GENERAL MONEY MARKET FUND INC
N-30D, 1995-09-28
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GENERAL MONEY MARKET FUND, INC.
LETTER TO SHAREHOLDERS
Dear Shareholder:
    The past six months have seen a slow decline in the rate of economic
activity. This has been accompanied, inevitably, by declining interest rates.
    In this environment, we are pleased that for the six months ended July
31, 1995, the General Money Market Fund, Inc. produced an annualized yield of
5.43% for Class A shares. The annualized effective yield for Class A shares
was 5.57% after taking into account the effect of compounding.* For the
Fund's Class B shares the corresponding yields were 5.21% and 5.33%.
    In managing your assets, we achieved the yield level by lengthening
maturities gradually during the six-month period. This was done in
anticipation of lower interest rates, which became more and more likely as
the economy gave continued signs of slowing down.
    The Federal Reserve Board, which raised interest rates seven times during
1994 and early 1995 to head off inflation, became concerned that the drop in
economic performance might turn into an actual business recession.
Accordingly, in early July the Federal Reserve Board reversed course and made
a modest cut in the Federal Funds rate.
    As this letter is written, the economy has cooled off from the activity
that prevailed last year. Thus, one could say that the Fed's policies have
been successful. Inflation has been held at bay and few observers believe
that the "soft landing" will turn into a full-blown economic recession.
    However, the Federal Reserve Board showed caution in the July reduction
of short-term rates. If more of that medicine is needed, we feel that the Fed
will not hesitate to act accordingly. Nonetheless, the central bank must be
ever watchful lest rate-cutting bring on the recurrence of inflation which
the Fed has so strenuously sought to avoid.
    The money markets have already discounted the possibility of further Fed
moves to lower interest rates. To a certain extent, that is already built
into current market prices. Our strategy under these circumstances is to
remain in the long end of the market as long as necessary, in an effort to
seek the best possible level of yields.
    We appreciate the opportunity to put your cash to work in the money
market, and will continue to exert our best efforts to attempt to obtain
competitive returns on your behalf.
                              Sincerely,
                          [Patricia A. Larkin signature logo]
                              Patricia A. Larkin
                              Portfolio Manager

August 11, 1995
New York, N.Y.
* Annualized effective yield is based upon dividends declared daily and
reinvested monthly.

<TABLE>
<CAPTION>


GENERAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS                                                                             JULY 31, 1995 (UNAUDITED)
                                                                                                    PRINCIPAL
NEGOTIABLE BANK CERTIFICATES OF DEPOSIT-32.9%                                                         AMOUNT         VALUE
                                                                                                      ------         ------
<S>                                                                                               <C>            <C>
Bayerische Landesbank Girozentrale (Yankee)
    5.95%, 7/18/96..........................................................                      $  10,000,000  $ 10,000,000
Bayerische Vereinsbank AG (Yankee)
    6.02%-6.10%, 7/11/96-7/17/96............................................                         30,000,000    30,000,000
Canadian Imperial Bank of Commerce (Yankee)
    6.09%, 7/29/96..........................................................                         10,000,000    10,000,000
Dai-Ichi Kangyo Bank Ltd. (London)
    5.85%, 8/14/95..........................................................                         10,000,000    10,000,036
Dai-Ichi Kangyo Bank Ltd. (Yankee)
    5.82%, 8/17/95..........................................................                         15,000,000    15,000,066
Fuji Bank Ltd. (Yankee)
    5.89%, 10/6/95..........................................................                          5,000,000     5,000,000
Industrial Bank of Japan Ltd. (Yankee)
    5.82%-6.37%, 9/12/95-1/17/96............................................                         30,000,000    30,000,000
Mitsubishi Bank Ltd. (Yankee)
    6.34%-6.55%, 12/18/95-1/31/96...........................................                         30,000,000    30,088,260
Sanwa Bank Ltd. (Yankee)
    6.02%-6.52%, 11/20/95-6/3/96............................................                         30,000,000    30,001,897
Sumitomo Bank Ltd. (Yankee)
    5.84%, 9/15/95..........................................................                         25,000,000    25,000,619
SwedBank (Yankee)
    5.94%, 10/3/95..........................................................                         10,000,000    10,000,000
                                                                                                                   ----------
TOTAL NEGOTIABLE BANK CERTIFICATES OF DEPOSIT
    (cost $205,090,878).....................................................                                     $205,090,878
                                                                                                                   ==========

BANKERS' ACCEPTANCE-1.6%
Bank of Tokyo Ltd. (Yankee)
    5.82%, 8/21/95
    (cost $9,968,055).......................................................                      $  10,000,000    $9,968,055
                                                                                                                   ==========
COMMERCIAL PAPER-24.6%
Abbey National North America
    5.92%, 10/3/95..........................................................                      $  15,000,000  $ 14,846,964
Chemical Banking Corp.
    6.31%, 8/28/95..........................................................                         10,000,000     9,953,875
Chrysler Financial Corp.
    6.05%, 10/16/95-10/17/95................................................                         20,000,000    19,747,975
Den Danske Corp. Inc.
    6.24%, 10/23/95.........................................................                         15,000,000    14,790,771

GENERAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                                JULY 31, 1995 (UNAUDITED)
                                                                                                     PRINCIPAL
COMMERCIAL PAPER (CONTINUED)                                                                           AMOUNT         VALUE
                                                                                                      -------         -----

General Motors Acceptance Corp.
    6.14%-6.51%, 10/2/95-11/6/95............................................                      $  30,000,000  $ 29,596,367
Lehman Brothers Holdings Inc.
    6.17%, 5/10/96..........................................................                         10,000,000     9,557,500
Sears Roebuck Acceptance Corp.
    6.02%-6.40%, 8/29/95-10/2/95............................................                         15,000,000    14,870,161
Spintab AB
    6.16%, 9/15/95..........................................................                         15,000,000    14,887,125
UBS Finance (DE) Inc.
    5.82%, 8/1/95...........................................................                         25,000,000    25,000,000
                                                                                                                   ----------
TOTAL COMMERCIAL PAPER
    (cost $153,250,738).....................................................                                     $153,250,738
                                                                                                                   ==========
BANK NOTES-8.0%
Bank of New York
    6.07%, 12/20/95.........................................................                      $  10,000,000  $ 10,045,398
First National Bank of Boston
    5.98%-6.02%, 6/7/96-6/24/96 (a).........................................                         30,000,000    30,000,000
PNC Bank, NA
    6.44%, 12/11/95.........................................................                         10,000,000    10,001,365
                                                                                                                   ----------
TOTAL BANK NOTES
    (cost $50,046,763)......................................................                                     $ 50,046,763
                                                                                                                   ==========
CORPORATE NOTES-12.5%
Bear Stearns Companies Inc.
    5.77%-5.99%, 8/25/95-7/17/96 (a)........................................                      $  30,000,000  $ 30,000,000
General Electric Capital Corp.
    6.01%-6.03%, 3/29/96-4/5/96 (a).........................................                         25,000,000    24,996,114
Lehman Brothers Holdings Inc.
    6.20%, 5/16/96 (a)......................................................                         10,000,000    10,000,000
Merrill Lynch & Co. Inc.
    6.06%, 7/2/96 (a).......................................................                         13,000,000    12,997,698
                                                                                                                   ----------
TOTAL CORPORATE NOTES
    (cost $77,993,812)......................................................                                     $ 77,993,812
                                                                                                                   ==========

U.S. GOVERNMENT AGENCIES-11.3%
Federal Home Loan Banks , Floating Rate Notes
    6.33%, 1/31/97 (a)......................................................                      $  15,000,000  $ 15,000,000
Federal Home Loan Mortgage Corp. , Floating Rate Notes
    6%, 6/30/98 (a).........................................................                         10,700,000    10,735,538

GENERAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                                JULY 31, 1995 (UNAUDITED)
                                                                                                  PRINCIPAL
U.S. GOVERNMENT AGENCIES (CONTINUED)                                                                AMOUNT           VALUE
                                                                                                    -------          -----

Federal National Mortgage Association , Floating Rate Notes
    5.93%-6.34%, 1/13/97-2/18/97 (a)........................................                      $  45,000,000  $ 45,000,000
                                                                                                                   ----------
TOTAL U.S. GOVERNMENT AGENCIES
    (cost $70,735,538)......................................................                                      $70,735,538
                                                                                                                   ==========
TIME DEPOSITS-6.2%
Berliner Handels-und Frankfurter Bank AG (Cayman)
    5.94%, 8/1/95...........................................................                      $  10,000,000  $ 10,000,000
Fleet Bank of New York (Cayman)
    5.81%, 8/1/95...........................................................                         25,000,000    25,000,000
Republic National Bank of New York (London)
    5.62%, 8/1/95...........................................................                          3,863,000     3,863,000
                                                                                                                   ----------
TOTAL TIME DEPOSITS
    (cost $38,863,000)......................................................                                      $38,863,000
                                                                                                                   ==========
REPURCHASE AGREEMENTS-5.1%
Aubrey G. Lanston & Co., Inc.
    dated 7/31/95, due 8/1/95 in the amount of
    $32,005,173 (fully collateralized by U.S.
    Treasury Bills, 5.82% due 12/21/95, value $32,417,212)
    (cost $32,000,000)......................................................                      $  32,000,000   $32,000,000
                                                                                                                   ==========
TOTAL INVESTMENTS
    (cost $637,948,784)............................................                 102.2%                       $637,948,784
                                                                                    =====                          ==========
LIABILITIES, LESS CASH AND RECEIVABLES.............................                 (2.2%)                       $(14,070,444)
                                                                                    =====                          ==========
NET ASSETS  .................................................                      100.0%                        $623,878,340
                                                                                    =====                          ==========
NOTE TO STATEMENT OF INVESTMENTS;
(a)    Variable interest rate subject to periodic change.


See independent accountants' review report and notes to financial
statements.
</TABLE>

<TABLE>
<CAPTION>

GENERAL MONEY MARKET FUND, INC.
STATEMENT OF ASSETS AND LIABILITIES                                                                    JULY 31, 1995 (UNAUDITED)
<S>                                                                                              <C>              <C>
ASSETS:
    Investments in securities, at value-Note 1(a,b).........................                                      $637,948,784
    Interest receivable.....................................................                                         4,469,957
    Prepaid expenses........................................................                                            80,511
                                                                                                                   -----------
                                                                                                                   642,499,252
LIABILITIES:
    Due to The Dreyfus Corporation..........................................                     $   268,303
    Due to Distributor......................................................                         107,321
    Due to Custodian........................................................                       8,475,459
    Payable for investment securities purchased.............................                       9,557,500
    Accrued expenses .......................................................                         212,329        18,620,912
                                                                                                  -----------       ----------
NET ASSETS..................................................................                                      $623,878,340
                                                                                                                    ==========
REPRESENTED BY:
    Paid-in capital.........................................................                                      $623,891,826
    Accumulated net realized (loss) on investments..........................                                           (13,486)
                                                                                                                    ----------
NET ASSETS at value.........................................................                                      $623,878,340
                                                                                                                    ==========
Shares of Common Stock outstanding:
    Class A Shares
      (15 billion shares of $.01 par value shares authorized)...............                                       615,053,822
                                                                                                                    ==========
    Class B Shares
      (1 billion shares of $.01 par value shares authorized)................                                         8,838,004
                                                                                                                    ==========
NET ASSET VALUE per share:
    Class A Shares
      ($615,040,296 / 615,053,822 shares)...................................                                             $1.00
                                                                                                                         =====
    Class B Shares
      ($8,838,044 / 8,838,004 shares).......................................                                             $1.00
                                                                                                                         =====
STATEMENT OF OPERATIONS                                                               SIX MONTHS ENDED JULY 31, 1995 (UNAUDITED)
INVESTMENT INCOME:
    INTEREST INCOME.........................................................                                     $  18,868,309
    EXPENSES:
      Management fee-Note 2(a)..............................................                      $1,499,635
      Distribution fees (Class A & B Shares)-Note 2(b)......................                         599,854
      Shareholder servicing costs-Note 2(c).................................                         274,797
      Registration fees.....................................................                          54,290
      Custodian fees........................................................                          49,580
      Professional fees.....................................................                          43,856
      Prospectus and shareholders' reports..................................                          24,688
      Directors' fees and expenses-Note 2(d)................................                          17,606
      Miscellaneous.........................................................                           6,047
                                                                                                      -----

          TOTAL EXPENSES....................................................                                         2,570,353
                                                                                                                   -----------
INVESTMENT INCOME-NET.......................................................                                        16,297,956
NET REALIZED GAIN ON INVESTMENTS-Note 1(b)..................................                                             2,151
                                                                                                                   -----------
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........................                                      $ 16,300,107
                                                                                                                    ==========
See independent accountants' review report and notes to financial statements.
</TABLE>

<TABLE>
<CAPTION>

GENERAL MONEY MARKET FUND, INC.
STATEMENT OF CHANGES IN NET ASSETS
                                                                                         YEAR ENDED          SIX MONTHS ENDED
                                                                                         JANUARY 31,          JULY 31, 1995
                                                                                           1995                (UNAUDITED)
                                                                                          --------              ----------
<S>                                                                                 <C>                    <C>
OPERATIONS:
    Investment income-net.............................................              $    20,951,934        $    16,297,956
    Net realized gain on investments..................................                        7,685                  2,151
                                                                                        -----------             ----------
      NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS............                   20,959,619             16,300,107
                                                                                        -----------             ----------
DIVIDENDS TO SHAREHOLDERS FROM;
    Investment income-net:
      Class A Shares..................................................                  (20,951,934)           (16,204,967)
      Class B Shares..................................................                      --                     (92,989)
                                                                                          ---------             ----------
          TOTAL DIVIDENDS.............................................                  (20,951,934)           (16,297,956)
                                                                                          ---------             ----------
CAPITAL STOCK TRANSACTIONS ($1.00 per share):
    Net proceeds from shares sold:
      Class A Shares..................................................                3,846,418,471          2,280,180,009
      Class B Shares..................................................                      --                  15,738,822
    Dividends reinvested:
      Class A Shares..................................................                   20,559,011             15,717,231
      Class B Shares..................................................                      --                         144
    Cost of shares redeemed:
      Class A Shares..................................................               (3,910,940,423)        (2,252,975,349)
      Class B Shares..................................................                      --                  (6,900,962)
                                                                                     --------------         --------------
          INCREASE (DECREASE) IN NET ASSETS FROM
            CAPITAL STOCK TRANSACTIONS................................                  (43,962,941)            51,759,895
                                                                                         ----------             ----------
            TOTAL INCREASE (DECREASE) IN NET ASSETS...................                  (43,955,256)            51,762,046
NET ASSETS:
    Beginning of period...............................................                  616,071,550            572,116,294
                                                                                          ---------             ----------
    End of period.....................................................            $    572,116,294          $  623,878,340
                                                                                        ==========            ============


See independent accountants' review report and notes to financial statements.
</TABLE>

<TABLE>
<CAPTION>

GENERAL MONEY MARKET FUND, INC.
FINANCIAL HIGHLIGHTS
    Contained below is per share operating performance data for a share of
Common Stock outstanding, total investment return, ratios to average net
assets and other supplemental data for each period indicated. This
information has been derived from the Fund's financial statements.

                                                                       CLASS A SHARES                   CLASS B SHARES
                                           ---------------------------------------------------          --------------

                                                                                        SIX MONTHS ENDED  PERIOD ENDED
                                                             YEAR ENDED JANUARY 31,       JULY 31, 1995   JULY 31, 1995
                                           -----------------------------------------     --------------   ------------
PER SHARE DATA:                            1991     1992      1993     1994     1995      (UNAUDITED)    (UNAUDITED)(1)
                                           ----     ----      ----     ----     ----     --------------   -------------
    <S>                                  <C>       <C>       <C>      <C>      <C>          <C>            <C>
    Net asset value,
      beginning of period...             $1.0000   $1.0000   $1.0000  $1.0000  $1.0000      $1.0000        $1.0000
                                           ------   ------    ------   ------   -------      -------        ------
    INVESTMENT OPERATIONS:
    Investment income-net...               .0739     .0547     .0321    .0253    .0369        .0269          .0175
    Net realized gain (loss)
      on investments........                 --         --      --       --       --            --            --
                                           ------    ------   ------   ------   -------      -------        ------
      TOTAL FROM INVESTMENT
          OPERATIONS........               .0739     .0547     .0321    .0253    .0369        .0269          .0175
                                           ------    ------   ------   ------   -------      -------        ------
    DISTRIBUTIONS;
    Dividends from investment
      income-net............              (.0739)   (.0547)   (.0321)  (.0253)  (.0369)      (.0269)        (.0175)
                                           ------    ------    ------   ------  -------      -------        ------
    Net asset value, end of period       $1.0000   $1.0000   $1.0000  $1.0000  $1.0000      $1.0000        $1.0000
                                           =====    ======    ======   ======   ======       ======         ======
TOTAL INVESTMENT RETURN.....              7.64%     5.61%     3.26%    2.56%    3.75%        5.49%(2)       5.25%(2)
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to
      average net assets....               .91%      .92%      .95%     .94%     .94%         .86%(2)        .98%(2)
    Ratio of net investment income
      to average net assets.              7.39%     5.44%     3.22%    2.53%    3.68%        5.44%(2)       5.21%(2)
    Decrease reflected in above
      expense ratios due to
undertaking by
the Manager                                 --        --       --       .02%     .04%           --            --
    Net Assets, end of period
      (000's Omitted).......             $677,257  $845,690  $688,785  $616,072 $572,116     $615,040       $8,838
- -------------------------
(1)    From March 31, 1995 (commencement of initial offering) to July 31, 1995.
(2)    Annualized.


See independent accountants' review report and notes to financial statements.

</TABLE>

GENERAL MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS (UNAUDITED)
NOTE 1-SIGNIFICANT ACCOUNTING POLICIES:
    The Fund is registered under the Investment Company Act of 1940 ("Act")
as a diversified open-end management investment company. Premier Mutual Fund
Services, Inc. (the "Distributor") acts as the distributor of the Fund's
shares. The Distributor, located at One Exchange Place, Boston, Massachusetts
02109, is a wholly-owned subsidiary of FDI Distribution Services, Inc., a
provider of mutual fund administration services, which in turn is a
wholly-owned subsidiary of FDI Holdings, Inc., the parent company of which is
Boston Institutional Group, Inc. The Dreyfus Corporation ("Manager") serves
as the Fund's investment adviser. The Manager is a direct subsidiary of
Mellon Bank, N.A.
    It is the Fund's policy to maintain a continuous net asset value per
share of $1.00; the Fund has adopted certain investment, portfolio valuation
and dividend and distribution policies to enable it to do so. There is no
assurance, however, that the Fund will be able to maintain a stable net asset
value of $1.00.
    On May 26, 1994, the Fund's Board of Directors approved an amendment to
the Fund's Charter to provide for the issuance of additional shares of the
Fund. The amendment was approved by Fund shareholders on August 3, 1994.
Pursuant to the amendment, the Fund's existing authorized shares were
classified as Class A shares and one billion newly authorized shares of the
Common Stock of the Fund, par value $.01 per share, were classified as Class
B shares. The Fund began offering both Class A and Class B shares on March
31, 1995. Class A shares and Class B shares are identical except for the
services offered to and the expenses borne by each class and certain voting
rights. Class A shares are subject to a Service Plan adopted pursuant to Rule
12b-1 under the Act, Class B shares are subject to a Distribution Plan
adopted pursuant to Rule 12b-1 under the Act and, in addition, Class B shares
are charged directly for sub-accounting services provided by service agents
at an annual rate of .05% of the value of the average daily net assets of
Class B shares.
    (A) PORTFOLIO VALUATION: Investments are valued at amortized cost, which
has been determined by the Fund's Board of Directors to represent the fair
value of the Fund's investments.
    (B) SECURITIES TRANSACTIONS AND INVESTMENT INCOME: Securities
transactions are recorded on a trade date basis. Realized gain and loss from
securities transactions are recorded on the identified cost basis. Interest
income is recognized on the accrual basis. Cost of investments represents
amortized cost.
    The Fund may enter into repurchase agreements with financial
institutions, deemed to be creditworthy by the Fund's Manager, subject to the
seller's agreement to repurchase and the Fund's agreement to resell such
securities at a mutually agreed upon price. Securities purchased subject to
repurchase agreements are deposited with the Fund's custodians and, pursuant
to the terms of the repurchase agreement, must have an aggregate market value
greater than or equal to the repurchase price plus accrued interest at all
times. If the value of the underlying securities falls below the value of the
repurchase price plus accrued interest, the Fund will require the seller to
deposit additional collateral by the next business day. If the request for
additional collateral is not met, or the seller defaults on its repurchase
obligation, the Fund maintains the right to sell the underlying securities at
market value and may claim any resulting loss against the seller.

GENERAL MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS (UNAUDITED) (CONTINUED)

    (C) DIVIDENDS TO SHAREHOLDERS: It is the policy of the Fund to declare
dividends from investment income-net on each business day; such dividends
are paid monthly. Dividends from net realized capital gain are normally
declared and paid annually, but the Fund may make distributions on a more
frequent basis to comply with the distribution requirements of the Internal
Revenue Code. To the extent that net realized capital gain can be offset by
capital loss carryovers, it is the policy of the Fund not to distribute such
gain.
    (D) FEDERAL INCOME TAXES: It is the policy of the Fund to continue to
qualify as a regulated investment company, if such qualification is in the
best interests of its shareholders, by complying with the applicable
provisions of the Internal Revenue Code, and to make distributions of taxable
income sufficient to relieve it from substantially all Federal income and
excise taxes.
    The Fund has an unused capital loss carryover of approximately $15,000
available for Federal income tax purposes to be applied against future net
securities profits, if any, realized subsequent to January 31, 1995. The
carryover does not include net realized securities losses from November 1,
1994 through January 31, 1995 which are treated, for Federal income tax
purposes, as arising in fiscal 1996. If not applied, the carryover expires in
2002.
    At July 31, 1995, the cost of investments for Federal income tax purposes
was substantially the same as the cost for financial reporting purposes (see
the Statement of Investments).
NOTE 2-MANAGEMENT FEE AND OTHER TRANSACTIONS WITH AFFILIATES:
    (A) Pursuant to a management agreement ("Agreement") with the Manager,
the management fee is computed at the annual rate of .50 of 1% of the average
daily value of the Fund's net assets and is payable monthly. The Agreement
provides for an expense reimbursement from the Manager should the Fund's
aggregate expenses, exclusive of taxes, interest on borrowings, brokerage
commissions and extraordinary expenses, exceed 1 1/2% of the average value of
the Fund's net assets for any full fiscal year. There was no expense
reimbursement for the six months ended July 31, 1995 pursuant to the
agreement.
    (B) Under the Service Plan (the "Plan") with respect to Class A shares
only, adopted pursuant to
Rule 12b-1 under the Act, the Fund directly bears the cost of preparing,
printing and distributing prospectuses and statements of additional
information and implementing and operating the Class A Service Plan, (a)
reimburses the Distributor for payments to certain Service Agents for
distributing Class A shares and servicing shareholder accounts and (b) pays
the Manager, Dreyfus Service Corporation, a wholly-owned subsidiary of the
Manager, or any affiliate (collectively "Dreyfus") for servicing shareholder
accounts, at an aggregate annual rate of .20 of 1% of the value of the
average daily net assets of Class A. Each of the Distributor and Dreyfus may
pay Service Agents (a securities dealer, financial institution or other
industry professional) a fee in respect of Class A shares owned by
shareholders with whom the Service Agent has a servicing relationship or for
whom the Service Agent is the dealer or holder of record. Each of the
Distributor and Dreyfus determine the amounts to be paid to Service Agents to
which it will make payments and basis on which such payments are made. During
the six months ended July 31, 1995, $596,284 was charged to the Fund pursuant
to the Plan.

GENERAL MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS (UNAUDITED) (CONTINUED)
    Under the Distribution Plan with respect to Class B shares ("Class B
Distribution Plan"), adopted pursuant to Rule 12b-1
under the Act, effective March 31, 1995, the Fund directly bears the costs of
preparing, printing and distributing prospectuses and statements of
additional information and of implementing and operating the Class B
Distribution Plan. In addition, the Fund reimburses the Distributor for
payments made to third parties for distributing the Fund's Class B shares at
an aggregate annual rate of .20% of 1% of the value of the average daily net
assets of Class B shares. From March 31, 1995 through July 31, 1995, $3,570
was charged to the Fund pursuant to the Class B Distribution Plan.
    (C) Pursuant to the Fund's Shareholder Services Plan with respect to
Class A ("Class A Shareholder Services Plan"), the Fund reimburses Dreyfus
Service Corporation, an amount not to exceed an annual rate of .25 of 1% of
the value of the Fund's average daily net assets of Class A for certain
allocated expenses of providing personal services and/or maintaining
shareholder accounts. The services provided may include personal services
relating to shareholder accounts, such as answering shareholder inquiries rega
rding the Fund and providing reports and other information, and services
related to the maintenance of shareholder accounts. During the six months
ended July 31, 1995, the Fund was charged an aggregate of $109,406 pursuant
to the Class A Shareholder Services Plan.
    Under the Shareholder Services Plan with respect to Class B ("Class B
Shareholder Services Plan"), effective March 31, 1995, the Fund pays the
Distributor, at an annual rate of .25 of 1% of the value of the average daily
net assets of Class B shares for servicing shareholder accounts. The services
provided may include personal services relating to shareholder accounts, such
as answering shareholder inquiries regarding the Fund and providing reports
and other information, and services related to the maintenance of shareholder
accounts. The Distributor may make payments to service agents in respect of
these services. The Distributor determines the amounts to be paid to service
agents. From March 31, 1995 through July 31, 1995, $4,463 was charged to Class
 B shares by the Distributor pursuant to the Class B Shareholder Services
Plan.
    (D) Each director who is not an "affiliated person" as defined in the Act
receives from the Fund an annual fee of $2,500 and an attendance fee of $500
per meeting. The Chairman of the Board receives an additional 25% of such
compensation.



GENERAL MONEY MARKET FUND, INC.
REVIEW REPORT OF ERNST & YOUNG LLP, INDEPENDENT ACCOUNTANTS
SHAREHOLDERS AND BOARD OF DIRECTORS
GENERAL MONEY MARKET FUND, INC.
    We have reviewed the accompanying statement of assets and liabilities of
General Money Market Fund, Inc., including the statement of investments, as
of July 31, 1995, and the related statements of operations and changes in net
assets and financial highlights for the six month period ended July 31, 1995.
These financial statements and financial highlights are the responsibility of
the Fund's management.
    We conducted our review in accordance with standards established by the
American Institute of Certified Public Accountants. A review of interim
financial information consists principally of applying analytical procedures
to financial data, and making inquiries of persons responsible for financial
and accounting matters. It is substantially less in scope than an audit
conducted in accordance with generally accepted auditing standards, which
will be performed for the full year with the objective of expressing an opinio
n regarding the financial statements and financial highlights taken as a
whole. Accordingly, we do not express such an opinion.
    Based on our review, we are not aware of any material modifications that
should be made to the interim financial statements and financial highlights
referred to above for them to be in conformity with generally accepted
accounting principles.
    We have previously audited, in accordance with generally accepted
auditing standards, the statement of changes in net assets for the year ended
January 31, 1995 and financial highlights for each of the five years in the
period ended January 31, 1995 and in our report dated March 7, 1995, we
expressed an unqualified opinion on such statement of changes in net assets
and financial highlights.
[Ernst and Young LLP signature logo]


New York, New York
September 6,1995

[Dreyfus lion "d" logo]
GENERAL MONEY MARKET FUND, INC.
200 Park Avenue
New York, NY 10166
Manager
THE DREYFUS CORPORATION
200 Park Avenue
New York, NY 10166
Custodian
THE BANK OF NEW YORK
90 Washington Street
New York, NY 10286
Transfer Agent &
Dividend Disbursing Agent
THE SHAREHOLDER SERVICES GROUP, INC.
P.O. Box 9671
Providence, RI 02940





Further information is contained
in the Prospectus, which must
precede or accompany this report.




Printed in U.S.A.                              196SA957
[Dreyfus logo]
GENERAL
MONEY MARKET
FUND, INC.






SEMI-ANNUAL REPORT
July 31, 1995



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