SCUDDER FUND INC
497, 1998-06-15
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                                                              SCUDDER  [logo]
Scudder Premium Money Market Shares

Supplement to Prospectus
Dated May 1, 1998

The last two  sentences of the first  paragraph  under the heading  "Transaction
information -- Processing time" on page 15 are replaced by the following:

Redemption  requests  received in good order by the Fund's transfer agent by the
close of regular  trading,  normally 4:00 p.m. eastern time, are executed at the
net  asset  value  calculated  at the  close on that day.  If  requested  by the
shareholder,  proceeds can be wired that day, but no dividend  will be earned on
the redeemed shares that day. All other redemption requests will be processed on
the day  received  and will earn a dividend  on the  redeemed  shares  that day;
however, the proceeds will be distributed on the next business day.

In the chart on page 19,  "Exchanges and  redemptions -- Redeeming  shares," the
sentence regarding "Write-A-Check" is replaced by the following:

You may redeem shares by writing checks against your account balance as often as
you like for at least $1,000, but no more than $5,000,000.


June 15, 1998



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