KEMPER INVESTORS FUND
497, 1995-03-15
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<PAGE>   1
 
                             KEMPER INVESTORS FUND
               SUPPLEMENT TO STATEMENT OF ADDITIONAL INFORMATION
                               DATED MAY 1, 1994
 
                           -------------------------
 
     Stephen B. Timbers, a Trustee of the Fund, has been elected President (31)
of the Fund replacing Charles M. Kierscht. Mr. Timbers (120 S. LaSalle St.,
Chicago, Illinois) is Chairman, Chief Executive Officer, Chief Investment
Officer and a Director of Kemper Financial Services, Inc. ("KFS"); President,
Chief Operating Officer and a Director of Kemper Corporation; and a Director of
Kemper Financial Companies, Inc., ("KFC") and Kemper Securities, Inc. Mr.
Timbers also serves as a Director of Gillett Holdings, Inc. and LTV Corporation.
 
     David B. Mathis has been elected a Trustee (28) of the Fund replacing
Charles M. Kierscht. Mr. Mathis (Kemper Center, Long Grove, Illinois) is
Chairman, Chief Executive Officer and a Director of Kemper Corporation; and a
Director of KFS and KFC. Mr. Mathis also serves as a Director of IMC Global Inc.
 
     The number following each person's new title is the number of investment
companies managed by KFS for which he holds similar positions.
 
March 15, 1995
KINF-5  3/95                                    (LOGO)printed on recycled paper


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