GENERAL MONEY MARKET FUND INC
N-30D, 1995-03-31
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LETTER TO SHAREHOLDERS
Dear Shareholder:
    For the fiscal year ended January 31, 1995, the yield of the General
Money Market Fund, Inc. was 3.69%. The effective yield, after compounding,
was 3.75%.*
    The year's returns for the General Money Market Fund, Inc. reflect both
the much lower level of interest rates when the year began and the continuous
rise in rates since then.
    The performance of the U.S. economy last year was most impressive, in
spite of slow retail sales during the Christmas season. During the year we
saw a robust housing market, booming automobile sales, notable expansion in
new jobs, a drop in the jobless rate, and expanding industrial production.
All of this was accomplished with a very modest level of inflation, whether
you measure inflation by the existing numbers or revise it downward, as has
been suggested by the Federal Reserve Board Chairman, Alan Greenspan. In
January, he told Congress he thinks the currently published inflation numbers
overstate the Consumer Price Index by 0.5% to 1.5%.
    On February 1, 1995, the Federal Reserve took the seventh of the series
of steps it initiated last February to try to head off inflation and moderate
the growth rate of the economy. In this latest step, the Federal Reserve
Board raised the Federal Funds rate to 6.00% and the closely watched discount
rate to 5.25%.
    With many economic indicators still signalling continued strength in
business activity, it is possible that the Federal Reserve may have to act
again. This could result in higher rates on short-term money market
instruments.
    We will be watching the economic developments closely and will make
portfolio adjustments as we deem appropriate.
    As announced by The Dreyfus Corporation, Joseph S. DiMartino resigned as
President of the Dreyfus Corporation in December of 1994, and as President of
the General Money Market Fund, Inc. in August of 1994. Mr. DiMartino assumed
the duties of Chairman of the Board of Directors for the General Money Market
Fund, Inc. in January, 1995. I have worked closely with Mr. DiMartino for the
past eight years and currently manage other Dreyfus money market funds.
    We are committed to continuing the investment service this Fund has
provided to you in the past, and look forward to serving your investment
needs in the future.
                              Sincerely,
                             (Robert P. Fort, Jr. Signature Logo)
                              Robert P. Fort, Jr.
                              Portfolio Manager
February 23, 1995
New York, N.Y.
  *    Effective yield is based upon dividends declared daily and reinvested
monthly.
<TABLE>
<CAPTION>


GENERAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS                                                                    JANUARY 31, 1995
                                                                                                    PRINCIPAL
NEGOTIABLE BANK CERTIFICATES OF DEPOSIT--34.1%                                                        AMOUNT          VALUE
                                                                                                 --------------  -------------
<S>                                                                                               <C>            <C>
ABN-AMRO Bank N.V. (Yankee)
    6.15%, 4/3/95-4/5/95....................................................                      $  20,000,000  $  20,000,171
Bank of Tokyo Ltd. (Yankee)
    6.31%-6.75%, 5/23/95-6/5/95.............................................                         25,000,000     25,007,576
Commerzbank AG (Yankee)
    6.27%, 4/6/95...........................................................                         25,000,000     25,001,559
Dai-Ichi Kangyo Bank Ltd. (London)
    5.21%-5.24%, 2/28/95....................................................                         20,000,000     20,000,131
Industrial Bank of Japan Ltd. (Yankee)
    6.05%-6.36%, 3/30/95-4/24/95............................................                         25,000,000     25,000,000
Mitsubishi Bank Ltd. (Yankee)
    6.24%, 4/13/95..........................................................                         10,000,000      9,999,701
Sanwa Bank Ltd. (Yankee)
    6.41%, 3/21/95-3/27/95..................................................                         20,000,000     19,997,632
Sumitomo Bank Ltd. (London)
    5.30%, 2/15/95..........................................................                          5,000,000      4,999,924
Sumitomo Bank Ltd. (Yankee)
    6.31%-6.59%, 4/17/95-5/12/95............................................                         20,000,000     20,001,965
SwedBank (Yankee)
    6.65%, 5/5/95...........................................................                         25,000,000     25,000,000
                                                                                                                 --------------
TOTAL NEGOTIABLE BANK CERTIFICATES OF DEPOSIT (cost $195,008,659)...........                                      $195,008,659
                                                                                                                 ==============

BANKERS' ACCEPTANCES--5.6%
Dai-Ichi Kangyo Bank Ltd. (Yankee)
    6.52%, 5/17/95..........................................................                        $ 5,000,000   $  4,906,958
Fuji Bank Ltd. (Yankee)
    6.31%, 4/18/95..........................................................                         22,000,000     21,712,044
Sanwa Bank Ltd. (Yankee)
    6.25%, 4/18/95..........................................................                          5,400,000      5,329,890
                                                                                                                 --------------
TOTAL BANKERS' ACCEPTANCES (cost $31,948,892)...............................                                      $ 31,948,892
                                                                                                                 ==============
COMMERCIAL PAPER--30.9%
Ford Motor Credit Co.
    6.24%, 4/28/95..........................................................                      $  15,000,000   $ 14,780,342
General Electric Capital Corp.
    5.11%-6.50%, 3/14/95-4/11/95............................................                         25,000,000     24,761,117
General Electric Capital Services Inc.
    6.40%, 6/20/95..........................................................                         10,000,000      9,759,453
General Motors Acceptance Corp.
    5.23%-6.37%, 2/6/95-5/8/95..............................................                         27,000,000     26,878,334
Goldman Sachs Group L.P.
    6.64%, 5/4/95...........................................................                         15,000,000     14,750,833
ITT Financial Corp.
    5.92%, 2/14/95..........................................................                         10,000,000      9,978,947
NYNEX Corp.
    5.94%, 2/16/95..........................................................                         10,000,000      9,975,625

GENERAL MONEY MARKET FUND, INC.
STATEMENT OF INVESTMENTS (CONTINUED)                                                                JANUARY 31, 1995
                                                                                                    PRINCIPAL
COMMERCIAL PAPER (CONTINUED)                                                                         AMOUNT           VALUE
                                                                                                 --------------  -------------
Sears Roebuck Acceptance Corp.
    6.58%, 6/13/95..........................................................                     $    5,000,000   $  4,882,667
Seventy Five State Street Capital Corp.
    6.11%, 3/10/95 (a)......................................................                         14,812,000     14,719,898
Spintab AB
    5.97%-6.07%, 3/15/95-3/24/95............................................                         27,000,000     26,791,662
Woolwich Building Society
    6.68%, 6/12/95..........................................................                         20,000,000     19,526,944
                                                                                                                 --------------
TOTAL COMMERCIAL PAPER (cost $176,805,822)..................................                                      $176,805,822
                                                                                                                 ==============
CORPORATE NOTES--5.2%
Bear Stearns Companies Inc.
    6.09%-6.12%, 8/25/95-1/26/96 (b)........................................                       $ 20,000,000   $ 20,000,000
Merrill Lynch & Co. Inc.
    5.94%, 2/23/95 (b)......................................................                         10,000,000     10,000,000
                                                                                                                 --------------
TOTAL CORPORATE NOTES (cost $30,000,000)....................................                                      $ 30,000,000
                                                                                                                 ==============
U.S.  GOVERNMENT AGENCIES--7.9%
Federal Home Loan Banks, Floating Rate Notes
    6.08%, 1/31/97 (b)......................................................                       $ 15,000,000   $ 15,000,000
Federal National Mortgage Association, Floating Rate Notes
    6.09%, 2/18/97 (b)......................................................                         30,000,000     30,000,000
                                                                                                                 --------------
TOTAL U.S. GOVERNMENT AGENCIES (cost $45,000,000)...........................                                      $ 45,000,000
                                                                                                                 ==============
TIME DEPOSITS--13.9%
Bayerische Landesbank Girozentrale (Cayman)
    5.87%, 2/1/95...........................................................                       $ 25,000,000   $ 25,000,000
Fifth Third Bank (Cayman)
    5.88%, 2/1/95...........................................................                         20,000,000     20,000,000
First Union National Bank (Nassau)
    5.87%, 2/1/95...........................................................                         25,000,000     25,000,000
Fleet Bank of New York N.A. (Cayman)
    5.88%, 2/1/95...........................................................                          6,000,000      6,000,000
Republic National Bank of New York (London)
    5.50%, 2/1/95...........................................................                          3,581,000      3,581,000
                                                                                                                 --------------
TOTAL TIME DEPOSITS (cost $79,581,000)......................................                                      $ 79,581,000
                                                                                                                 ==============
TOTAL INVESTMENTS (cost $558,344,373)..............................                 97.6%                         $558,344,373
                                                                                   ======                       ==============
CASH AND RECEIVABLES (NET).........................................                  2.4%                         $ 13,771,921
                                                                                   ======                       ==============
NET ASSETS  ..................................................                     100.0%                         $572,116,294
                                                                                   ======                       ==============
NOTES TO STATEMENT OF INVESTMENTS:
    (a)  Backed by an irrevocable letter of credit.
    (b)  Variable interest rate subject to periodic change.
See notes to financial statements.
</TABLE>

<TABLE>
<CAPTION>

GENERAL MONEY MARKET FUND, INC.
STATEMENT OF ASSETS AND LIABILITIES                                                                JANUARY 31, 1995
ASSETS:
    <S>                                                                                             <C>          <C>
    Investments in securities, at value--Note 1(a)..........................                                     $558,344,373
    Cash....................................................................                                       11,981,467
    Interest receivable.....................................................                                        2,487,582
    Prepaid expenses........................................................                                          148,287
                                                                                                                --------------
                                                                                                                  572,961,709
LIABILITIES:
    Due to The Dreyfus Corporation..........................................                        $  90,647
    Payable for Common Stock redeemed.......................................                          392,111
    Accrued expenses........................................................                          362,657         845,415
                                                                                                    ----------   ------------
NET ASSETS  ................................................................                                     $572,116,294
                                                                                                                 ============
REPRESENTED BY:
    Paid-in capital.........................................................                                     $572,131,931
    Accumulated net realized (loss) on investments..........................                                          (15,637)
                                                                                                                --------------
NET ASSETS at value applicable to 572,131,931 shares outstanding
    (15 billion shares of $.01 par value Common Stock authorized)...........                                     $572,116,294
                                                                                                                 ============
NET ASSET VALUE, offering and redemption price per share
    ($572,116,294 / 572,131,931 shares).....................................                                            $1.00
                                                                                                                        =====

See notes to financial statements.
</TABLE>

<TABLE>
<CAPTION>

GENERAL MONEY MARKET FUND, INC.
STATEMENT OF OPERATIONS                                                                      YEAR ENDED JANUARY 31, 1995
INVESTMENT INCOME:
    <S>                                                                                              <C>          <C>
    INTEREST INCOME.........................................................                                      $26,282,840
    EXPENSES:
      Management fee--Note 2(a).............................................                         $2,850,622
      Shareholder servicing costs_Note 2(b,c)...............................                          2,443,175
      Custodian fees........................................................                            113,975
      Professional fees.....................................................                             53,757
      Prospectus and shareholders' reports..................................                             42,856
      Registration fees.....................................................                             35,982
      Directors' fees and expenses_Note 2(d)................................                             23,338
      Miscellaneous.........................................................                             11,140
                                                                                                   ------------
                                                                                                     $5,574,845
      Less_reduction in shareholder servicing costs due
          to undertaking_Note 2(c)..........................................                            243,939
                                                                                                   ------------
            TOTAL EXPENSES..................................................                                        5,330,906
                                                                                                                -------------
INVESTMENT INCOME--NET......................................................                                       20,951,934
NET REALIZED GAIN ON INVESTMENTS--Note 1(b).................................                                            7,685
                                                                                                                -------------
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS........................                                      $20,959,619
                                                                                                                =============


See notes to financial statements.
</TABLE>

<TABLE>
<CAPTION>

GENERAL MONEY MARKET FUND, INC.
STATEMENT OF CHANGES IN NET ASSETS
                                                                                            YEAR ENDED JANUARY 31,
                                                                                      -----------------------------------
                                                                                            1994             1995
                                                                                      ----------------    ----------------
<S>                                                                                   <C>                   <C>
OPERATIONS:
    Investment income--net..................................................          $     16,251,231      $   20,951,934
    Net realized gain on investments........................................                     8,097               7,685
                                                                                      ----------------    ----------------
      NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS..................                16,259,328          20,959,619
                                                                                      ----------------    ----------------
DIVIDENDS TO SHAREHOLDERS FROM;
    Investment income--net..................................................               (16,251,231)        (20,951,934)
                                                                                      ----------------    ----------------
CAPITAL STOCK TRANSACTIONS ($1.00 per share):
    Net proceeds from shares sold...........................................             4,434,832,280       3,846,418,471
    Dividends reinvested....................................................                15,136,179          20,559,011
    Cost of shares redeemed.................................................            (4,522,690,497)     (3,910,940,423)
                                                                                      ----------------    ----------------
      (DECREASE) IN NET ASSETS FROM CAPITAL STOCK TRANSACTIONS..............               (72,722,038)        (43,962,941)
                                                                                      ----------------    ----------------
          TOTAL (DECREASE) IN NET ASSETS....................................               (72,713,941)        (43,955,256)
NET ASSETS:
    Beginning of year.......................................................               688,785,491         616,071,550
                                                                                      ----------------    ----------------
    End of year.............................................................           $   616,071,550     $   572,116,294
                                                                                      ================    ================


See notes to financial statements.

</TABLE>
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 year indicated.  This information
has been derived from the Fund's financial statements.
<TABLE>
<CAPTION>


                                                                                YEAR ENDED JANUARY 31,
                                                             --------------------------------------------------------
PER SHARE DATA:                                                1991         1992       1993         1994        1995
                                                             -------      -------    -------      -------     -------
    <S>                                                      <C>          <C>        <C>          <C>         <C>
    Net asset value, beginning of year...........            $1.0000      $1.0000    $1.0000      $1.0000     $1.0000
                                                             -------      -------    -------      -------     -------
    INVESTMENT OPERATIONS:
    Investment income--net.......................              .0739        .0547      .0321        .0253       .0369
    Net realized gain (loss) on investments......              --           --         --           --          --
                                                             -------      -------    -------      -------     -------
      TOTAL FROM INVESTMENT OPERATIONS...........              .0739        .0547      .0321        .0253       .0369
                                                             -------      -------    -------      -------     -------
    DISTRIBUTIONS;
    Dividends from investment income--net........             (.0739)      (.0547)    (.0321)      (.0253)     (.0369)
                                                             -------      -------    -------      -------     -------
    Net asset value, end of year.................            $1.0000      $1.0000    $1.0000      $1.0000     $1.0000
                                                             =======      =======    =======      =======     =======
TOTAL INVESTMENT RETURN                                       7.64%        5.61%      3.26%        2.56%       3.75%
RATIOS/SUPPLEMENTAL DATA:
    Ratio of expenses to average net assets......              .91%         .92%       .95%         .94%        .94%
    Ratio of net investment income to average net assets      7.39%        5.44%      3.22%        2.53%       3.68%
    Decrease reflected in above expense ratios due to
      undertaking by the Manager.................              --          --         --            .02%        .04%
    Net Assets, end of year (000's Omitted)......           $677,257     $845,690   $688,785     $616,072    $572,116


See notes to financial statements.

</TABLE>

GENERAL MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS
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. Dreyfus Service
Corporation, until August 24, 1994, acted as the distributor of the Fund's
shares, which are sold to the public without a sales load. Dreyfus Service
Corporation is a wholly-owned subsidiary of The Dreyfus Corporation
("Manager"). Effective August 24, 1994, the Manager became a direct
subsidiary of Mellon Bank, N.A.
    On August 24, 1994, Premier Mutual Fund Services, Inc. (the
"Distributor") was engaged as the Fund's Distributor. The Distributor,
located at One Exchange Place Boston, Massachusetts 02109, is a wholly-owned
subsidiary of Institutional Administration Services, Inc., a provider of
mutual fund administration services, the parent company of which is Boston
Institutional Group, Inc.
    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.
    (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.
    (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 January 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).

GENERAL MONEY MARKET FUND, INC.
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
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 11/2% of the average value of
the Fund's net assets for any full fiscal year. There was no expense
reimbursement for the year ended January 31, 1995 pursuant to the agreement.
    (B) On August 3, 1994, Fund shareholders approved a revised Service Plan
(the "Plan") pursuant to Rule 12b-1 under the Act. Pursuant to the Plan,
effective August 24, 1994, the Fund (a) reimburses the Distributor for
payments to third parties for distributing the Fund's shares and servicing
shareholder accounts and (b) pays the Manager, Dreyfus Service Corporation or
any affiliate (collectively "Dreyfus") for advertising and marketing relating
to the Fund and servicing Shareholders accounts, at an aggregate annual rate
of .20 of 1% of the value of the Fund's average daily net assets. Each of the
Distributor and Dreyfus may pay Service Agents (a securities dealer,
financial institution or other industry professional) a fee in respect of the
Fund's 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 the basis on which
such payments are made.
    Prior to August 24, 1994, the Fund's Service Plan ("prior Service Plan")
provided that the Fund pay Dreyfus Service Corporation at an annual rate of
.20 of 1% of the value of the Fund's average daily net assets, for costs and
expenses in connection with advertising, marketing and distributing the
Fund's shares and for servicing shareholder accounts. Dreyfus service
corporation made payments to one or more Service Agents based on the value of
the Fund's shares owned by clients of the Service Agent.
    During the year ended January 31, 1995, $493,882 was charged to the Fund
pursuant to the Plan and $646,367 was charged pursuant to the prior Service
Plan.
    (C) Pursuant to the Fund's 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 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. During the year ended
January 31, 1995, $529,002 was charged to the Fund pursuant to the Plan, of
which $243,939 was reimbursed pursuant to an undertaking by the Manager.
    (D) Prior to August 24, 1994, certain officers and directors of the Fund
were "affiliated persons," as defined in the Act, of the Manager and/or
Dreyfus Service Corporation. Each director who is not an "affiliated person"
receives an annual fee of $2,500 and an attendance fee of $500 per meeting.

GENERAL MONEY MARKET FUND, INC.
REPORT OF ERNST & YOUNG LLP, INDEPENDENT AUDITORS
SHAREHOLDERS AND BOARD OF DIRECTORS
GENERAL MONEY MARKET FUND, INC.
    We have audited the accompanying statement of assets and liabilities of
General Money Market Fund, Inc., including the statement of investments, as
of January 31, 1995, and the related statement of operations for the year
then ended, the statement of changes in net assets for each of the two years
in the period then ended, and financial highlights for each of the years
indicated therein. These financial statements and financial highlights are
the responsibility of the Fund's management. Our responsibility is to express
an opinion on these financial statements and financial highlights based on
our audits.
    We conducted our audits in accordance with generally accepted auditing
standards. Those standards require that we plan and perform the audit to
obtain reasonable assurance about whether the financial statements and
financial highlights are free of material misstatement. An audit includes
examining, on a test basis, evidence supporting the amounts and disclosures
in the financial statements. Our procedures included confirmation of
securities owned as of January 31, 1995 by correspondence with the custodians.
 An audit also includes assessing the accounting principles used and
significant estimates made by management, as well as evaluating the overall
financial statement presentation. We believe that our audits provide a
reasonable basis for our opinion.
    In our opinion, the financial statements and financial highlights
referred to above present fairly, in all material respects, the financial
position of General Money Market Fund, Inc. at January 31, 1995, the results
of its operations for the year then ended, the changes in its net assets for
each of the two years in the period then ended, and the financial highlights
for each of the indicated years, in conformity with generally accepted
accounting principles.

                              (Ernst & Young LLP Signature Logo)
New York, New York
March 7, 1995


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.                              196AR951


GENERAL
MONEY MARKET
FUND, INC.



(General `G' Logo)


ANNUAL REPORT
January 31, 1995



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