PIONEER MONEY MARKET TRUST
N-30D, 1996-02-20
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DEAR FELLOW SHAREOWNERS,
- --------------------------------------------------------------------------------

This annual report covers the progress and  performance of Pioneer's three money
market funds: Pioneer Cash Reserves Fund, Pioneer U.S. Government Money Fund and
Pioneer Tax-Free Money Fund. Several important events occurred during the Funds'
fiscal year ended December 31, 1995: shareowners approved proposals updating the
Funds' structure; Class B shares were introduced for Pioneer Cash Reserves Fund;
and in  November,  we announced  plans to close  Pioneer Tax- Free Money Fund in
January 1996.

                           INTEREST RATES MOVED LOWER
                               AS YEAR PROGRESSED
 
In 1994, the Federal Reserve (the Fed) increased  short-term  interest rates six
times in an  attempt to stem  strong  economic  growth  and avert any  potential
increase in the rate of inflation.  Going into 1995, economic indicators led the
Fed to act yet again,  and it hiked  short  rates one final time on  February 1,
moving  the  federal  funds  rate to a  three-year  high of 6%.  Following  this
increase,  economic  growth  appeared to slow, but while heading toward a ``soft
landing'' (enough growth to prevent inflation but avoid recession),  the economy
threatened to stall. In response,  the Fed shifted gears and lowered short- term
rates,  first on July 7 and again on December  19. By  December  31, the federal
funds rate stood at 5.5%, near where it began the year.

Since money fund yields follow  short-term  rates,  February's  hike boosted the
Funds'  income,  and the rate cuts  later in the year  reduced  it.  Longer-term
interest rates dropped  dramatically  during the year,  however, at times making
money  market  rates  higher  than  those  offered  by  longer-term  securities,
particularly  two-year  issues.  Uncertain about the next direction of financial
markets and interest  rates,  and the resulting  effect on various  investments,
many investors  turned to money funds for the stable $1 share price they seek to
maintain. Historically, money funds have provided ``safe harbors'' -- and liquid
cash -- during unsettling times.

                            HOW YOUR FUND PERFORMED
 
We are pleased to present the following  results for Pioneer Cash Reserves Fund,
Pioneer U.S.  Government Money Fund and Pioneer Tax-Free Money Fund.  Throughout
1995, all three funds provided a steady stream of income while adhering to their
objective of maintaining a $1 share price. Preserving capital and providing high
current income by investing in high-quality  securities remains the objective as
Pioneer  Cash  Reserves  Fund and Pioneer U.S.  Government  Money Fund move into
1996.

PIONEER CASH RESERVES  FUND invests in high-  quality  money market  instruments
issued by the U.S.  government,  corporations  and banks to provide  shareowners
with high current  income and to preserve  capital.  On March 31, Class B shares
were added to the Fund to give  investors in the Class B shares of other Pioneer
funds the flexibility to move into a money market fund to meet their  short-term
cash needs.

As of December 31, 1995: 

o    81% of the Fund's portfolio was invested in commercial  paper,  with 11% in
     U.S. government agency  obligations.  Overnight  repurchase  agreements and
     banker's acceptances accounted for 5% and 3%, respectively.

o    Average  portfolio  maturity  was 25 days,  versus 27 days on December  31,
     1994.

Class A Shares 

o    Shareowners had received total  distributions of $0.0505 per share over the
     year.

o    Net 7-day annualized yield was 4.91%, the same as at the end of 1994.

o    The 7-day  effective  yield (taking into account the  compounding  of daily
     dividends) was 5.03%, the same as the effective yield on December 31, 1994.

Class B Shares 

o    Shareowners had received total distributions of $0.0324 per share since the
     Fund's inception.

o    Net 7-day annualized yield was 4.03%.

o    The 7-day  effective  yield (taking into account the  compounding  of daily
     dividends) was 4.11%.

We  focused  on  portfolio  liquidity  during  the  period,  and  placed a large
percentage of the portfolio in overnight repurchase agreements. Again this year,
the Fund  bought  only issues  given the  highest  rating  (A1/P1) by Standard &
Poor's and Moody's rating organizations.
<PAGE>
- --------------------------------------------------------------------------------

PIONEER  U.S.  GOVERNMENT  MONEY  FUND  invests  in U.S.  government  and agency
obligations to provide high current income and to preserve  capital.  Generally,
the Fund's income is free from state and local income taxes.

As of December 31, 1995:

o    Shareowners had received total  distributions of $0.0504 per share over the
     year.

o    Net 7-day annualized yield was 4.96%, compared with 5.03% a year earlier.

o    The 7-day  effective  yield (taking into account the  compounding  of daily
     dividends) was 5.09%, down slightly from 5.15% on December 31, 1994.

o    100%  of the  Fund's  portfolio  was  invested  in U.S.  government  agency
     obligations.

o    Average  portfolio  maturity  was 38 days,  versus 32 days on December  31,
     1994.

The increase in  portfolio  maturity  reflects  your  manager's  efforts to hold
higher yields in the portfolio as long as possible as short-term rates declined.
As usual,  the Fund invested in only the highest  quality issues -- those of the
U.S. Treasury and government agencies.

PIONEER  TAX-FREE  MONEY FUND  invested in short- term  municipal  securities to
provide  income  free from  federal  income  taxes and to preserve  capital.  As
shareowners were notified in November and December,  Pioneer Tax-Free Money Fund
ceased shareowner  operations on January 5, 1996. The Fund's Trustees authorized
this course of action because they believed the Fund's  continued small size was
not in shareowners' best interests.

As of December 31, 1995: 

o    Shareowners had received total  distributions  of $0.0305 per share for the
     year.

o    Net 7-day annualized  yield was 3.01%,  equivalent to a 4.98% taxable yield
     for shareowners in the 39.6% federal income tax bracket.

o    The 7-day  effective  yield (taking into account the  compounding  of daily
     dividends) was 3.05%,  the same as a taxable yield of 5.05% for shareowners
     in the 39.6% federal income tax bracket.

o    94% of the Fund's portfolio was invested in variable rate securities,  with
     the remaining 6% in tax-free commercial paper.

o    Average portfolio maturity was 5 days.

To keep Fund dividends  stable, we added high- quality general market notes with
longer  maturities to the  portfolio.  Throughout  the year,  however,  the Fund
essentially held to its strategy of investing in very short-term securities.

The  following  pages  present  audited  financial  statements  and schedules of
portfolio  holdings at the period's  end. If you have any  questions  about your
investment in Pioneer Cash Reserves Fund, Pioneer U.S.  Government Money Fund or
Pioneer Tax-Free Money Fund, please consult your investment  representative,  or
call Pioneer at 1-800-225-6292.

Respectfully,

/s/ John F. Cogan, Jr.

John F. Cogan, Jr.
Chairman and President,
Pioneer Money Market Trust

The Funds are currently waiving all or a portion of their management fees and/or
expenses.  Otherwise 7-day annualized  yields would have been: 4.63% for Class A
shares and 3.80% for Class B shares of Pioneer  Cash  Reserves  Fund;  4.34% for
Pioneer U.S. Government Money Fund; and 1.26% for Pioneer Tax-Free Money Fund.

Past  performance  does not guarantee  future  results.  Investment  return will
fluctuate, and there can be no guarantee that the Funds will be able to maintain
a stable  net asset  value of $1.00 per  share.  An  investment  in the Funds is
neither insured nor guaranteed by the U.S. government.  

                                       2
<PAGE>
<TABLE>
<CAPTION>

SCHEDULE OF INVESTMENTS -- PIONEER CASH RESERVES FUND -- DECEMBER 31, 1995
- -----------------------------------------------------------------------------------------------------
PRINCIPAL
 AMOUNT                        INVESTMENT IN SECURITIES                                      VALUE
- -----------------------------------------------------------------------------------------------------
<S>        <C>                                                                           <C>
           COMMERCIAL PAPER -- 80.7%
$7,000,000 Abbott Laboratories, 5.65%, 1/3/96                                            $  6,998,901 
 7,700,000 American Express Credit Corp., 5.60%, 2/2/96                                     7,662,869
 7,000,000 American General Finance Corp., 5.78%, 1/18/96                                   6,982,017
 4,100,000 Avco Financial, 5.68%, 2/2/96                                                    4,079,946
 5,000,000 Banc One Corp., 5.66%, 1/10/96                                                   4,993,711
 6,014,000 Bell South Capital, 5.62%, 2/7/96                                                5,980,201
 1,040,000 Beneficial Corp., 5.80%, 1/26/96                                                 1,035,979
 2,880,000 Chevron Oil Finance Co., 5.77%, 1/31/96                                          2,866,614
 6,600,000 Coca-Cola Co., 5.55%, 1/8/96                                                     6,593,895 
 3,775,000 Corestates Capital Corp., 5.67%, 1/4/96                                          3,773,811
 7,500,000 John Deere Capital Corp., 5.73%, 1/19/96                                         7,479,706
 3,285,000 E.I. dupont de Nemours & Co., 5.68%, 1/19/96                                     3,276,189
 6,500,000 Ford Motor Credit Co., 5.75%, 1/17/96                                            6,484,427
 3,200,000 Gannett Co., 5.77%, 1/12/96                                                      3,194,871
 6,400,000 Golden Peanut Co., 5.60%, 2/12/96                                                6,359,182
 5,000,000 Hewlett Packard Co., 5.60%, 2/15/96                                              4,965,778
 5,600,000 Motorola, Inc., 5.65%, 1/9/96                                                    5,593,848
 7,200,000 National Rural Utilities Corp., 5.66%, 1/12/96                                   7,188,680
 5,000,000 Pepsico, 5.54%, 2/5/96                                                           4,973,839
 4,950,000 Pfizer Inc., 5.52%, 2/5/96                                                       4,924,194
 5,300,000 Prudential Funding Corp., 5.75%, 1/11/96                                         5,292,381
 3,800,000 Republic New York Corp., 5.73%, 1/3/96                                           3,799,395
 6,000,000 Southern California Edison Co., 5.63%, 1/30/96                                   5,973,727
 1,500,000 Southwestern Bell Telephone Co., 5.62%, 2/20/96                                  1,488,526
 3,750,000 Southwestern Bell Telephone Co., 5.65%, 2/13/96                                  3,725,281
 5,200,000 State Street Bank, 5.60%, 1/26/96                                                5,180,587
 6,500,000 Transamerica Finance Corp., 5.70%, 1/16/96                                       6,485,592
 5,800,000 Xerox Corp., 5.68%, 1/19/96                                                      5,784,443
             TOTAL COMMERCIAL PAPER                                                      $143,138,590
             U.S. GOVERNMENT AGENCIES  -- 11.3%
 5,000,000 Federal Farm Credit Bank, 5.32%, 4/1/96                                       $  5,000,000
 5,000,000 Federal Farm Credit Bank, 5.63%, 3/1/96                                          5,000,000
 5,000,000 Federal Farm Credit Bank, 5.65%, 1/2/96                                          5,000,000
 5,000,000 Federal Farm Credit Bank, 5.66%, 2/1/96                                          5,000,000
             TOTAL U.S. GOVERNMENT AGENCIES                                              $ 20,000,000
           BANKER'S ACCEPTANCE -- 3.4%
 6,000,000 Wachovia Bank, 5.74%, 1/4/96                                                  $  5,998,087
           REPURCHASE AGREEMENT -- 4.6%
 8,100,000 Agreement with Chase Manhattan Bank, dated 12/29/95, bearing 5.65%, to
            be repurchased at $8,105,085 on 1/2/96, collateralized by $7,916,000 U.S.
            Treasury Note, bearing 6.125%, due 9/30/00                                   $  8,100,000
             TOTAL INVESTMENT IN SECURITIES(a)                                           $177,236,677
</TABLE>

- --------

(a)  At December 31, 1995,  Pioneer  Cash  Reserves  Fund had a net capital loss
     carryforward  of $276,063,  which will expire  between 2002 and 2003 if not
     utilized.

   The accompanying notes are an integral part of these financial statements.

                                       3

<PAGE>
<TABLE>
<CAPTION>
PIONEER CASH RESERVES FUND
BALANCE SHEET -- DECEMBER 31, 1995
- --------------------------------------------------------------------------------------------------------------------
<S>                                                                                                     <C>
ASSETS:
  Investment in securities, at value based on amortized cost (see Schedule of Investments and Note 1)   $177,236,677
  Cash                                                                                                        70,013
  Receivables -- 
    Trust shares sold                                                                                      2,255,983
    Interest                                                                                                 148,136
  Other                                                                                                       24,411
      Total assets                                                                                      $179,735,220
LIABILITIES:
  Payables -- 
    Investment securities purchased                                                                     $  5,000,000
    Trust shares repurchased                                                                               3,097,071
    Dividends                                                                                                 40,001
  Due to affiliates (Notes 2, 3 and 4)                                                                       170,778
  Accrued expenses                                                                                            32,855
      Total liabilities                                                                                 $  8,340,705 
NET ASSETS:
  Trust shares                                                                                          $171,670,578
  Accumulated net realized loss on investments                                                              (276,063)
      Total net assets                                                                                  $171,394,515
NET ASSET VALUE PER SHARE (OFFERING AND REDEMPTION PRICE):
  Class A -- (based on $163,820,328 / 164,096,391 shares of beneficial interest outstanding -- 
   unlimited number of shares authorized with no par value)                                             $       1.00
  Class B -- (based on $7,574,187 / 7,574,187 shares of beneficial interest outstanding -- 
   unlimited number of shares authorized with no par value)                                             $       1.00
</TABLE>

   The accompanying notes are an integral part of these financial statements.

                                       4

<PAGE>
<TABLE>
<CAPTION>
PIONEER CASH RESERVES FUND
STATEMENT OF OPERATIONS -- FOR THE YEAR ENDED DECEMBER 31, 1995
- --------------------------------------------------------------------------------------------------------------------
<S>                                                                                                     <C>
INVESTMENT INCOME (NOTE 1):
  Interest                                                                                              $10,082,013
EXPENSES:
  Management fees (Note 2)                                                                              $   684,689
  Distribution fees (Note 4)
    Class A                                                                                                 207,029
    Class B                                                                                                  37,445
  Transfer agent fees (Note 3)
    Class A                                                                                                 633,428
    Class B    8,385 
  Registration fees                                                                                         129,500
  Professional fees                                                                                          70,610
  Accounting (Note 2)                                                                                        77,037
  Custodian fees                                                                                             47,689
  Printing                                                                                                   47,812
  Fees and expenses of nonaffiliated trustees                                                                 7,320
  Miscellaneous                                                                                              45,188
    Total expenses                                                                                      $ 1,996,132
  Less fees paid indirectly (Note 5)                                                                        (89,612)
  Less management fees waived by Pioneering Management Corporation (Note 2)                                (463,300)
    Net expenses                                                                                        $ 1,443,220
      Net investment income                                                                             $ 8,638,793
    Net realized loss on investments (Note 1)                                                                  (639)
      Net increase in net assets resulting from operations                                              $ 8,638,154
</TABLE>

   The accompanying notes are an integral part of these financial statements.

                                       5

<PAGE>
<TABLE>
<CAPTION>
PIONEER CASH RESERVES FUND
STATEMENTS OF CHANGES IN NET ASSETS -- 
FOR THE YEARS ENDED DECEMBER 31, 1995 AND 1994
- --------------------------------------------------------------------------------------------------------------------
                                                                                         1995             1994
<S>                                                                                 <C>             <C>            
FROM OPERATIONS:
  Net investment income                                                             $   8,638,793   $   4,449,118  
  Net realized loss on investments                                                           (639)       (275,424)
  Net increase in net assets resulting from operations                              $   8,638,154   $   4,173,694
DISTRIBUTIONS TO SHAREHOLDERS FROM:
  Net investment income:
    Class A ($0.05 and $0.03, respectively)                                         $  (8,479,787)  $  (4,449,118)
    Class B ($0.03 and $0.00, respectively)                                              (159,006)         --
  Decrease in net assets resulting from distributions to shareholders               $  (8,638,793)  $  (4,449,118)
FROM TRUST SHARE TRANSACTIONS (AT $1.00 PER SHARE):
  Net proceeds from sale of shares                                                  $ 571,316,827   $ 510,388,826  
  Net asset value of shares issued to shareholders in reinvestment of dividends         7,861,453       4,140,612
  Cost of shares repurchased                                                         (580,978,330)   (405,899,999)
    Net increase (decrease) in net assets resulting from trust share transactions   $  (1,800,050)  $ 108,629,439
      Net increase (decrease) in net assets                                         $  (1,800,689)  $ 108,354,015
NET ASSETS:
  Beginning of year                                                                   173,195,204      64,841,189
  End of year                                                                       $ 171,394,515   $ 173,195,204
</TABLE>

<TABLE>
<CAPTION>
                                                                                    YEAR ENDED         YEAR ENDED
                                                                                DECEMBER 31, 1995  DECEMBER 31, 1994
                                                                                       AMOUNT           AMOUNT
<S>                                                                                 <C>             <C>
Class A
  Shares sold                                                                       $ 548,292,258   $ 510,388,826
  Shares issued to shareholders in reinvestment of distributions                        7,715,889       4,140,612
  Less shares repurchased                                                            (565,382,384)   (405,899,999)
    Net increase (decrease)                                                         $  (9,374,237)  $ 108,629,439
Class B*
  Shares sold                                                                       $  23,024,569              
  Shares issued to shareholders in reinvestment of distributions                          145,564
  Less shares repurchased                                                             (15,595,946)
    Net increase                                                                    $   7,574,187
</TABLE>

* Class B shares were first publicly offered on March 31, 1995.

   The accompanying notes are an integral part of these financial statements.

                                           6

<PAGE>
PIONEER CASH RESERVES FUND
FINANCIAL HIGHLIGHTS
SELECTED DATA FOR A SHARE OUTSTANDING FOR THE PERIODS PRESENTED
- --------------------------------------------------------------------------------
<TABLE>
                                                                                                                          JUNE 22,
                                                                                                                          1987 TO  
                                                                  FOR THE YEAR ENDED DECEMBER 31,                       DECEMBER 31,
                                        1995       1994       1993      1992      1991      1990       1989      1988       1987
<S>                                     <C>        <C>        <C>       <C>       <C>       <C>        <C>       <C>       <C>    
CLASS A
Net asset value, beginning of period    $   1.00   $   1.00   $  1.00   $  1.00   $  1.00   $   1.00   $  1.00   $  1.00   $  1.00
Income from investment operations:
  Net investment income                 $   0.05   $   0.03   $  0.02   $  0.03   $  0.05   $   0.07   $  0.08   $  0.07   $  0.03
Distributions to shareholders from:
  Net investment income                    (0.05)     (0.03)    (0.02)    (0.03)    (0.05)     (0.07)    (0.08)    (0.07)    (0.03) 
  Net increase in net asset value       $   0.00   $   0.00   $  0.00   $  0.00   $  0.00   $   0.00   $  0.00   $  0.00   $  0.00
  Net asset value, end of period        $   1.00   $   1.00   $  1.00   $  1.00   $  1.00   $   1.00   $  1.00   $  1.00   $  1.00
Total return*                              5.17%      3.57%     2.47%     3.06%     5.29%      7.74%     8.80%     7.05%     3.48%
Ratio of net operating expenses to
 average net assets                        0.88%+     0.50%     0.75%     0.81%     0.88%      0.75%     0.82%     0.78%     0.53%**
Ratio of net investment income to
 average net assets                        5.00%+     2.59%     2.44%     3.03%     5.23%      7.53%     8.43%     6.91%     6.94%**
Net assets end of period (in thousands) $163,820   $173,195   $64,841   $59,097   $73,010   $101,120   $80,121   $59,592   $34,756
Ratios assuming no waiver of manage-
 ment fees or assumption of ex-
 penses by PMC and no reduction for
 fees paid indirectly:
  Net operating expenses                   1.15%      0.65%     1.10%     1.01%     0.88%      0.75%     0.82%     0.91%     1.01%**
  Net investment income                    4.73%      2.44%     2.09%     2.82%     5.23%      7.53%     8.43%     6.77%     6.46%**
Ratios assuming waiver of manage-
 ment fees and assumption of ex-
 penses by PMC and reduction for
 fees paid indirectly:
  Net operating expenses                   0.82%       --         --        --        --         --        --        --        --
  Net investment income                    5.06%       --         --        --        --         --        --        --        --   
</TABLE>  

<TABLE>
<CAPTION>
                                        MARCH 31,
                                         1995 TO
                                       DECEMBER 31,
                                           1995
<S>                                     <C>
CLASS B***
Net asset value, beginning of period    $ 1.00 
Income from investment operations:
  Net investment income                 $ 0.03
Distributions to shareholders from:
  Net investment income                  (0.03)
  Net increase in net asset value       $ 0.00
  Net asset value, end of period        $ 1.00
Total return*                            3.28%
Ratio of net operating expenses to
 average net assets                      1.66%**+
Ratio of net investment income to
 average net assets                      4.20%**+
Net assets end of period (in thousands) $7,574
Ratios assuming no waiver of manage-
 ment fees or assumption of ex-
 penses by PMC and reduction for
 fees paid indirectly:
  Net operating expenses                 1.86%**
  Net investment income                  4.00%**
Ratios assuming waiver of manage-
 ment fees and assumption of ex-
 penses by PMC and reduction for fees
 paid indirectly:
  Net operating expenses                 1.61%**
  Net investment income                  4.25%**
</TABLE>

+    Ratios assuming no reduction for fees paid indirectly.

*    Assumes  initial  investment  at net asset value at the  beginning  of each
     period,  reinvestment of all distributions,  and the complete redemption of
     the investment at the net asset value at the end of each period.

**   Annualized.

***  Class B shares were first publicly offered on March 31, 1995.

   The accompanying notes are an integral part of these financial statements.
                                       7
<PAGE>
<TABLE>
<CAPTION>
SCHEDULE OF INVESTMENTS -- PIONEER U.S. GOVERMENT MONEY FUND -- 
DECEMBER 31, 1995
- -----------------------------------------------------------------------------------------------------
PRINCIPAL
 AMOUNT                        INVESTMENT IN SECURITIES                                      VALUE
- -----------------------------------------------------------------------------------------------------
<S>        <C>                                                                           <C>
           U.S. GOVERNMENT AGENCIES -- 100%
$2,000,000 Federal Farm Credit Bank, 5.32%, 4/1/96                                       $ 2,000,000 
 3,000,000 Federal Farm Credit Bank, 5.58%, 2/2/96                                         2,985,613 
 1,000,000 Federal Farm Credit Bank, 5.61%, 1/8/96                                           999,065
 2,000,000 Federal Farm Credit Bank, 5.63%, 3/1/96                                         2,000,000
   810,000 Federal Farm Credit Bank, 5.64%, 1/4/96                                           809,746
 2,000,000 Federal Farm Credit Bank, 5.65%, 1/2/96                                         2,000,000
 2,000,000 Federal Farm Credit Bank, 5.66%, 2/1/96                                         2,000,000
 2,075,000 Federal Home Loan Bank, 5.43%, 3/20/96                                          2,050,588
 1,110,000 Federal Home Loan Bank, 5.44%, 1/23/96                                          1,106,478
   900,000 Federal Home Loan Bank, 5.52%, 2/27/96                                            892,272
 1,125,000 Federal Home Loan Bank, 5.53%, 2/29/96                                          1,114,977
 1,000,000 Federal Home Loan Bank, 5.54%, 2/2/96                                             995,229
   790,000 Federal Home Loan Bank, 5.54%, 2/16/96                                            784,529
 1,500,000 Federal Home Loan Bank, 5.58%, 1/9/96                                           1,498,373
 1,085,000 Federal Home Loan Bank, 5.60%, 1/16/96                                          1,082,637
   860,000 Federal Home Loan Bank, 5.60%, 1/22/96                                            857,324
 1,000,000 Federal Home Loan Bank, 5.67%, 1/2/96                                           1,000,000
 1,000,000 Tennessee Valley Authority, 5.53%, 2/1/96                                         995,392
 1,000,000 Tennessee Valley Authority, 5.53%, 2/12/96                                        993,702
 1,500,000 Tennessee Valley Authority, 5.59%, 1/19/96                                      1,496,040
 1,800,000 Tennessee Valley Authority, 5.59%, 1/25/96                                      1,793,572
             TOTAL INVESTMENT IN SECURITIES                                              $29,455,537
</TABLE>

   The accompanying notes are an integral part of these financial statements.

                                       8

<PAGE>
<TABLE>
<CAPTION>
PIONEER U.S. GOVERNMENT MONEY FUND
BALANCE SHEET -- DECEMBER 31, 1995
- --------------------------------------------------------------------------------------------------------------------
<S>                                                                                                     <C>
ASSETS:
  Investment in securities, at value based on amortized cost (see Schedule of Investments and Note 1)   $29,455,537
  Receivables -- 
    Trust shares sold                                                                                     2,646,543
    Interest                                                                                                 57,221
  Other                                                                                                       3,648
      Total assets                                                                                      $32,162,949
LIABILITIES:
  Payables -- 
    Investment securities purchased                                                                     $ 2,000,000
    Trust shares repurchased                                                                                563,479
    Dividends                                                                                                 7,425
    Due to bank                                                                                           1,247,056
  Due to affiliates (Notes 2, 3 and 4)                                                                       21,737
  Accrued expenses                                                                                           11,481
      Total liabilities                                                                                 $ 3,851,178

NET ASSETS:
  Trust shares (unlimited number of shares authorized), amount paid in on 28,311,771 shares outstanding $28,311,771
      Total net assets (offering and redemption price of $1.00 per share)                               $28,311,771
</TABLE>

<TABLE>
<CAPTION>
PIONEER U.S. GOVERNMENT MONEY FUND
STATEMENT OF OPERATIONS -- FOR THE YEAR ENDED DECEMBER 31, 1995
- -------------------------------------------------------------------------------------------------------------------
<S>                                                                                                     <C>
INVESTMENT INCOME (NOTE 1):
  Interest                                                                                              $1,746,071
EXPENSES:
  Management fees (Note 2)                                                                              $  119,725
  Distribution fees (Note 4)                                                                                37,232
  Transfer agent fees (Note 3)                                                                              73,080
  Registration fees                                                                                         28,878
  Professional fees                                                                                         52,257
  Accounting (Note 2)                                                                                       53,887
  Custodian fees                                                                                            15,180
  Printing                                                                                                   4,490
  Fees and expenses of nonaffiliated trustees                                                                8,516
  Miscellaneous                                                                                             15,744
    Total expenses                                                                                      $  408,989
  Less fees paid indirectly (Note 5)                                                                       (21,473)
  Less management fees waived and expenses assumed by Pioneering Management
   Corporation (Note 2)                                                                                   (150,483)
    Net expenses                                                                                        $  237,033
      Net increase in net assets resulting from operations                                              $1,509,038
</TABLE>

   The accompanying notes are an integral part of these financial statements.

                                       9
<PAGE>
<TABLE>
<CAPTION>
PIONEER U.S. GOVERNMENT MONEY FUND
STATEMENTS OF CHANGES IN NET ASSETS -- 
FOR THE YEARS ENDED DECEMBER 31, 1995 AND 1994
- --------------------------------------------------------------------------------------------------------------------
                                                                                         1995             1994
<S>                                                                                 <C>             <C>            
FROM OPERATIONS:
  Net increase in net assets resulting from operations                              $   1,509,038   $  1,093,789
DISTRIBUTIONS TO SHAREHOLDERS FROM:
  Net investment income ($0.05 and $0.04, respectively)                             $  (1,509,038)  $ (1,093,789)
FROM TRUST SHARE TRANSACTIONS (AT $1.00 PER SHARE):
  Net proceeds from sale of shares                                                  $ 125,746,780   $ 62,195,011
  Net asset value of shares issued to shareholders in reinvestment of dividends         1,352,576        996,345
  Cost of shares repurchased                                                         (127,888,164)   (57,965,900)
    Increase (decrease) in net assets resulting from trust share transactions       $    (788,808)  $  5,225,456
      Net increase (decrease) in net assets                                         $    (788,808)  $  5,225,456
NET ASSETS:
  Beginning of year                                                                    29,100,579     23,875,123
  End of year                                                                       $  28,311,771   $ 29,100,579
</TABLE>

<TABLE>
<CAPTION>
PIONEER U.S. GOVERNMENT MONEY FUND
FINANCIAL HIGHLIGHTS
SELECTED DATA FOR A SHARE OUTSTANDING FOR THE PERIODS PRESENTED
- ------------------------------------------------------------------------------------------------------------------------------------
                                                                                                              APRIL 11,
                                                                                                               1988 TO  
                                                                   FOR THE YEAR ENDED DECEMBER 31,           DECEMBER 31,
                                         1995       1994       1993      1992      1991      1990       1989    1988
<S>                                      <C>       <C>       <C>       <C>       <C>       <C>       <C>       <C>    
Net asset value, beginning of period     $  1.00   $  1.00   $  1.00   $  1.00   $  1.00   $  1.00   $  1.00   $ 1.00
Income from investment operations:
  Net investment income                  $  0.05   $  0.04   $  0.03   $  0.03   $  0.05   $  0.07   $  0.08   $ 0.05
Distributions to shareholders from:
  Net investment income                    (0.05)    (0.04)    (0.03)    (0.03)    (0.05)    (0.07)    (0.08)   (0.05)
  Net increase in net asset value        $  0.00   $  0.00   $  0.00   $  0.00   $  0.00   $  0.00   $  0.00   $ 0.00
  Net asset value, end of period         $  1.00   $  1.00   $  1.00   $  1.00   $  1.00   $  1.00   $  1.00   $ 1.00

Total return*                              5.16%     3.65%     2.63%     3.19%     5.41%     7.61%     8.80%    5.34%
Ratio of net operating expenses to
 average net assets                        0.86%+    0.63%     0.55%     0.59%     0.60%     0.60%     0.53%    0.50%**
Ratio of net investment income to
 average net assets                        4.96%+    3.64%     2.61%     3.15%     5.29%     7.37%     8.37%    7.52%**
Net assets, end of period (in thousands) $28,312   $29,101   $23,875   $23,619   $28,373   $27,828   $20,508   $9,503
Ratios assuming no waiver of manage-
 ment fees and assumption of ex-
 penses by PMC and no reduction for
 fees paid indirectly:
  Net operating expenses                   1.36%     1.08%     1.37%     1.24%     1.08%     0.80%     1.12%     1.13%**
  Net investment income                    4.46%     3.19%     1.79%     2.50%     4.81%     7.17%     7.77%     6.88%**
Ratio assuming waiver of manage-
 ment fees and assumption of ex-
 penses by PMC and reduction for
 fees paid indirectly:
  Net operating expenes                    0.79%      --        --        --        --        --        --        --
  Net investment income                    5.03%      --        --        --        --        --        --        --
</TABLE>

+    Ratios assuming no reduction for fees paid indirectly.

*    Assumes  initial  investment  at net asset value at the  beginning  of each
     period,  reinvestment of all distributions,  and the complete redemption of
     the investment at the net asset value at the end of each period.

**   Annualized.

   The accompanying notes are an integral part of these financial statements.

                                       10

<PAGE>
<TABLE>
<CAPTION>
SCHEDULE OF INVESTMENTS -- PIONEER TAX-FREE MONEY FUND -- DECEMBER 31, 1995
- -------------------------------------------------------------------------------------------------------------------------
                 RATINGS
PRINCIPAL      (UNAUDITED)
 AMOUNT      MOODY'S  S&P         INVESTMENT IN SECURITIES*                       LOC/GUARANTOR**                VALUE
- -------------------------------------------------------------------------------------------------------------------------
<S>           <C>    <C>    <C>                                                   <C>                          <C>
                            VARIABLE RATE SECURITIES -- 94.4%
                            DAILY RATE SECURITIES -- 38.9%
$100,000      VMIG   A-1+   California Pollution Control Financing Authority, 
                             Pollution Control Revenue, 5.90%, 11/1/00            Shell Oil                    $  100,000
 100,000       Aaa   A-1+   Harris County, Texas Industrial Development 
                             Corporation Pollution Control Revenue, 6.00%,
                             3/1/24                                               Exxon Guarantee                 100,000
 100,000        P1     NR   Jackson County, Mississippi, Pollution Control
                             Revenue, 5.90%, 6/1/23                               Chevron Guarantee               100,000
 100,000        P1   A-1+   Lincoln County, Wyoming, Pollution Control Revenue,
                             Series A, 5.90%, 11/1/14                             Exxon Guarantee                 100,000
 100,000        P1   A-1+   Louisiana Offshore Terminal Authority, Series 1986,
                             5.90%, 9/1/06                                        Union Bank of Switzerland       100,000
 100,000        P1     NR   Perry County, Mississippi, Pollution Control Revenue,
                             5.90%, 3/1/02                                        Credit Suisse                   100,000
 100,000        P1     NR   Uinta County, Wyoming, Pollution Control Revenue, 
                             5.90%, 12/1/22                                       Chevron Corp.                   100,000
                                                                                                               $  700,000
                            WEEKLY RATE SECURITIES -- 44.4%
 100,000    VMIG-1   A-1+   Arkansas Development Finance Authority, 5.00%, 
                             12/1/15                                              Citibank                     $  100,000
 100,000    VMIG-1   A-1+   Colorado Student Obligation Bond Authority, 5.05%, 
                             8/1/00                                               SLMA                            100,000
 100,000    VMIG-1   A-1+   City of Duluth, Minnesota, Tax Increment Revenue for
                             Lake Superior Paper Industries, 5.10%, 9/1/10        National Australia Bank         100,000
 100,000        NR   A-1+   Eddy County, New Mexico, Pollution Control Revenue,
                             5.05%, 2/1/03                                        Harris Trust & Savings Bank     100,000
 100,000        NR   A-1+   Illinois Development Finance Authority for Columbia
                             Graphics Corp., 5.25%, 6/1/04                        Harris Trust & Savings Bank     100,000 
 100,000    VMIG-1    AAA   New Jersey Turnpike Authority Revenue, 3.00%,
                             1/1/00   MBIA                                                                        100,000
 100,000    VMIG-1     NR   North Carolina Education Facilities Authority for
                             Bowman Grey School of Medicine, 5.00%, 9/1/20        Wachovia Bank                   100,000
 100,000       Aa2    AAA   Peninsula Ports Authority of Virginia, Port Facility
                             Revenue, 5.90%, 12/1/05                              Shell Oil                       100,000
                                                                                                               $  800,000
                            MONTHLY RATE SECURITIES -- 11.1%
 100,000       P-1   A-1+   Baltimore, Maryland, Port Series 1981, Oxy Petroleum,
                             4.05%, 10/14/11                                      Morgan Guaranty              $  100,000
 100,000    VMIG-1   A-1+   Cuyahoga County, Ohio, Industrial Development 
                             Revenue, 3.85%, 12/1/09                              Marine Midland Bank             100,000
                                                                                                               $  200,000
                              TOTAL VARIABLE RATE SECURITIES                                                   $1,700,000
                            COMMERCIAL PAPER -- 5.6%
 100,000       P-1   A-1+   Nebraska Public Power District, Series B, 3.60%, 
                             1/18/96                                              Morgan Guaranty              $  100,000
                              TOTAL INVESTMENT IN SECURITIES                                                   $1,800,000
</TABLE>

*    Coupon rates shown reflect rates as of December 31, 1995.

**   Name of the issuer of the Letter of Credit (LOC) or Guarantor  securing the
     investment.

   The accompanying notes are an integral part of these financial statements.

                                       11

<PAGE>
<TABLE>
<CAPTION>
PIONEER TAX-FREE MONEY FUND
BALANCE SHEET -- DECEMBER 31, 1995
- --------------------------------------------------------------------------------------------------------------------
<S>                                                                                                     <C>
ASSETS:
  Investment in securities, at value based on amortized cost (see Schedule of Investments and Note 1)   $ 1,800,000
  Cash                                                                                                      696,528
  Receivables --
    Trust shares sold                                                                                           726
    Interest                                                                                                  9,030  
    Due from Pioneering Management Corporation (Note 2)                                                      34,995
      Total assets                                                                                      $ 2,541,279
LIABILITIES:
  Payables --
    Trust shares repurchased                                                                            $   219,387
    Dividends                                                                                                 2,682
  Due to affiliates (Notes 2, 3 and 4)                                                                        2,967
  Accrued expenses                                                                                           21,545
      Total liabilities                                                                                 $   246,581
NET ASSETS:
  Trust shares (unlimited number of shares authorized), amount paid in on 2,295,823 shares outstanding  $ 2,295,823
  Accumulated net realized loss on investments                                                           (1,125)
      Total net assets (offering and redemption price of $1.00 per share)                               $ 2,294,698
</TABLE>

<TABLE>
<CAPTION>
PIONEER TAX-FREE MONEY FUND
STATEMENT OF OPERATIONS -- FOR THE YEAR ENDED DECEMBER 31, 1995
- --------------------------------------------------------------------------------------------------------------------
<S>                                                                                                <C>
INVESTMENT INCOME (NOTE 1):
  Interest                                                                                         $ 256,904
EXPENSES:
  Management fees (Note 2)                                                                         $  27,588
  Distribution fees (Note 4)                                                                           7,812
  Transfer agent fees (Note 3)                                                                        15,967
  Registration fees                                                                                   18,548
  Professional fees                                                                                   46,659
  Accounting (Note 2)                                                                                 42,329
  Custodian fees                                                                                      10,572
  Printing                                                                                               771
  Fees and expenses of nonaffiliated trustees                                                          4,471
  Regulatory reporting                                                                                 8,907
  Miscellaneous                                                                                        5,851
    Total expenses                                                                                 $ 189,475
  Less fees paid indirectly (Note 5)                                                                  (3,802)
  Less management fees waived and expenses assumed by Pioneering Management Corporation (Note 2)    (138,921)
    Net expenses                                                                                   $  46,752  
      Net investment income                                                                        $ 210,152
  Net realized loss on investments (Note 1)                                                           (1,125)
      Net increase in net assets resulting from operations                                         $ 209,027
</TABLE>

   The accompanying notes are an integral part of these financial statements.

                                       12

<PAGE>
<TABLE>
<CAPTION>
PIONEER TAX-FREE MONEY FUND
STATEMENTS OF CHANGES IN NET ASSETS -- 
FOR THE YEARS ENDED DECEMBER 31, 1995 AND 1994
- --------------------------------------------------------------------------------------------------------------------
                                                                                         1995             1994
<S>                                                                                 <C>             <C>            
FROM OPERATIONS:
  Net investment income                                                               $210,152         $209,639
  Net realized loss on investments                                                      (1,125)             --
  Net increase in net assets resulting from operations                                $209,027         $209,639
DISTRIBUTIONS TO SHAREHOLDERS FROM:
  Net investment income ($0.03 and $0.02 per share, respectively)                   $ (210,152)       $(209,639)
FROM TRUST SHARE TRANSACTIONS (AT $1.00 PER SHARE):
  Net proceeds from sale of shares                                                 $11,315,345       $9,036,859
  Net asset value of shares issued to shareholders in reinvestment of dividends        180,768          197,844
  Cost of shares repurchased                                                       (19,259,298)      (7,289,256)
    Net increase (decrease) in net assets resulting from trust share transactions  $(7,763,185)      $1,945,447
      Net increase (decrease) in net assets                                        $(7,764,310)      $1,945,447
NET ASSETS:
  Beginning of year                                                                 10,059,008        8,113,561
  End of year                                                                       $2,294,698      $10,059,008
</TABLE>

<TABLE>
<CAPTION>
PIONEER TAX-FREE MONEY FUND
FINANCIAL HIGHLIGHTS
SELECTED DATA FOR A SHARE OUTSTANDING FOR THE PERIODS PRESENTED
- --------------------------------------------------------------------------------
                                                                                                           April 11,  
                                                                                                           1988 to   
                                                               For the Year Ended December 31,            December 31,
                                                   1995      1994      1993      1992     1991      1990     1989     1988     
                                       
                                                  
<S>                                             <C>       <C>       <C>       <C>      <C>       <C>      <C>      <C>  
Net asset value, beginning of period              $1.00     $1.00     $1.00     $1.00    $1.00     $1.00    $1.00    $1.00

Income from investment operations:
   Net investment income                          $0.03     $0.02     $0.02     $0.02    $0.04     $0.05    $0.06    $0.04
Distributions to shareholders from:
   Net investment income                          (0.03)    (0.02)    (0.02)    (0.02)   (0.04)    (0.05)   (0.06)   (0.04)
   Net increase in net asset value                $0.00     $0.00     $0.00     $0.00    $0.00     $0.00    $0.00    $0.00
   Net asset value, end of period                 $1.00     $1.00     $1.00     $1.00    $1.00     $1.00    $1.00    $1.00
Total return*                                     3.09%     2.40%     1.92%     2.38%    4.00%     5.48%    6.06%    3.71%
Ratio of net operating expenses to average
 net assets                                      0.73%+     0.50%     0.50%     0.50%    0.50%     0.50%    0.50%    4.98%**
Ratio of net investment income to average
 net assets                                      3.00%+     2.34%     1.92%     2.33%    3.91%     5.37%    5.86%    5.13%**
Net assets end of period (in thousands)          $2,295   $10,059    $8,114    $7,241   $7,539    $6,968   $5,351   $3,272
Ratios assuming no waiver of management
 fees and assumption of expenses by PMC
 and no reduction for fees paid indirectly:
   Net operating expenses                        2.75%     1.87%     1.85%     2.07%    1.08%     1.91%    2.27%    1.50%**
   Net investment income                         0.98%     0.97%     0.57%     0.77%    4.81%     3.96%    4.09%    4.13%**
Ratios assuming waiver of management
 fees and assumption of expenses by PMC
 and reduction for fees paid indirectly:
   Net operating expenses                         0.68%      --        --        --        --       --        --       --
   Net investment income                          3.05%      --        --        --        --       --        --       --
</TABLE>

 + Ratios assuming no reduction for fees paid indirectly.

 * Assumes initial investment at net asset value at the beginning of each 
   period, reinvestment of all distributions, and the complete redemption of the
   investment at the net asset value at the end of each period.
** Annualized.

   The accompanying notes are an integral part of these financial statements.

                                       13

<PAGE>

NOTES TO FINANCIAL STATEMENTS -- DECEMBER 31, 1995
- --------------------------------------------------------------------------------
 
     1. Pioneer Money Market Trust (the Trust) is a Massachusetts business trust
registered under the Investment  Company Act of 1940 as a diversified,  open-end
management  investment  company.  The Trust consists of three  separate  no-load
money market funds (the Funds):  Pioneer Cash  Reserves  Fund (the Cash Reserves
Fund), Pioneer U.S. Government Money Fund (the U.S. Government Fund) and Pioneer
Tax-Free Money Fund (the Tax-Free Money Fund).  The investment  objective of the
Trust is to provide high current  income,  preservation of capital and liquidity
through investments in high quality,  short-term  securities.  Each Fund employs
different investment policies to achieve this investment objective.

     On June 30, 1994, the Cash Reserves Fund acquired the assets of the Pioneer
Money Market Account, Inc. (the Money Market Account) in exchange solely for (i)
the  issuance  of  shares  of  beneficial  interest  of the  Fund  and  (ii) the
assumption by the Fund of the liabilities of the Money Market Account. Following
this tax-free  transfer,  the Money Market  Account was liquidated and dissolved
and the  shares  of the  Cash  Reserves  Fund  were  distributed  to the  former
shareholders of the Money Market Account.

     The Board of Trustees has  authorized  the issuance of two share classes of
the Cash Reserves Fund, designated as Class A and Class B shares. Class B shares
were first  publicly  offered on March 31, 1995.  Shares issued and  outstanding
prior to March 31, 1995 were  designated  as Class A shares.  The shares of each
class represent an interest in the same portfolio of investments of the Fund and
have equal rights to voting, redemptions, dividends and liquidation, except that
each class of shares can bear different transfer agent and distribution fees and
have exclusive  voting rights with respect to the  distribution  plans that have
been adopted by shareholders of Class A and Class B shares, respectively.

     The Trust's  financial  statements  have been prepared in  conformity  with
generally  accepted  accounting  principles  that require the  management of the
Trust to, among other things,  make  estimates and  assumptions  that affect the
reported amounts of assets and liabilities,  the disclosure of contingent assets
and  liabilities  at the  date of the  financial  statements,  and the  reported
amounts of revenues and expenses  during the reporting  periods.  Actual results
could differ from those estimates.

     The following is a summary of significant  accounting policies consistently
followed by the Funds,  which are in conformity with those generally accepted in
the investment company industry:

     A. Security Valuation -- Security  transactions are recorded on trade date.
Securities  are valued at  amortized  cost,  which  approximates  market  value.
Interest  income for securities  purchased at face (par) value is accrued daily.
Investments  purchased  at a discount  or premium are valued by  amortizing  the
difference  between the original  purchase price and maturity value of the issue
over the period to maturity.  All variable rate  securities held by the Tax-Free
Money Fund may be redeemed on seven days' notice.

     B.  Federal  Income  Taxes -- It is the  Trust's  policy to comply with the
requirements  of the Internal  Revenue Code  applicable to regulated  investment
companies and to distribute all of its taxable  income and net realized  capital
gains, if any, to its shareholders.  Therefore,  no federal income tax provision
is required.

     The   characterization  of  distributions  to  shareholders  for  financial
reporting  purposes is determined in accordance  with federal  income tax rules.
Therefore,  the  source  of  the  Funds'  distributions  may  be  shown  in  the
accompanying  financial statements as either from or in excess of net investment
income or net realized gain on investment transactions, or from paid-in capital,
depending on the type of book/tax differences that may exist.

     C. Trust  Shares -- The Funds  record  sales and  repurchases  of its trust
shares on trade date.  Shares are sold and redeemed on a continuous basis at net
asset value per share. The Funds declare as daily dividends substantially all of
their  respective  net  investment  income.  All dividends are paid on a monthly
basis. Short-term capital gains distributions,  if any, may be declared with the
daily dividends.  Dividends paid by the Cash Reserves Fund, if any, with respect
to each class of shares are calculated in the same manner,  at the same time, on
the same day and in the same amount,  except that Class A and Class B shares can
bear different transfer agent and distribution fees.

     D. Class  Allocations  --  Distribution  fees are  calculated  based on the
average daily net asset value  attributable to Class A and Class B shares of the
Cash Reserves Fund.  Shareholders  of Class A and Class B share all expenses and
fees paid to the transfer agent,  Pioneering  Services  Corporation  (PSC),  for
their  services,  which are  allocated  based on the number of  accounts in each
class and the ratable allocation of related  out-of-pocket expense (see Note 3).
Income,  common  expenses  and  realized  and  unrealized  gains and  losses are
calculated at the Fund level and  allocated  daily to each class of shares based
on the respective percentage of adjusted net assets at the beginning of the day.

                                       14
<PAGE>
NOTES TO FINANCIAL STATEMENTS -- DECEMBER 31, 1995 -- CONTINUED
- --------------------------------------------------------------------------------
 
     E. Repurchase Agreements -- The Funds may enter into repurchase agreements.
At the time the  Funds  enter  into a  repurchase  agreement,  the  value of the
underlying security (collateral),  including accrued interest,  will be equal to
or exceed the value of the repurchase  agreement,  and in the case of repurchase
agreements  exceeding one day, the value of the underlying  security,  including
accrued interest, is required during the term of the agreement to be equal to or
exceed the value of the repurchase agreement.  The underlying securities for all
repurchase  agreements are held in safekeeping in the  customer-only  account of
the Funds' custodian, or at the Federal Reserve Bank. If the seller defaults and
the value of the collateral declines, or if bankruptcy proceedings commence with
respect to the seller of the  security,  realization  of the  collateral  by the
Funds may be delayed or limited.

     2. Pioneering Management Corporation (PMC), the Trust's investment adviser,
manages the Trust's  portfolios and is a wholly owned  subsidiary of The Pioneer
Group,  Inc. (PGI).  Management fees are calculated  daily at the annual rate of
0.40% of each Fund's average daily net assets.

     Effective April 1, 1995, PMC has agreed to waive its management fees and to
assume other operating  expenses for the Trust to the extent  necessary to limit
the Trust's expenses according to the following schedule:

                                      EXPENSES LIMITED BY
                                      PMC AS A PERCENTAGE OF
          FUND                       AVERAGE DAILY NET ASSETS
U.S. Government Money Fund                   0.85% 
Tax-Free Money Fund                          0.75% 

     PMC has agreed not to impose a portion of its  management fee and to assume
other  operating  expenses of the Cash Reserves Fund to the extent  necessary to
limit Class A expenses to 0.85% of the average daily net assets  attributable to
Class A shares;  the portion of the Fund-wide  expenses  attributable to Class B
shares  will be reduced  only to the extent that such  expenses  are reduced for
Class A shares. PMC's agreement is voluntary and temporary and may be revised or
terminated at any time.

     Prior to April 1, 1995,  PMC waived its  management  fees and assumed other
operating  expenses of each Fund to the extent  necessary  to limit  expenses of
each Fund according to the following schedule:

                      EXPENSES LIMITED BY
   NET ASSETS        PMC AS A PERCENTAGE OF
    PER FUND        AVERAGE DAILY NET ASSETS
Up to $20 million           0.50% 
Up to $25 million           0.55% 
Up to $30 million           0.60%
Up to $35 million           0.65%
Up to $40 million           0.70%
Over $40 million            0.75%

     In addition,  under the  management  agreement,  certain other services and
costs,  including accounting,  regulatory reporting and insurance premiums,  are
paid by the Funds.  Included in due to affiliates  are management and accounting
fees payable to PMC at December 31, 1995:

                          ACCOUNTING    MANAGEMENT
        FUND                FEES           FEES 
Cash Reserves Fund         $5,586         $51,578
U.S. Government Fund        4,458            --
Tax-Free Money Fund         6,557            --

     3. PSC,  a wholly  owned  subsidiary  of PGI,  provides  substantially  all
transfer  agent  and  shareholder  services  to the Funds at  negotiated  rates.
Included in due to affiliates are transfer agent fees payable to PSC at December
31, 1995:

FUND                   AMOUNT
Cash Reserves Fund    $51,124 
U.S. Government Fund    8,311
Tax-Free Money Fund     1,144

     4. The Trust adopted a Plan of  Distribution  (the Plan) in accordance with
Rule 12b-1 of the Investment  Company Act of 1940. The Plan allows for the Funds
to reimburse Pioneer Funds  Distributor,  Inc. (PFD) for expenditures to finance
any  activities  primarily  intended  to result in the sale of the Funds'  trust
shares.  The Plan provides for  reimbursement of such  expenditures in an amount
not to exceed  0.15% of the U.S.  Government  Money  Fund's  and Tax- Free Money
Fund's respective average daily net assets.

     The Cash  Reserves Fund adopted a Plan of  Distribution  for Class A shares
(Class A Plan) and Class B shares (Class B Plan) in  accordance  with Rule 12b-1
of the Investment  Company Act of 1940. These plans allow for Class A shares and
Class B shares to reimburse  and  compensate,  respectively,  PFD for  providing
varying levels of distribution services and other account maintenance services.

                                       15
<PAGE>

NOTES TO FINANCIAL STATEMENTS -- DECEMBER 31, 1995 -- CONTINUED
- --------------------------------------------------------------------------------
 
     The  Class A Plan  and  Class B Plan  provide  for  reimbursement  of PFD's
distribution services in an amount up to 0.25% and 0.75%,  respectively,  of the
average daily net assets of the respective  classes of shares. The Fund may also
compensate  PFD for  additional  services in an amount up to 0.25% of the Fund's
average  daily net assets  attributable  to Class B shares.  Included  in due to
affiliates are distribution fees payable to PFD at December 31, 1995:

FUND                   AMOUNT
Cash Reserves Fund    $62,490
U.S. Government Fund    8,968 
Tax-Free Money Fund     1,823

     In addition,  Class B shares that are redeemed within six years of purchase
are subject to a  contingent  deferred  sales charge  (CDSC) at declining  rates
beginning  at 4.0%  based on the lower of cost or market  value of shares  being
redeemed.  Proceeds  from the CDSC are paid to PFD. For the year ended  December
31, 1995, CDSC in the amount of $12,858 was paid to PFD.

     5. The Trust has entered into certain expense offset arrangements resulting
in a reduction in each Fund's total  expenses.  For the year ended  December 31,
1995, the Funds' expenses were reduced by the following:

FUND                   AMOUNT
Cash Reserves Fund    $89,612 
U.S. Government Fund   21,473 
Tax-Free Money Fund     3,802

     6. On January 8, 1996, the Tax-Free Money Fund ceased operations  following
the distribution of the Fund's remaining assets to shareholders. The liquidation
of the  Tax-Free  Money  Fund had no effect on any of the other  Pioneer  mutual
funds, including the Cash Reserves Fund and U.S. Government Money Fund.



- --------------------------------------------------------------------------------

REPORT OF INDEPENDENT PUBLIC ACCOUNTANTS
- --------------------------------------------------------------------------------

TO THE SHAREHOLDERS AND TRUSTEES OF PIONEER MONEY MARKET TRUST:

We have audited the  accompanying  balance  sheets of Pioneer Money Market Trust
(comprising  the Pioneer Cash Reserves Fund, the Pioneer U.S.  Government  Money
Fund  and  the  Pioneer  Tax-Free  Money  Fund),   including  the  schedules  of
investments,  as of December 31, 1995, and the related statements of operations,
statements  of changes in net assets and  financial  highlights  for the periods
presented.   These  financial   statements  and  financial  highlights  are  the
responsibility of the Trust'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
December 31, 1995 by correspondence  with the custodian.  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 each
of the respective Funds composing  Pioneer Money Market Trust as of December 31,
1995,  the  results  of their  operations,  the  changes in their net assets and
financial  highlights for the periods  presented,  in conformity  with generally
accepted accounting principles.

                                                             ARTHUR ANDERSEN LLP

Boston, Massachusetts
February 2, 1996

                                       16

<PAGE>

RESULTS OF FEBRUARY 7, 1995 SHAREOWNER MEETING (UNAUDITED)
- --------------------------------------------------------------------------------
 
On  February  7, 1995,  Pioneer  Money  Market  Trust held a special  meeting of
shareowners.  All Proposals  were passed by shareowner  vote.  Following are the
detailed results of the vote for each Proposal presented.

PROPOSAL 1 -- TO ELECT EIGHT TRUSTEES TO SERVE ON THE BOARD OF TRUSTEES

<TABLE>
<CAPTION>
                                    PIONEER CASH RESERVES FUND              PIONEER U.S. GOVERNMENT MONEY FUND 
  
NOMINEE                              AFFIRMATIVE     WITHHELD                   AFFIRMATIVE       WITHHELD
<S>                                <C>             <C>                        <C>              <C>           
John F. Cogan, Jr.                 99,943,956.278  5,657,296.730              20,286,573.963   1,511,235.880 
Richard H. Egdahl, M.D.            99,609,138.848  5,992,114.160              20,209,316.193   1,588,493.650 
Margaret B.W. Graham               99,876,929.778  5,724,323.230              20,222,362.863   1,575,446.980
John W. Kendrick                   99,770,435.148  5,830,817.860              20,299,364.003   1,498,445.840
Marguerite A. Piret                99,888,835.338  5,712,417.670              20,225,835.873   1,571,973.970 
David D. Tripple                   99,965,672.388  5,635,580.620              20,299,364.003   1,498,445.840 
Stephen K. West                    99,830,655.218  5,770,597.790              20,233,197.083   1,564,612.760 
John Winthrop                      99,996,713.788  5,604,539.220              20,299,364.003   1,498,445.840
</TABLE>

<TABLE>
<CAPTION>

                                                       PIONEER TAX-FREE MONEY FUND NOMINEE
                                                          AFFIRMATIVE           WITHHELD 
<S>                                                      <C>                  <C>        
John F. Cogan, Jr.                                       6,222,899.120        233,415.650
Richard H. Egdahl, M.D.                                  6,119,782.660        336,532.110 
Margaret B.W. Graham                                     6,208,695.970        247,618.800
John W. Kendrick                                         6,222,899.120        233,415.650 
Marguerite A. Piret                                      6,222,899.120        233,415.650 
David D. Tripple                                         6,222,899.120        233,415.650 
Stephen K. West                                          6,208,149.110        248,165.660 
John Winthrop                                            6,222,899.120        233,415.650

</TABLE>
PROPOSAL 2 -- TO APPROVE  THE NEW  MANAGEMENT  CONTRACT  BETWEEN  THE TRUST, 
              ON BEHALF  OF  THE  FUND,  AND PIONEERING  MANAGEMENT CORPORATION,
              THE  TRUST'S INVESTMENT ADVISER

<TABLE>
<CAPTION>
                                     PIONEER                PIONEER                PIONEER    
                                  CASH RESERVES         U.S. GOVERNMENT            TAX-FREE   
                                      FUND                 MONEY FUND             MONEY FUND  
                                                
<S>                              <C>                     <C>                    <C>           
Affirmative                      95,759,931.180          19,909,501.363         6,094,905.630 
Against                           2,675,955.720             603,734.420            60,953.600
Abstain                           7,165,366.108           1,284,574.060           300,455.540

</TABLE>
PROPOSAL 3 -- TO APPROVE AN AGREEMENT AND PLAN OF REORGANIZATION PURSUANT TO 
              WHICH THE FUND WILL BE ORGANIZED AS A SERIES OF A DELAWARE 
              BUSINESS TRUST

<TABLE>
<CAPTION>


                                     PIONEER                PIONEER                PIONEER    
                                  CASH RESERVES         U.S. GOVERNMENT            TAX-FREE   
                                      FUND                 MONEY FUND             MONEY FUND  

<S>                               <C>                   <C>                     <C>           
Affirmative                       93,284,577.628        19,221,920.033          5,905,660.110 
Against                            4,098,613.752         1,064,679.240             44,313.550 
Abstain                            8,218,061.628         1,511,210.570            506,341.110
</TABLE>

                                       17

<PAGE>

RESULTS OF FEBRUARY 7, 1995 SHAREOWNER MEETING (UNAUDITED) -- CONTINUED
 
PROPOSAL 4A. -- TO CONSIDER AND ACT ON A PROPOSAL TO AMEND THE FUND'S EXISTING
                FUNDAMENTAL INVESTMENT RESTRICTION NUMBER 2

<TABLE>
<CAPTION>

                                     PIONEER                PIONEER                PIONEER    
                                  CASH RESERVES         U.S. GOVERNMENT            TAX-FREE   
                                      FUND                 MONEY FUND             MONEY FUND  

<S>                              <C>                    <C>                     <C>           
Affirmative                      90,923,707.230         18,715,132.803          6,024,318.732 
Against                           4,223,344.250          1,161,329.810             99,500.720
Abstain                           8,218,061.628          1,654,680.230            332,495.318 
Not Voting                           13,881.000            266,667.000 
</TABLE>

PROPOSAL 4B. -- TO CONSIDER AND ACT ON A PROPOSAL TO AMEND THE FUND'S EXISTING
                FUNDAMENTAL INVESTMENT RESTRICTION NUMBER 12

<TABLE>
<CAPTION>

                                     PIONEER                PIONEER                PIONEER    
                                  CASH RESERVES         U.S. GOVERNMENT            TAX-FREE   
                                      FUND                 MONEY FUND             MONEY FUND  

<S>                              <C>                    <C>                     <C>          
Affirmative                      90,278,684.050         18,652,818.273          6,003,918.732
Against                           5,080,604.720          1,151,529.810            119,900.720 
Abstain                          10,228,083.238          1,726,794.760            332,495.318 
Not Voting                           13,881.000            266,667.000      

</TABLE>
PROPOSAL 4C. -- TO CONSIDER AND ACT ON A PROPOSAL TO AMEND THE FUND'S EXISTING
                FUNDAMENTAL INVESTMENT RESTRICTION NUMBER 7

<TABLE>
<CAPTION>

                                     PIONEER                PIONEER                PIONEER    
                                  CASH RESERVES         U.S. GOVERNMENT            TAX-FREE   
                                      FUND                 MONEY FUND             MONEY FUND  

<S>                              <C>                     <C>                    <C>          
Affirmative                      89,854,968.039          18,542,831.373         5,804,107.842
Against                           5,624,469.291           1,331,373.110           319,711.610
Abstain                          10,107,934.678           1,656,938.360           332,495.318 
Not Voting                           13,881.000             266,667.000 

</TABLE>
PROPOSAL 4D. -- TO CONSIDER AND ACT ON A PROPOSAL TO REDESIGNATE THE FUND'S 
                EXISTING FUNDAMENTAL INVESTMENT RESTRICTION NUMBER 9 AS
                NON-FUNDAMENTAL

<TABLE>
<CAPTION>

                                     PIONEER                PIONEER                PIONEER    
                                  CASH RESERVES         U.S. GOVERNMENT            TAX-FREE   
                                      FUND                 MONEY FUND             MONEY FUND  

<S>                              <C>                     <C>                    <C>           
Affirmative                      89,959,184.240          18,585,151.603         5,881,704.842 
Against                           5,545,313.750             960,800.520           242,114.610 
Abstain                          10,082,874.018           1,985,190.720           332,495.318 
Not Voting                           13,881.000             266,667.000 

</TABLE>
     
PROPOSAL 5 -- TO RATIFY THE SELECTION OF ARTHUR ANDERSEN LLP AS THE TRUST'S 
              INDEPENDENT PUBLIC ACCOUNTANTS FOR THE FISCAL YEAR ENDING DECEMBER
              31, 1995

<TABLE>
<CAPTION>
                                     PIONEER                PIONEER                PIONEER    
                                  CASH RESERVES         U.S. GOVERNMENT            TAX-FREE   
                                      FUND                 MONEY FUND             MONEY FUND  

<S>                              <C>                     <C>                    <C>           
Affirmative                      95,900,131.408          19,656,823.453         6,147,954.810 
Against                           2,244,776.520             493,731.670             1,546.950 
Abstain                           7,456,345.080           1,701,254.720           306,813.010
</TABLE>

                                       18
<PAGE>

                         TAX TREATMENT OF DISTRIBUTIONS
                  MADE DURING THE YEAR ENDED DECEMBER 31, 1995
- --------------------------------------------------------------------------------
 
During the year ended December 31, 1995, the Funds paid the following
distributions: 
<TABLE>
<CAPTION>

                                                 DISTRIBUTIONS PER SHARE FROM NET INVESTMENT INCOME
     
                                         PIONEER            PIONEER        
                                      CASH RESERVES      CASH RESERVES         PIONEER           PIONEER   
                                          FUND               FUND           U.S. GOVERNMENT      TAX-FREE  
                                         CLASS A            CLASS B           MONEY FUND        MONEY FUND 
                                                                                                
PAYMENT DATE 
<S>                                     <C>                 <C>               <C>                <C>     
January 31, 1995                        $ 0.004             $ --              $ 0.004            $ 0.002 
February 28, 1995                         0.004               --                0.004              0.003 
March 31, 1995                            0.005               --                0.005              0.003 
April 30, 1995                            0.004              0.003              0.004              0.003 
May 31, 1995                              0.005              0.004              0.004              0.003 
June 30, 1995                             0.004              0.004              0.005              0.003 
July 31, 1995                             0.004              0.004              0.004              0.002 
August 31, 1995                           0.004              0.004              0.004              0.003
September 30, 1995                        0.004              0.003              0.004              0.002 
October 31, 1995                          0.004              0.003              0.004              0.003 
November 30, 1995                         0.004              0.003              0.004              0.002 
December 31, 1995                         0.004              0.004              0.004              0.002  
                                        $ 0.050            $ 0.032            $ 0.050            $ 0.031 

</TABLE>
None of the Funds had any long or short-term gains in the periods presented. 

For the purposes of the 70% dividends received deduction allowed by Corporate
Shareholders, none of the total distributions presented above represent 
qualifying dividends. 

Of the $0.03 per share distributed by Pioneer Tax-Free Money Fund during 1995,
100% is tax-exempt and should be reported on Form 1040, line 8B, U.S. Individual
Tax Return. 


                   TRUSTEES' FEES, PRINCIPAL SHAREHOLDERS AND
              SHARE OWNERSHIP OF TRUSTEES AND OFFICERS (UNAUDITED)
- --------------------------------------------------------------------------------

The aggregate direct  remuneration  paid by the Funds to nonaffiliated  trustees
and officers during the year ended December 31, 1995, plus expenses  incurred by
the trustees in attending  Fund meetings are described  below.  Fees of trustees
who are  affiliated  with or  ``interested  persons'' of  Pioneering  Management
Corporation,  investment  adviser of the Funds,  are  reimbursed to the Funds by
Pioneering  Management  Corporation in accordance  with the management  contract
with the Funds and are described  below.  At December 31, 1995, the trustees and
officers of the Funds owned  beneficially  shares in the Funds as listed  below,
together with the  corresponding  percentages to shares  outstanding at December
31, 1995. The Pioneer Group,  Inc., the parent company of Pioneering  Management
Corporation and Pioneer Funds Distributor,  Inc., is a publicly held corporation
of which Mr. Cogan, Chairman and President of the Trust, owned approximately 15%
of the outstanding shares of capital stock at December 31, 1995.
<TABLE>
<CAPTION>
                                  
                                                                  PIONEER             PIONEER         PIONEER  
                                                               CASH RESERVES      U.S. GOVERNMENT     TAX-FREE 
                                                                   FUND              MONEY FUND      MONEY FUND

<S>                                                              <C>                  <C>             <C>    
Direct remuneration paid to trustees and officers                 $7,000               $6,800          $6,700 
Expenses incurred in attending trustees meetings                  $2,700               $2,700          $2,700 
Trustee fees of ``interested persons'' reimbursed by
 Pioneering Management Corporation                                $  333               $  333          $  333 
Shares beneficially owned by trustees and officers at
 December 31, 1995                                               767,610               16,504             --
Percentage of shares outstanding at December 31, 1995               0.47%                0.06%            --%

</TABLE>

                                       19
<PAGE>
[LOGO]

PIONEER CASH
RESERVES FUND

PIONEER U.S.
GOVERNMENT
MONEY FUND

PIONEER TAX-FREE
MONEY FUND


Annual Report
December 31, 1995


PIONEER CASH
RESERVES FUND

PIONEER U.S.
GOVERNMENT
MONEY FUND

PIONEER TAX-FREE
MONEY FUND

60 State Street
Boston, Massachusetts 02109

OFFICERS

JOHN F. COGAN, JR., Chairman and President
DAVID D. TRIPPLE, Executive Vice President
SHERMAN B. RUSS, Vice President
WILLIAM H. KEOUGH, Treasurer
JOSEPH P. BARRI, Secretary

TRUSTEES

JOHN F. COGAN, JR.                  MARGUERITE A. PIRET
RICHARD H. EGDAHL, M.D.             DAVID D. TRIPPLE   
MARGARET B.W. GRAHAM                STEPHEN K. WEST    
JOHN W. KENDRICK                    JOHN WINTHROP      
                                                       

INDEPENDENT PUBLIC ACCOUNTANTS
ARTHUR ANDERSEN LLP

INVESTMENT ADVISER
PIONEERING MANAGEMENT CORPORATION

PRINCIPAL UNDERWRITER
PIONEER FUNDS DISTRIBUTOR, INC.

CUSTODIAN
BROWN BROTHERS HARRIMAN & CO.

LEGAL COUNSEL
HALE AND DORR

SHAREHOLDER SERVICES AND TRANSFER AGENT
PIONEERING SERVICES CORPORATION
60 State Street
Boston, Massachusetts 02109

 
Please call Pioneer for information on:
Existing accounts, new accounts,
prospectuses, applications and
services forms............................... 1-800-225-6292
Fund yields and prices....................... 1-800-225-4321
Toll-free fax................................ 1-800-225-4240
Retirement plans............................. 1-800-622-0176
Telecommunications Device for the
Deaf (TDD)................................... 1-800-225-1997

When distributed to persons who are not shareowners of
the Funds, this report must be accompanied by an official 
prospectus, which discusses the objectives, policies and
other information concerning the Funds.

0296-2995
(C)Pioneer Funds Distributor, Inc.



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