KEMPER HORIZON FUND
497, 1999-12-16
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                              KEMPER HORIZON FUNDS

                            SUPPLEMENT TO PROSPECTUS
                             DATED DECEMBER 1, 1999
                            ------------------------
                                 CLASS I SHARES
                            ------------------------
                          KEMPER HORIZON 20+ PORTFOLIO
                          KEMPER HORIZON 10+ PORTFOLIO
                           KEMPER HORIZON 5 PORTFOLIO
                            ------------------------

The above funds currently offer 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 funds'  prospectus,  and Class I shares,  which are
described in the  prospectus  as  supplemented  hereby.  When  placing  purchase
orders,  investors must specify whether the order is for Class A, Class B, Class
C or Class I shares.

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; (5) policy holders under  Zurich-American  Insurance  Group's  collateral
investment  program  investing at least  $200,000 in a Fund;  and (6) investment
companies  managed by Scudder Kemper that invest  primarily in other  investment
companies.

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.


                                       1
<PAGE>


The following information supplements the indicated sections of the prospectus.

PERFORMANCE

The following  table shows how the funds Class I Shares'  returns over different
periods average out. For context,  the table has two broad-based  market indices
(which, unlike the fund, have no fees or expenses).  All figures in this section
assume reinvestment of dividends and distributions.  As always, past performance
is no guarantee of future results.

Average Annual Total Returns -- Class I Shares (as of 12/31/1998)

                                 Since 12/31/97          Since April 8, 1996
                                     1 Year                 Life of Class
                                     ------                 -------------

Kemper Horizon 20+
Portfolio                            12.47%                    15.28%

Kemper Horizon 10+
Portfolio                             13.06                     14.12

Kemper Horizon 5 Portfolio            10.62                     11.03

Index 1                               28.58                    28.69*

Index 2                                9.47                     8.96*

*   Since 3/31/96

Index 1:  Standard  and Poor's 500  Composite  Stock Price  Index (S&P 500),  an
unmanaged capitalization-weighted index that includes 500 large-cap U.S. stocks.

Index 2: Lehman  Brothers  Government/Corporate  Bond Index,  an unmanaged index
comprised  of  intermediate  and  long-term   government  and   investment-grade
corporate debt securities.

In the table total returns for 1996 would have been lower if operating  expenses
hadn't been reduced.


                                       2
<PAGE>


HOW MUCH INVESTORS PAY

This table  describes the fees and expenses that you may pay if you buy and hold
shares of the fund.

Shareholder fees: Fees paid directly from your investment.

                  Maximum
                   Sales       Maximum
                   Charge      Deferred
                   (Load)       Sales        Maximum     Redemption
                 Imposed on     Charge    Sales Charge   Fee (as %
                 Purchases      (Load)         on        of amount
                  (as % of     (as % of    Reinvested    redeemed,
                 offering     redemption   Dividends/        if      Exchange
                   price)     proceeds)   Distributions applicable)     Fee
                   ------     ---------   ------------- -----------     ---
Kemper Horizon
20+ Portfolio       None         None         None          None        None

Kemper Horizon
10+ Portfolio       None         None         None          None        None

Kemper Horizon
5 Portfolio         None         None         None          None        None


Annual fund operating expenses: Expenses that are deducted from fund assets.

                  Investment      Distribution     Other     Total annual fund
                management fee    (12b-1) fees   expenses*  operating expenses
                --------------    ------------   ---------  ------------------
Kemper
Horizon 20+
Portfolio          0.57%              None        0.35%           0.92%

Kemper
Horizon 10+
Portfolio          0.57%              None        0.52%           1.09%

Kemper
Horizon 5
Portfolio          0.57%              None        0.58%           1.15%

*   "Other Expenses" are restated to reflect current shareholder servicing fees.


                                       3
<PAGE>


Example

Based on the  figures  above,  this  example is designed to help you compare the
expenses  of a fund to those of  other  funds.  The  example  assumes  operating
expenses remain the same and that you invested $10,000, earned 5% annual returns
and reinvested all dividends and distributions.  This is only an example; actual
expenses will be different.

Fees and expenses if you sold shares after:

                    1 Year        3 Years        5 Years        10 Years
                    ------        -------        -------        --------
 Kemper
 Horizon 20+
 Portfolio             $94           $293           $509         $1,131

 Kemper
 Horizon 10+
 Portfolio            $111           $347           $601         $1,329

 Kemper
 Horizon 5
 Portfolio            $117           $365           $633         $1,398


                                       4
<PAGE>


FINANCIAL HIGHLIGHTS

Kemper Horizon 20+ Portfolio



                                       Year ended July 31,         April 8
                              --------------------------------   to July 31,
CLASS I                          1999        1998       1997        1996
- ----------------------------------------------------------------------------
Per share operating performance
Net asset value, beginning
of period                       $13.62       12.96       9.73       10.03
- ----------------------------------------------------------------------------
Income from investment
operations:
  Net investment income            .27         .17        .19         .07
- ----------------------------------------------------------------------------
  Net realized and unrealized
  gain (loss)                      .46        1.09       3.17        (.37)
- ----------------------------------------------------------------------------
Total from investment
operations                         .73        1.26       3.36        (.30)
- ----------------------------------------------------------------------------
Less dividends
  Distribution from net
  investment income                .17         .12        .13          --
- ----------------------------------------------------------------------------
  Distribution from net
  realized gain                    .02         .48         --          --
- ----------------------------------------------------------------------------
Total dividends                    .19         .60        .13          --
- ----------------------------------------------------------------------------
Net asset value, end of
period                          $14.16       13.62      12.96        9.73
- ----------------------------------------------------------------------------
Total return (not annualized)    5.43%       10.29      34.84       (2.99)
- ----------------------------------------------------------------------------
Ratios to average net assets
(annualized)
Expenses                          .84%         .85       1.04         .73
- ----------------------------------------------------------------------------
Net investment income            2.01%        1.64       1.73        2.32
- ----------------------------------------------------------------------------





                                                                  Dec. 29,
                                     Year ended July 31,           1995 to
                              ------------------------------      July 31,
                                 1999        1998       1997        1996
- ----------------------------------------------------------------------------
Supplemental data for all classes
Net assets at end of period
(in thousands)                $136,971      110,076     62,673      18,251
- ----------------------------------------------------------------------------
Portfolio turnover rate
(annualized)                       72%          44        130         122
- ----------------------------------------------------------------------------


                                       5
<PAGE>


Kemper Horizon 10+ Portfolio



                                       Year ended July 31,           April 8
                              -----------------------------------  to July 31,
CLASS I                          1999        1998       1997          1996
- ----------------------------------------------------------------------------
Per share operating performance
Net asset value, beginning
of period                       $12.46       11.97       9.57        9.83
- ----------------------------------------------------------------------------
Income from investment operations:
  Net investment income            .36         .35        .26         .09
- ----------------------------------------------------------------------------
  Net realized and unrealized
  gain (loss)                      .36         .84       2.40        (.26)
- ----------------------------------------------------------------------------
Total from investment
operations                         .72        1.19       2.66        (.17)
- ----------------------------------------------------------------------------
Less dividends
  Distribution from net
  investment income                .31         .29        .26         .09
- ----------------------------------------------------------------------------
  Distribution from net
  realized gain                    .11         .41         --          --
- ----------------------------------------------------------------------------
Total dividends                    .42         .70        .26         .09
- ----------------------------------------------------------------------------
Net asset value, end of
period                          $12.76       12.46      11.97        9.57
- ----------------------------------------------------------------------------
Total return (not annualized)    5.86%       10.47      28.09       (1.74)
- ----------------------------------------------------------------------------
Ratios to average net assets
(annualized)
Expenses                         1.07%         .99       1.06         .73
- ----------------------------------------------------------------------------
Net investment income            3.10%        2.75       2.81        3.21
- ----------------------------------------------------------------------------


                                                                  Dec. 29,
                                     Year ended July 31,           1995 to
                              ------------------------------      July 31,
                                 1999        1998       1997        1996
- ----------------------------------------------------------------------------
Supplemental data for all classes
Net assets at end of period
(in thousands)                 $138,110    111,687     63,400      18,912
- ----------------------------------------------------------------------------
Portfolio turnover rate
(annualized)                       64%          37        126          87
- ----------------------------------------------------------------------------



                                       6
<PAGE>


Kemper Horizon 5 Portfolio

                                       Year ended July 31,           April 8
                              -----------------------------------  to July 31,
CLASS I                          1999        1998       1997          1996
- ----------------------------------------------------------------------------
Per share operating performance
Net asset value, beginning
of period                       $11.28       11.06       9.58        9.69
- ----------------------------------------------------------------------------
Income from investment operations:
  Net investment income            .41         .41        .32         .08
- ----------------------------------------------------------------------------
  Net realized and unrealized
  gain (loss)                      .18         .47       1.49        (.11)
- ----------------------------------------------------------------------------
Total from investment
operations                         .59         .88       1.81        (.03)
- ----------------------------------------------------------------------------
Less dividends
  Distribution from net
  investment income                .44         .39        .33         .08
- ----------------------------------------------------------------------------
  Distribution from net
  realized gain                    .12         .27         --          --
- ----------------------------------------------------------------------------
Total dividends                    .56         .66        .33         .08
- ----------------------------------------------------------------------------
Net asset value, end of
period                          $11.31       11.28      11.06        9.58
- ----------------------------------------------------------------------------
Total return (not annualized)    5.47%        8.29      19.27        (.31)
- ----------------------------------------------------------------------------
Ratios to average net assets
(annualized)
Expenses                         1.13%        1.03       1.20         .73
- ----------------------------------------------------------------------------
Net investment income            3.75%        3.89       3.61        4.11
- ----------------------------------------------------------------------------


                                                                  Dec. 29,
                                     Year ended July 31,           1995 to
                              ------------------------------      July 31,
                                 1999        1998       1997        1996
- ----------------------------------------------------------------------------
Supplemental data for all classes
Net assets at end of period
(in thousands)                  $59,953     55,335     30,700      10,831
- ----------------------------------------------------------------------------
Portfolio turnover rate
(annualized)                       58%          43        150          57
- ----------------------------------------------------------------------------



                                       7
<PAGE>


SPECIAL FEATURES

Shareholders of a Fund'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  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.

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,  typically will be higher for Class I shares than
for Class A, Class B and Class C shares.





December 1, 1999
KHF-1I


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