KEMPER INVESTORS FUND
497, 1996-01-08
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<PAGE>   1
 
                             KEMPER INVESTORS FUND
                            SUPPLEMENT TO PROSPECTUS
                               DATED MAY 1, 1995
 
                           -------------------------
 
     The following supplements the "Investment Manager" section of the
prospectus.
 
INVESTMENT MANAGER
 
     Kemper Financial Services, Inc. ("KFS"), the investment manager, is a
subsidiary of Zurich Insurance Company, an insurance and financial services
holding company.
 
     With respect to the Equity Portfolio, Steven H. Reynolds and the KFS Equity
Investment Committee have managed the portfolio since September, 1995. Mr.
Reynolds joined KFS in September, 1995 as an executive vice president and chief
investment officer -- equities. Immediately prior to joining KFS, he was a
senior vice president and equity portfolio manager of an investment manager; and
prior thereto, he was a senior vice president, managing director and head of
active equities at a national bank. Mr. Reynolds received a bachelor's degree
from Johns Hopkins University, Baltimore, Maryland and an M.B.A. in finance from
the University of Virginia, Charlottesville, Virginia. Additional information
regarding the KFS Equity Investment Committee can be found in the "Investment
Manager" section of the prospectus.
 
January 5, 1996
KINF-1  1/96(LOGO)printed on recycled paper


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