<PAGE>
EXHIBIT 10.32

                             FIRST AMENDMENT TO THE
                   AMENDED AND RESTATED STOCK PLEDGE AGREEMENT

      THIS FIRST AMENDMENT to the AMENDED AND RESTATED STOCK PLEDGE AGREEMENT
(the "First Amendment") entered into as of this 11th day of July, 2002, is
intended to amend the terms of the Amended and Restated Stock Pledge Agreement,
dated as of December 28, 2001, (the "Pledge Agreement") by and between FIRST
NATIONAL BANK OF OMAHA, a national banking association having its principal
place of business in Omaha, Nebraska, as agent ("FNB-O" or the "Agent") for
itself and such additional Revolving Lenders as may from time to time enter the
Amended and Restated Revolving Credit Agreement, dated as of December 28, 2001
(the "Revolving Credit Agreement"), (collectively the "Revolving Lenders"), and
AMERITRADE HOLDING CORPORATION (the "Borrower"). All terms and conditions of the
Pledge Agreement shall remain in full force and effect except as expressly
amended herein. All capitalized terms used but not otherwise defined herein
shall have the respective meanings prescribed in the Revolving Credit Agreement.

      WHEREAS, the Borrower has requested that the Revolving Lenders release
their lien on the NITE Stock that is currently pledged to the Revolving Lenders
as collateral under the Pledge Agreement and the Revolving Credit Agreement; and

      WHEREAS, the Borrower has requested that, after the Revolving Lenders
release the NITE Stock that is currently pledged as collateral, it be permitted
to sell any and all of its shares of NITE Stock with the proceeds of such sale
to be used for general corporate purposes to the extent permitted under the
Revolving Credit Agreement; and

      WHEREAS, the Revolving Lenders have agreed to release the lien on the NITE
Stock currently pledged as collateral and have agreed to permit the Borrower to
sell any and all of its shares of NITE Stock with the proceeds of such sale to
be used for general corporate purposes to the extent permitted under the
Revolving Credit Agreement, on the terms and conditions specified below and in
the First Amendment to the Amended and Restated Revolving Credit Agreement,
dated as of July 11, 2002;

      NOW, THEREFORE, the Borrower and the Revolving Lenders hereby agree as
follows:

      1.    The following definition in Section 1.1 of the Pledge Agreement is
hereby deleted:

      "Pledged NITE Stock" means the NITE stock pledged by the Borrower to the
      Agent under this Stock Pledge Agreement, as shown on Schedule A, including
      any additional NITE Stock pledged to the Agent, including without
      limitation, additional NITE Stock pledged in accordance with the
      provisions of Section 4.3 of this Stock Pledge Agreement.


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<PAGE>
      2.    The following definitions in Section 1.1 of the Pledge Agreement are
hereby amended to read as follows:

      "Permitted Encumbrance" means any and all encumbrances existing as of this
      date which are listed on Schedule B attached hereto.

      "Pledged Stock" means the Subsidiary Stock.

      3.    Section 2.1 of the Pledge Agreement shall be amended to read as
follows:

            Section 2.1 Grant of Security Interest. The Borrower hereby grants
      to the Agent for the benefit of the Revolving Lenders a security interest
      in the Pledged Stock and all related Stock Rights to secure payment and
      performance of the Obligations, including, without limitation, payment of
      the Notes. The Pledged Stock shall be delivered to the Agent for the
      Revolving Lenders together with appropriate stock powers duly executed in
      blank.

      4.    Clause (a) of Section 4.l of the Pledge Agreement is hereby amended
to read as follows:

            (a)   Delivery of Certain Items. Deliver to the Agent any stock
      certificate or instrument evidencing or constituting Collateral, including
      subsequent shares of stock (including stock dividends) of any Subsidiary
      issued to the Borrower.

      5.    Section 4.3 of the Pledge Agreement is hereby deleted.

      6.    Section 7.3 of the Pledge Agreement is hereby amended to read as
follows:

            Section 7.3 Registration of Pledged Stock. At the option of the
      Agent, any registerable Collateral may at any time after the occurrence of
      an Event of Default and upon the expiration of any applicable cure period,
      if any, be registered in the name of FNB-O or its nominee as agent for the
      Revolving Lenders.

      7.    The "Acknowledgement and Consent" attached to the Pledge Agreement
is hereby terminated.

      8.    Schedule A to the Pledge Agreement shall be amended to read as shown
on Attachment A to this First Amendment.

      9.    Advanced Clearing, Inc. has changed its name to Ameritrade, Inc. All
references in the Pledge Agreement to Advanced Clearing, Inc. shall be deemed to
be references to Ameritrade, Inc.

      10.   This First Amendment may be executed in several counterparts and
such counterparts together shall constitute one and the same instrument.


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<PAGE>
      11.   Any references herein to the Pledge Agreement shall mean this
amendment and the Amended and Restated Stock Pledge Agreement, dated as of
December 28, 2001, as amended from time to time (including this First
Amendment), and any references herein to the Revolving Credit Agreement shall
mean the Amended and Restated Revolving Credit Agreement, dated as of December
28, 2001, as amended from time to time.

      IN WITNESS WHEREOF, the Borrower and the Revolving Lenders have caused
this First Amendment to the Pledge Agreement to be executed by their duly
authorized corporate officers as of the day and year first above written.

                            [Signature Page Follows.]


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<PAGE>
                                        AMERITRADE HOLDING CORPORATION


                                        By   /s/ William J. Gerber
                                          --------------------------------------

                                        Title  Managing Director of Finance
                                             -----------------------------------







                                        FIRST NATIONAL BANK OF OMAHA,


                                        By   /s/ James P. Bonham
                                          --------------------------------------

                                        Title  Vice President
                                             -----------------------------------


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<PAGE>
                                  ATTACHMENT A
                          TO THE FIRST AMENDMENT TO THE
                   AMENDED AND RESTATED STOCK PLEDGE AGREEMENT
                                 BY AND BETWEEN
                          FIRST NATIONAL BANK OF OMAHA
                             AS AGENT FOR ITSELF AND
                             OTHER REVOLVING LENDERS
                                       AND
                   AMERITRADE HOLDING CORPORATION ("BORROWER")

                                   SCHEDULE A

                                  PLEDGED STOCK

<TABLE>
<CAPTION>
Owner                             Issuer                                No. of Shares      Certificate No.(s)
-----                             ------                                -------------      ------------------
<S>                               <C>                                   <C>                <C>
World Securities, Inc.(1)         First National Brokerage Services,          5,000                   2
                                  Inc.(2)

Ameritrade Holding Corporation    Advanced Clearing, Inc.(7)                  7,559                  20

Ameritrade Holding Corporation    Ameritrade (Inc.)(8)                        6,000                   3

Ameritrade Holding Corporation    The R.J. Forbes Group, Inc.(6)              1,250                  12
</TABLE>

--------

      (1)   World Securities, Inc. changed its name to TransTerra Co. on
November 18, 1987. Trans Terra Co. merged with Ameritrade Holding Corporation on
September 27, 1996 with Ameritrade Holding Corporation being the surviving
entity.

      (2)   First National Brokerage Services, Inc. changed its name to
Accutrade, Inc. on May 24, 1983.

      (3)   K. Aufthauser & Company, Inc. changed its name to Freetrade.com,
Inc. on January 10, 2000.

      (4)   All American Brokers, Inc. changed its name to AmeriVest, Inc. on
November 18, 1997.

      (5)   OnMoney, Inc. was merged with OnMoney Financial Services Corporation
on May 24, 1997.

      (6)   The R.J. Forbes Group, Inc. changed its name to Ameritrade
Institutional Services, Inc as of ___________, 2001.

      (7)   Advanced Clearing, Inc. changed its name to Ameritrade, Inc. as of
_____________, 2002.

      (8)   Ameritrade (Inc.) changed its name to J.P. Securities, Inc. as of
____________, 2002.


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<PAGE>
<TABLE>
<CAPTION>
Owner                             Issuer                                No. of Shares      Certificate No.(s)
-----                             ------                                -------------      ------------------
<S>                               <C>                                   <C>                <C>
Ameritrade Holding Corporation    K. Aufhauser & Company, Inc.(3)              25                     6

American Holding Corporation      All American Brokers, Inc.(4)              100,000                  8

Ameritrade Holding Corporation    OnMoney, Inc.(5)                            1,000                   2

Ameritrade Holding Corporation    TradeCast, Inc.                             1,000                   1

OnMoney Financial Services        Financial Passport, Inc.                    1,000                 00254
Corporation

Ameritrade Holding Corporation    Nebraska Hudson Company, Inc.              ______                ______

Ameritrade Holding Corporation    Ten Bagger Incorporated                    ______                ______

Ameritrade Holding Corporation    Ameritrade Canada, Inc.                    ______                ______

Ameritrade Holding Corporation    Ameritrade Services Company                ______                ______

Ameritrade Holding Corporation    Ameritrade IP Company                      ______                ______

Ameritrade Holding Corporation    Ameritrade Development                     ______                ______
                                  Company

Ameritrade Holding Corporation    Ameritrade International                   ______                ______
                                  Company, Inc.
</TABLE>


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