prepare a quarterly financial statement of income and expenses, a balance
     sheet, and other financial statements as may be required by Company's
     Board, for distribution to such persons as are designated in writing by the
     Board; such reports shall include:

     (a)  premiums received;

     (b)  losses paid:
<PAGE>

     (c) loss adjustment expenses paid; and

     (d)  loss reserves information.

(4)  Complete and file Statutory Financial Return and Statutory Financial
     Statements as required by Bermuda insurance regulators.

(5)  Liaise with service providers preparing Premium Tax and COMPANY Tax and
     other regulatory returns in accordance with state and federal laws, and
     cause such returns to be filed with the appropriate authorities.

(6)  Ensure compliance with the regulations pertaining to books and records and
     Bermuda home office.

(7)  Prepare and maintain minutes of all board and shareholder meetings.  Assist
     in the preparation of the agenda and materials for the meetings.  Have a
     representative attend all board meetings and Committee meetings where
     necessary.

(8)  Advise the Board on matters of interest.

SHAREHOLDER RELATIONS ADDENDUM
------------------------------

COMPANY will:

(1)  Follow standard procedures for monitoring and responding to shareholder
     inquireies and requests as set forth by and under the direction of the
     Shareholder Relations Committee;

(2)  Receive and respond to shareholder telephone calls received on the 1-800
     number;

(3)  Maintain telephone log, including name of caller and brief description of
     nature of call. (Copy of which is sent to Chairman of Shareholder Relations
     Committee at end of every month);

(4)  Review and respond to shareholder inquiries and request received via email;

(5)  Compile and prepare stock transfer cases for Committee approval;

(6)  Compile and prepare stock redemption cases for Board approval;

(7)  Advise Committee members of abnormal shareholder calls or mail on cases
     requiring further assistance;

(8)  Maintain Buy-Sell Trading System list and prepare mailings to participants
     on a quarterly basis or as requested by the Committee;

(9)  Prepare special mailings as requested by the Committee;

(10) Coordinate with Harris Bank Shareholder Services Division, Transfer Agent
     for AmerInst Insurance Group, Ltd., on shareholder relations matters
     including transfer and redemption of
<PAGE>

     stock, change of address, dividends, proxy mailings, shareholder listings
     and other items relevant to shareholder relations.

(11) Maintain shareholder relations records.

MANAGEMENT AGREEMENT ADDENDUM
-----------------------------

COMPANY will:

(1)  Compensate MANAGER at a rate of $22,500 for the period ended December 31,
     1999.

(1)  Compensate MANAGER at a rate of $140,000 per annum through December 31,
     2001.

(2)  Cause the above agreement to be paid in quarterly installments in advance
     at the beginning of each calendar quarter.

(3)  Reimburse MANAGER for reasonable out-of-pocket expenses incurred during the
     management of the COMPANY including:  courier and express mail service;
     long-distance telephone calls; travel and meeting expenses incurred at the
     request of the COMPANY; costs of COMPANY stationery; filing fees; and
     similar expenses.

COMPANY agrees that special projects will be invoiced separately at agreed upon
fees or rates.

IN WITNESS WHEREOF, the parties have duly executed this Addendum this 2nd day of
July, 2000.

                                         USA OFFSHORE MANAGEMENT, LTD.
WITNESS:

/s/ Richard Lowther                           /s/ Andrew Sargeant
--------------------------------              -------------------------------
                                              It's Duly Authorized Agent

                                              AMERINST INSURANCE
WITNESS:                                      COMPANY, LTD.

/s/ Richard Lowther                           /s/ Ronald Katch
--------------------------------              -------------------------------
                                              It's Duly Authorized Agent

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