ARCH FUNDS INC
497, 1998-02-04
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<PAGE>   1
 
                             THE ARCH FUND(R), INC.
 
                    SUPPLEMENT DATED JANUARY 29, 1998 TO THE
                       PROSPECTUS DATED SEPTEMBER 2, 1997
                         (AS REVISED NOVEMBER 21, 1997)
 
                            GROWTH EQUITY PORTFOLIO
 
                                  TRUST SHARES
 
     THIS SUPPLEMENT PROVIDES NEW AND ADDITIONAL INFORMATION BEYOND THAT
CONTAINED IN THE PROSPECTUS AND SHOULD BE RETAINED AND READ IN CONJUNCTION WITH
THE PROSPECTUS.
 
     (1) The last sentence of the first paragraph on the cover page (page 1) of
the Prospectus is replaced with the following:
 
          Trust Shares are offered to financial institutions acting on their own
     behalf or on behalf of discretionary and non-discretionary accounts for
     which they may receive account-level asset-based management fees.
 
     (2) The following information replaces the section entitled "Expense
Summary for Trust Shares" on page 5 of the Prospectus:
 
                        EXPENSE SUMMARY FOR TRUST SHARES
 
<TABLE>
<CAPTION>
                                                                                 GROWTH EQUITY
                                                                                   PORTFOLIO
                                                                                 -------------
<S>                                                                              <C>
ANNUAL PORTFOLIO OPERATING EXPENSES
  (as a percentage of average net assets)
  Investment Advisory Fees...................................................          .75%
  12b-1 Fees.................................................................          .00%
  Other Expenses (including administration fees, administrative services fees
     and other expenses) (net of fee waivers and expense
     reimbursements)(1,2)....................................................          .25%
                                                                                      ----
TOTAL PORTFOLIO OPERATING EXPENSES (net of fee waivers and expense
  reimbursements)(3).........................................................         1.00%
                                                                                      ====
</TABLE>
 
- ---------------
 
(1) Administrative services fees are payable at an annual rate not to exceed
    .30%. Without fee waivers, administration fees would be .20%.
 
(2) Without fee waivers and expense reimbursements, Other Expenses would be .65%
    and Total Portfolio Operating Expenses would be 1.40%.
 
EXAMPLE
 
<TABLE>
<CAPTION>
                                                              1 YEAR    3 YEARS    5 YEARS    10 YEARS
                                                              ------    -------    -------    --------
<S>                                                           <C>       <C>        <C>        <C>
You would pay the following expenses on a $1,000
  investment, assuming (1) a 5% annual return and (2)
  redemption at the end of each period:
Growth Equity Portfolio....................................    $ 10       $32        $55        $122
</TABLE>
<PAGE>   2
 
     THE FOREGOING EXAMPLE SHOULD NOT BE CONSIDERED A REPRESENTATION OF PAST OR
FUTURE EXPENSES OR RATES OF RETURN. ACTUAL EXPENSES AND RATES OF RETURN MAY BE
MORE OR LESS THAN THOSE SHOWN. Information about the actual performance of the
Predecessor Portfolio is contained in the financial statements included in the
Statement of Additional Information.
 
     The purpose of the foregoing table is to assist in understanding the
various costs and expenses that an investor in the Portfolio's Trust Shares will
bear directly or indirectly. The table reflects the expenses which the Portfolio
expects to incur during the current fiscal year on its Trust Shares. For more
complete descriptions of the various costs and expenses, see "Management of the
Fund" in this Prospectus and the Statement of Additional Information. The table
and example have not been audited by the Fund's independent auditors and do not
reflect any charges that may be imposed by financial institutions on their
customers.
 
     (3) The first sentence of the first paragraph of the section entitled "How
to Purchase and Redeem Shares -- Purchase of Shares" on page 14 of the
Prospectus is deleted and replaced by the following:
 
          Trust Shares are sold to financial institutions, such as banks, trust
     companies, thrift institutions, mutual funds or other financial
     institutions (collectively "financial institutions"), acting on their own
     behalf or on behalf of discretionary and non-discretionary accounts for
     which they may receive account-level asset-based management fees.
 
     (4) The third paragraph of the section entitled "Taxes" on page 19 of the
Prospectus is replaced with the following:
 
          Substantially all of the Portfolio's net realized long-term capital
     gains, if any, will be distributed at least annually to its shareholders.
     The Portfolio will generally have no tax liability with respect to such
     gains and the distributions will be taxable to shareholders who are not
     currently exempt from federal income taxes as long-term capital gains,
     regardless of how long the shareholders have held the Shares and whether
     such dividends are received in cash or reinvested in additional Shares.
     Such long-term capital gain will be 20% or 28% rate gain, depending upon
     the Portfolio's holding period for the assets the sale of which generated
     the capital gain.
 
     (5) The sixth paragraph of the section entitled "Taxes on page 19 of the
Prospectus is replaced with the following:
 
          The Portfolio may be required in certain cases to withhold and remit
     to the U.S. Treasury 31% of taxable dividends or gross sale proceeds paid
     to shareholders who have failed to provide a correct tax identification
     number in the manner required, who are subject to backup withholding by the
     Internal Revenue Service for prior failure to properly include on their
     return payments of prior failure to properly include on their return
     payments of taxable interest or dividends, or who have failed to certify to
     the Portfolio that they are not subject to backup withholding when required
     to do so or that they are "exempt recipients."
 
                                        2
<PAGE>   3
 
     (6) The following replaces the section entitled "Management of the
Fund -- Investment Adviser" on page 20 of the Prospectus:
 
INVESTMENT ADVISER
 
     Mississippi Valley Advisors Inc. ("MVA") serves as the investment adviser
to the Portfolio. MVA's principal office is located at One Mercantile Center,
Seventh & Washington Streets, St. Louis, Missouri 63101. MVA is a wholly-owned
subsidiary of Mercantile. As of December 31, 1997, MVA had approximately $9.4
billion in assets under investment management, including the Fund's assets,
which were approximately $3.9 billion. MVA also serves as investment adviser to
each of the Fund's other portfolios.
 
     Subject to the general supervision of the Fund's Board of Directors and in
accordance with the Fund's investment policies, MVA manages the Portfolio, makes
investment decisions with respect to and places orders for all purchases and
sales of the Portfolio's securities and other investments, and directs the
maintenance of the Portfolio's records relating to such purchases and sales.
 
     For the services provided and expenses assumed pursuant to the investment
advisory agreement, MVA is entitled to receive fees, computed daily and payable
monthly, at the annual rate of .75% of the Portfolio's average daily net assets.
 
     MVA may from time to time voluntarily reduce all or a portion of its
advisory fee to increase the net income of the Portfolio available for
distributions as dividends. The voluntary fee reduction will cause the return of
the Portfolio to be higher than it would otherwise be in the absence of such
reduction.
 
     The Predecessor Portfolio bore advisory fees during the fiscal year ended
September 30, 1997 pursuant to the investment advisory agreements then in effect
with MVA (or the predecessor adviser, Mark Twain Bank) at the effective annual
rate of .75% of its average daily net assets after fee waivers. Without fee
waivers, the Predecessor Portfolio would have borne advisory fees at the annual
rate of .75% of its average daily net assets.
 
     The organizational arrangements of MVA require that all investment
decisions with respect to the Growth Equity Portfolio be made by MVA's Equity
Committee, and no one person is responsible for making recommendations to the
Committee.
 
     (7) The fourth paragraph of the section entitled "Management of the
Funds -- Administrator" on page 21 of the Prospectus is replaced with the
following:
 
          The Predecessor Portfolio bore administrative fees during the fiscal
     year ended September 30, 1997 pursuant to the administrative services
     agreement then in effect with Federated Administrative Services, its former
     administrator, at the effective annual rate of .15% of its average daily
     net assets.
 
     (8) The third sentence of the fourth paragraph of the section entitled
"Other Information Concerning the Fund and Its Shares -- Description of Shares"
on page 24 of the Prospectus is replaced with the following:
 
          Institutional Shares, which are offered to financial institutions
     acting on behalf of discretionary and non-discretionary amounts for which
     they do not receive account-level asset-based management fees, are sold
     without a sales charge.
 
                                        3
<PAGE>   4
 
     (9) The first sentence of the second paragraph of the section entitled
"Other Information Concerning the Fund and Its Shares -- Miscellaneous" on page
25 of the Prospectus is replaced with the following:
 
          As of December 31, 1997, Mercantile and its affiliates possessed, of
     record on behalf of their underlying customer accounts, voting or
     investment power with respect to more than 25% of the Fund's outstanding
     Shares.
 
                                        4


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