KEMPER INVESTORS FUND
497, 1996-12-27
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<PAGE>   1
 
                             KEMPER INVESTORS FUND
                            SUPPLEMENT TO PROSPECTUS
                               DATED MAY 1, 1996
 
                           -------------------------
 
INVESTMENT MANAGER
 
Zurich Investment Management Limited ("ZIML"), 1 Fleet Place, London, U.K. EC4M
7RQ, an affiliate of Zurich Kemper Investments, Inc. ("ZKI"), the Fund's
investment manager, is a sub-adviser for certain Portfolios of the Fund
described below. ZIML has served as sub-adviser for mutual funds since December,
1996 and investment adviser for certain institutional accounts since August,
1988. Under the terms of the Sub-Advisory Agreement between ZIML and ZKI for the
Total Return, High Yield, Growth, Small Cap Growth, Investment Grade Bond,
Value+Growth and Horizon Portfolios, ZIML renders investment advisory and
management services with regard to that portion of a Portfolio's assets as may
be allocated by ZKI to ZIML from time to time for management of foreign
securities, including foreign currency transactions and related investments.
Under the terms of the Sub-Advisory Agreement between ZIML and ZKI for the
International Portfolio, ZIML renders investment advisory and management
services with regard to that portion of the Portfolio's assets as may be
allocated by ZKI to ZIML from time to time for management, including services
related to foreign securities, foreign currency transactions and related
investments. ZKI pays ZIML for its services a sub-advisory fee, payable monthly
at the following annual rates applied to the portion of the average daily net
assets of the applicable Portfolio allocated by ZKI to ZIML for management: .35%
for the Growth, International, Small Cap Growth, Total Return, Value+Growth and
Horizon Portfolios; and .30% for the High Yield and Investment Grade Bond
Portfolios.
 
December 17, 1996
KINF-1B 12/96                                    (LOGO)printed on recycled paper


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