KEMPER INVESTORS FUND
497, 1995-10-02
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<PAGE>   1
 
                             KEMPER INVESTORS FUND
                            SUPPLEMENT TO PROSPECTUS
                               DATED MAY 1, 1995
 
                           -------------------------
 
     Kemper Corporation ("Kemper"), the parent of Kemper Financial Services,
Inc. ("KFS," the investment manager for the Fund), has entered into a definitive
agreement with an investor group led by Zurich Insurance Company ("Zurich")
pursuant to which Kemper would be acquired by the investor group in a merger
transaction. As part of the transaction, Zurich or an affiliate would purchase
KFS. The Kemper and Zurich boards have approved the transaction. In addition,
because the transaction would constitute an assignment of the Fund's investment
management agreement with KFS under the Investment Company Act of 1940, and
therefore a termination of such agreement, KFS has received approval of a new
agreement from the Fund's board and shareholders. Remaining contingencies
include approval by the stockholders of Kemper and state insurance department
regulatory approvals. The investor group has informed Kemper that it expects the
transaction to close early in 1996.
 
     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 and Underwriter" section of the prospectus.
October 2, 1995
 
KINF-1  10/95
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