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                                                                 EXHIBIT h(5)(e)

                                 AMENDMENT NO. 4
                                       TO
                      MASTER ACCOUNTING SERVICES AGREEMENT
                                     BETWEEN
                                AIM GROWTH SERIES
                                       AND
                              A I M ADVISORS, INC.


         The Master Accounting Services Agreement between AIM Growth Series, a
Delaware business trust, and A I M Advisors, Inc., a Delaware corporation, (the
"Agreement"), dated as of July 1, 1999, as amended, is hereby amended as
follows:

         Appendix A to the Agreement is hereby deleted in its entirety and
replaced with the following:

                                   "APPENDIX A
                                       TO
                      MASTER ACCOUNTING SERVICES AGREEMENT
                                       OF
                                AIM GROWTH SERIES

AIM Euroland Growth Fund
AIM Japan Growth Fund
AIM Mid Cap Equity Fund"

All other terms and provisions of the Agreement not amended herein shall remain
in full force and effect.

Dated: September 11, 2000

                                             AIM GROWTH SERIES


Attest: /s/ OFELIA M. MAYO                   By: /s/ ROBERT H. GRAHAM
       ----------------------------             ---------------------------
       Assistant Secretary                      President

(SEAL)

                                             A I M ADVISORS, INC.


Attest: /s/ OFELIA M. MAYO                   By: /s/ ROBERT H. GRAHAM
       ----------------------------             ---------------------------
       Assistant Secretary                      President

(SEAL)