EXHIBIT h(5)

                                 FIRST AMENDMENT
                    TO FUND ACCOUNTING AND SERVICES AGREEMENT
                               DATED JULY 1, 2001,
                                  BY AND AMONG
            AMERISTOCK MUTUAL FUND, INC., AMERISTOCK CORPORATION AND
                        ALPS MUTUAL FUNDS SERVICES, INC.

     THIS AMENDMENT is made as of August 5, 2002, by and between Ameristock
Mutual Fund, Inc., a Maryland corporation (the "Fund"), Ameristock Corporation,
a California corporation ("Ameristock"), and ALPS Mutual Funds Services, Inc., a
Colorado corporation ("ALPS").

     WHEREAS, the Fund, Ameristock, and ALPS have entered into a Fund Accounting
and Services Agreement (the "Agreement") dated July 1, 2001.

     WHEREAS, the Fund, Ameristock, and ALPS wish to modify the provisions of
the Agreement to reflect a two (2) year term.

     NOW, THEREFORE, the parties hereto, intending to be legally bound, agree as
follows:

     1.   TERM. The first paragraph of Section 12 of the Agreement shall be
     deleted and replaced with: The initial term of the Agreement shall be until
     August 4, 2004. Thereafter, the Agreement shall continue unless terminated
     by either Party upon sixty (60) days prior written notice to the other
     Party.

     2.   MISCELLANEOUS. Other than as amended hereby, all terms and conditions
     of the Agreement are unchanged and remain in full force and effect. This
     Amendment shall be deemed to be an amendment to the Agreement and shall be
     governed by the laws of the State of Colorado.

     IN WITNESS WHEREOF, this Amendment has been executed by a duly authorized
representative of each of the parties hereto as of the date of the Amendment
first set forth above.

AMERISTOCK MUTUAL FUND, INC.                AMERISTOCK CORPORATION

By:                                         By:
    --------------------------------            --------------------------------
Name:                                       Name:
      ------------------------------             -------------------------------
Title:                                      Title:
       -----------------------------               -----------------------------


ALPS MUTUAL FUNDS SERVICES, INC.

By:
    --------------------------------
Name:  Jeremy O. May
Title: Senior Vice President