KEMPER HORIZON FUND
497, 1998-11-30
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                               KEMPER HORIZON FUND
                                   PORTFOLIOS
                          KEMPER HORIZON 20+ PORTFOLIO
                          KEMPER HORIZON 10+ PORTFOLIO
                           KEMPER HORIZON 5 PORTFOLIO
                            SUPPLEMENT TO PROSPECTUS
                             DATED NOVEMBER 30, 1998
                                 CLASS I SHARES
                                ----------------

The Kemper Horizon Fund consists of three investment portfolios,  Kemper Horizon
20+ Portfolio ("Horizon 20+ Portfolio"),  Kemper Horizon 10+ Portfolio ("Horizon
10+  Portfolio")  and  Kemper  Horizon  5  Portfolio   ("Horizon  5  Portfolio")
(collectively the "Portfolios"),  each currently offering four classes of shares
to provide investors with different purchasing options. These are Class A, Class
B and Class C shares, which are described in the prospectus, and Class I shares,
which are described in the prospectus as supplemented hereby.

Class  I  shares  are  available  for  purchase  exclusively  by  the  following
categories of institutional  investors:  (1) tax-exempt retirement plans (Profit
Sharing,  401(k),  Money Purchase  Pension and Defined Benefit Plans) of Scudder
Kemper  Investments,  Inc.  ("Scudder  Kemper") and its  affiliates and rollover
accounts from those plans;  (2) the  following  investment  advisory  clients of
Scudder Kemper and its investment  advisory  affiliates  that invest at least $1
million in a Fund:  unaffiliated  benefit  plans,  such as qualified  retirement
plans (other than individual  retirement  accounts and self-directed  retirement
plans);  unaffiliated  banks and insurance  companies  purchasing  for their own
accounts;  and endowment funds of  unaffiliated  non-profit  organizations;  (3)
investment-only accounts for large qualified plans, with at least $50 million in
total  plan  assets or at least  1000  participants;  (4)  trust  and  fiduciary
accounts  of trust  companies  and bank trust  departments  providing  fee based
advisory  services  that  invest at least $1 million in a Fund on behalf of each
trust; and (5) policy holders under Zurich-American Insurance Group's collateral
investment  program  investing  at  least  $200,000  in a Fund.  Class I  shares
currently  are  available  for  purchase  only from  Kemper  Distributors,  Inc.
("KDI"),  principal  underwriter  for the Funds,  and, in the case of category 4
above,  selected dealers authorized by KDI. Share certificates are not available
for Class I shares.

The primary  distinctions  among the classes of shares lie in their  initial and
contingent  deferred  sales  charge  schedules  and in their  ongoing  expenses,
including asset-based sales charges in the form of Rule 12b-1 distribution fees.
Class I shares are offered at net asset value  without an initial  sales  charge
and are not  subject  to a  contingent  deferred  sales  charge or a Rule  12b-1

<PAGE>

distribution fee. Also, there is no administrative services fee charged to Class
I shares.  As a result of the relatively lower expenses for Class I shares,  the
level of income  dividends  per share (as a percentage  of net asset value) and,
therefore,  the overall investment return,  will typically be higher for Class I
shares than for Class A, Class B and Class C shares.

The following information supplements the indicated sections of the prospectus.

SUMMARY OF EXPENSES

Shareholder Transaction Expenses (applicable to all Portfolios)

CLASS I SHARES



Maximum Sales Charge on Purchases
  (as a percentage of offering price)................................  None

Maximum Sales Charge on Reinvested Dividends.........................  None

Redemption Fees......................................................  None

Exchange Fee.........................................................  None

Deferred Sales Charge (as a percentage of redemption proceeds).......  None 



Annual Fund Operating Expenses


               HORIZON 20+      HORIZON 10+          HORIZON 5
               PORTFOLIO        PORTFOLIO            PORTFOLIO
               ---------        ---------            ---------


Management          0.58%          0.58%               0.58%
Fees

12b-1 Fees           None           None                None

Other Expenses      0.27%          0.41%               0.45%
                    -----          -----               -----
Total   
Operating
Expenses            0.85%          0.99%               1.03%
                    =====          =====               =====


EXAMPLE

You would pay the  following  expenses on a $1,000  investment,  assuming (1) 5%
annual return and (2) redemption at the end of each time period:

PORTFOLIO          1 YEAR   3 YEARS   5 YEARS  10 YEARS
- ---------          ------   -------   -------  --------

Horizon 20+           $9      $27       $47      $105

Horizon 10+          $10      $32       $55      $121

Horizon 5            $11      $33       $57      $126


<PAGE>

The purpose of the preceding table is to assist investors in  understanding  the
various  costs and  expenses  that an  investor in Class I shares of a Portfolio
will bear directly or indirectly.

The Example  assumes a 5% annual rate of return  pursuant to requirements of the
Securities  and Exchange  Commission.  This  hypothetical  rate of return is not
intended to be representative of past or future  performance of any Portfolio of
the Fund. THE EXAMPLE SHOULD NOT BE CONSIDERED TO BE A REPRESENTATION OF PAST OR
FUTURE EXPENSES. ACTUAL EXPENSES MAY BE GREATER OR LESSER THAN THOSE SHOWN.

FINANCIAL HIGHLIGHTS

                          KEMPER HORIZON 20+ PORTFOLIO
- --------------------------------------------------------------------------

                                   Year ended July 31,        April 8 to
                                   1998          1997       July 31, 1996
- --------------------------------------------------------------------------
PER SHARE OPERATING                
PERFORMANCE:

Net asset value, beginning of
period                             $12.96           9.73            10.03
- --------------------------------------------------------------------------
Income from investment
operations:

Net investment income              0.17          0.19             0.07
- --------------------------------------------------------------------------
Net realized and unrealized 
  gain (loss)                      1.09          3.17            (0.37)
- --------------------------------------------------------------------------
Total from investment
  operations                       1.26          3.36            (0.30)
- --------------------------------------------------------------------------
Less Dividends                     
  Distribution from net
  investment income                0.12          0.13               --
- --------------------------------------------------------------------------
  Distribution from net
  realized gain                    0.48            --               --
- --------------------------------------------------------------------------
Total Dividends                    0.60          0.13               --
- --------------------------------------------------------------------------
Net asset value, end of period   $13.62         12.96             9.73
- --------------------------------------------------------------------------
TOTAL RETURN (NOT
ANNUALIZED):                      10.29%        34.84            (2.99)
- --------------------------------------------------------------------------
RATIOS TO AVERAGE NET
ASSETS (ANNUALIZED):
Expenses                           0.85%        1.04             0.73
- --------------------------------------------------------------------------
Net investment income              1.64%        1.73             2.32
- --------------------------------------------------------------------------

<PAGE>


                          KEMPER HORIZON 10+ PORTFOLIO
- --------------------------------------------------------------------------

                                   Year ended July 31,        April 8 to
                                   1998          1997       July 31, 1996
- --------------------------------------------------------------------------

PER SHARE OPERATING
PERFORMANCE:
Net asset value,
  beginning of period              $11.97        9.57            9.83
- --------------------------------------------------------------------------
Income from investment
operations:
Net investment income                0.35        0.26            0.09
- --------------------------------------------------------------------------
Net realized and unrealized
gain (loss)                          0.84        2.40           (0.26)
- --------------------------------------------------------------------------
Total from investment
operations                           1.19        2.66           (0.17)
- --------------------------------------------------------------------------
Less Dividends 
  Distribution from net
  investment income                  0.29        0.26            0.09
- --------------------------------------------------------------------------
  Distribution from net
  realized gain                      0.41          --              --
- --------------------------------------------------------------------------
Total Dividends                      0.70        0.26            0.09
- --------------------------------------------------------------------------
Net asset value,
end of period                      $12.46       11.97            9.57
- --------------------------------------------------------------------------
TOTAL RETURN
(NOT ANNUALIZED):                   10.47%      28.09           (1.74)
- --------------------------------------------------------------------------
RATIOS TO AVERAGE
NET ASSETS
(ANNUALIZED):
Expenses                            0.99%        1.06            0.73
- --------------------------------------------------------------------------
Net investment
income                              2.75%          2.81            3.21
- --------------------------------------------------------------------------
<PAGE>


                           KEMPER HORIZON 5 PORTFOLIO
- --------------------------------------------------------------------------

                                   Year ended July 31,        April 8 to
                                   1998          1997       July 31, 1996
- --------------------------------------------------------------------------

PER SHARE OPERATING
PERFORMANCE:
Net asset value, beginning
  of period                      $11.06          9.58            9.69
- --------------------------------------------------------------------------
Income from investment
operations:

Net investment income              0.41          0.32            0.08
- --------------------------------------------------------------------------
Net realized and unrealized
gain (loss)                        0.47          1.49           (0.11)
- --------------------------------------------------------------------------
Total from investment
operations                         0.88          1.81           (0.03)
- --------------------------------------------------------------------------
Less Dividends
  Distribution from net
  investment income                0.39          0.33            0.08
- --------------------------------------------------------------------------
  Distribution from net
  realized gain                    0.27           --               --
- --------------------------------------------------------------------------
Total Dividends                   0.66          0.33            0.08
- --------------------------------------------------------------------------
Net asset value, end of
  period                        $11.28         11.06            9.58
- --------------------------------------------------------------------------
TOTAL RETURN (NOT
ANNUALIZED):                     8.29%         19.27           (0.31)
- --------------------------------------------------------------------------
RATIOS TO AVERAGE
NET ASSETS
(ANNUALIZED):
Expenses                         1.03%          1.20            0.73
- --------------------------------------------------------------------------
Net investment
income                           3.89%          3.61            4.11
- --------------------------------------------------------------------------

NOTES TO ALL PORTFOLIOS:  Per share data for the period ended July 31, 1996, was
determined based on average shares outstanding. For the fiscal period ended July
31, 1996, the investment manager agreed to temporarily reduce its management fee
and absorb  certain  operating  expenses  of the  Portfolios.  If these  expense
waivers had not been in effect,  the expense ratio would have increased by 0.06%
of average  net assets for  Horizon  20+,  0.04% for  Horizon  10+ and 0.05% for
Horizon 5. There would have been a corresponding  decrease in the net investment
income ratio for the period. The waivers were discontinued on August 1, 1996.


<PAGE>

SPECIAL FEATURES

Shareholders  of a Portfolio's  Class I shares may exchange their shares for (i)
shares of Zurich Money  Funds--Zurich  Money Market Fund if the  shareholders of
Class I shares have purchased shares because they are participants in tax-exempt
retirement plans of Scudder Kemper and its affiliates and (ii) Class I shares of
any other "Kemper Mutual Fund" listed under "Special Features-- Class A Shares--
Combined Purchases" in the prospectus. Conversely,  shareholders of Zurich Money
Funds--Zurich  Money  Market Fund who have  purchased  shares  because  they are
participants in tax-exempt retirement plans of Scudder Kemper and its affiliates
may  exchange  their shares for Class I shares of "Kemper  Mutual  Funds" to the
extent that they are available through their plan. Exchanges will be made at the
relative  net  asset  values  of  the  shares.  Exchanges  are  subject  to  the
limitations  set forth in the  prospectus  under  "Special  Features--  Exchange
Privilege-- General."

November 30, 1998
KHF-1I


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