UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

FORM N-CSRS

CERTIFIED SHAREHOLDER REPORT OF REGISTERED
MANAGEMENT INVESTMENT COMPANIES

Investment Company Act file number: 811-03159

Active Assets Money Trust
(Exact name of registrant as specified in charter)

1221 Avenue of the Americas, New York, New York 10020
(Address of principal executive offices) (Zip code)

Ronald E. Robison
1221 Avenue of the Americas, New York, New York 10020
(Name and address of agent for service)

Registrant's telephone number, including area code: 212-762-4000

Date of fiscal year end: June 30, 2005

Date of reporting period: December 31, 2004

Item 1 - Report to Shareholders

Welcome, Shareholder:

In this report, you'll learn about how your investment in Active Assets Money
Trust performed during the semiannual period. We will provide an overview of the
market conditions, and discuss some of the factors that affected performance
during the reporting period. In addition, this report includes the Fund's
financial statements and a list of Fund investments.

This material must be preceded or accompanied by a prospectus for the fund being
offered. Market forecasts provided in this report may not necessarily come to
pass. There is no assurance that the Fund will achieve its investment objective.
The Fund is subject to market risk, which is the possibility that market values
of securities owned by the Fund will decline and, therefore, the value of the
Fund's shares may be less than what you paid for them. Accordingly, you can lose
money investing in this Fund.

FUND REPORT

For the six-month period ended December 31, 2004

MARKET CONDITIONS

The Federal Open Market Committee ("the Fed") increased its target rate for
federal funds to 1.25 percent on June 30, 2004, its first increase in four
years. The Fed then took four more steps of the same size during the next six
months. As a result, the Fed bumped its target upward "in measured steps" at all
five scheduled meetings from June 30 through December 14, 2004, to the current
level of 2.25 percent, which is a three-year high.

PERFORMANCE ANALYSIS

As of December 31, 2004, Active Assets Money Trust had net assets of more than
$21.5 billion and an average portfolio maturity of 42 days. For the six-month
period ended December 31, 2004, the Fund returned 0.65 percent. For the
seven-day period ended December 31, 2004, the Fund provided an effective
annualized yield of 1.82 percent and a current yield of 1.80 percent, while its
30-day average yield for December was 1.75 percent. PAST PERFORMANCE IS NO
GUARANTEE OF FUTURE RESULTS.

Our strategy in managing the Fund remained consistent with the Fund's long-term
focus on maintaining preservation of capital and liquidity. By shortening the
maturities of the portfolio's investments slightly, the Fund was able to
reinvest in higher yielding money market securities as rates climbed. We adhered
to a conservative approach in managing the Fund that emphasized purchasing
high-quality money market obligations and avoided the use of derivatives or
structured notes that might fluctuate excessively with changing interest rates.

<Table>
<Caption>
PORTFOLIO COMPOSITION

Commercial Paper 67.7%
US Government & Agency Obligations 16.0
Certificates of Deposit 11.4
Short-Term Bank Notes 4.9
</Table>

<Table>
<Caption>
MATURITY SCHEDULE

1 - 30 Days 40.0%
31 - 60 Days 42.0
61 - 90 Days 9.5
91 - 120 Days 5.4
121+ Days 3.1
</Table>

Data as of December 31, 2004. Subject to change daily. All percentages for
portfolio composition and maturity schedule are as a percentage of total
investments. Provided for informational purposes only and should not be deemed a
recommendation to buy or sell the securities mentioned. Morgan Stanley is a
full-service securities firm engaged in securities trading and brokerage
activities, investment banking, research and analysis, financing and financial
advisory services.

INVESTMENT STRATEGY

THE FUND INVESTS IN HIGH QUALITY, SHORT-TERM DEBT OBLIGATIONS. IN SELECTING
INVESTMENTS, THE "INVESTMENT MANAGER," MORGAN STANLEY INVESTMENT ADVISORS INC.,
SEEKS TO MAINTAIN THE FUND'S SHARE PRICE AT $1.00. THE SHARE PRICE REMAINING
STABLE AT $1.00 MEANS THAT THE FUND WOULD PRESERVE THE PRINCIPAL VALUE OF YOUR
INVESTMENT.

AN INVESTMENT IN THE FUND IS NOT INSURED OR GUARANTEED BY THE FEDERAL DEPOSIT
INSURANCE CORPORATION OR ANY OTHER GOVERNMENT AGENCY. ALTHOUGH THE FUND SEEKS TO
PRESERVE THE VALUE OF YOUR INVESTMENT AT $1.00 PER SHARE, IT IS POSSIBLE TO LOSE
MONEY BY INVESTING IN THE FUND.

FOR MORE INFORMATION ABOUT PORTFOLIO HOLDINGS

EACH MORGAN STANLEY FUND PROVIDES A COMPLETE SCHEDULE OF PORTFOLIO HOLDINGS IN
ITS SEMIANNUAL AND ANNUAL REPORTS WITHIN 60 DAYS OF THE END OF THE FUND'S SECOND
AND FOURTH FISCAL QUARTERS BY FILING THE SCHEDULE ELECTRONICALLY WITH THE
SECURITIES AND EXCHANGE COMMISSION (SEC). THE SEMIANNUAL REPORTS ARE FILED ON
FORM N-CSRS AND THE ANNUAL REPORTS ARE FILED ON FORM N-CSR. MORGAN STANLEY ALSO
DELIVERS THE SEMIANNUAL AND ANNUAL REPORTS TO FUND SHAREHOLDERS AND MAKES THESE
REPORTS AVAILABLE ON ITS PUBLIC WEB SITE, WWW.MORGANSTANLEY.COM. EACH MORGAN
STANLEY FUND ALSO FILES A COMPLETE SCHEDULE OF PORTFOLIO HOLDINGS WITH THE SEC
FOR THE FUND'S FIRST AND THIRD FISCAL QUARTERS ON FORM N-Q. MORGAN STANLEY DOES
NOT DELIVER THE REPORTS FOR THE FIRST AND THIRD FISCAL QUARTERS TO SHAREHOLDERS,
NOR ARE THE REPORTS POSTED TO THE MORGAN STANLEY PUBLIC WEB SITE. YOU MAY,
HOWEVER, OBTAIN THE FORM N-Q FILINGS (AS WELL AS THE FORM N-CSR AND N-CSRS
FILINGS) BY ACCESSING THE SEC'S WEB SITE, HTTP://WWW.SEC.GOV. YOU MAY ALSO
REVIEW AND COPY THEM AT THE SEC'S PUBLIC REFERENCE ROOM IN WASHINGTON, DC.
INFORMATION ON THE OPERATION OF THE SEC'S PUBLIC REFERENCE ROOM MAY BE OBTAINED
BY CALLING THE SEC AT (800) SEC-0330. YOU CAN ALSO REQUEST COPIES OF THESE
MATERIALS, UPON PAYMENT OF A DUPLICATING FEE, BY ELECTRONIC REQUEST AT THE SEC'S
E-MAIL ADDRESS (PUBLICINFO@SEC.GOV) OR BY WRITING THE PUBLIC REFERENCE SECTION
OF THE SEC, WASHINGTON, DC 20549-0102. YOU MAY OBTAIN COPIES OF A FUND'S FISCAL
QUARTER FILINGS BY CONTACTING MORGAN STANLEY CLIENT RELATIONS AT (800) 869-NEWS.

HOUSEHOLDING NOTICE

TO REDUCE PRINTING AND MAILING COSTS, THE FUND ATTEMPTS TO ELIMINATE DUPLICATE
MAILINGS TO THE SAME ADDRESS. THE FUND DELIVERS A SINGLE COPY OF CERTAIN
SHAREHOLDER DOCUMENTS, INCLUDING SHAREHOLDER REPORTS, PROSPECTUSES AND PROXY
MATERIALS, TO INVESTORS WITH THE SAME LAST NAME WHO RESIDE AT THE SAME ADDRESS.
YOUR PARTICIPATION IN THIS PROGRAM WILL CONTINUE FOR AN UNLIMITED PERIOD OF TIME
UNLESS YOU INSTRUCT US OTHERWISE. YOU CAN REQUEST MULTIPLE COPIES OF THESE
DOCUMENTS BY CALLING (800) 350-6414, 8:00 A.M. TO 8:00 P.M., ET. ONCE OUR
CUSTOMER SERVICE CENTER HAS RECEIVED YOUR INSTRUCTIONS, WE WILL BEGIN SENDING
INDIVIDUAL COPIES FOR EACH ACCOUNT WITHIN 30 DAYS.

EXPENSE EXAMPLE

As a shareholder of the Fund, you incur ongoing costs, including management
fees; distribution and service (12b-1) fees; and other Fund expenses. This
example is intended to help you understand your ongoing costs (in dollars) of
investing in the Fund and to compare these costs with the ongoing costs of
investing in other mutual funds.

The example is based on an investment of $1,000 invested at the beginning of the
period and held for the entire period 07/01/04 - 12/31/04.

ACTUAL EXPENSES

The first line of the table below provides information about actual account
values and actual expenses. You may use the information in this line, together
with the amount you invested, to estimate the expenses that you paid over the
period. Simply divide your account value by $1,000 (for example, an $8,600
account value divided by $1,000 = 8.6), then multiply the result by the number
in the first line under the heading entitled "Expenses Paid During Period" to
estimate the expenses you paid on your account during this period.

HYPOTHETICAL EXAMPLE FOR COMPARISON PURPOSES

The second line of the table below provides information about hypothetical
expenses based on the Fund's actual expense ratio and an assumed rate of return
of 5% per year before expenses, which is not the Fund's actual return. The
hypothetical account values and expenses may not be used to estimate the actual
ending account balance or expenses you paid for the period. You may use this
information to compare the ongoing cost of investing in the Fund and other
funds. To do so, compare this 5% hypothetical example with the 5% hypothetical
examples that appear in the shareholder reports of the other funds.

Please note that the expenses shown in the table are meant to highlight your
ongoing costs only. Therefore, the second line of the table is useful in
comparing ongoing costs, and will not help you determine the relative total cost
of owning different funds that have transactional costs, such as sales charges
(loads), and redemption fees, or exchange fees.

<Table>
<Caption>
BEGINNING ENDING EXPENSES PAID
ACCOUNT VALUE ACCOUNT VALUE DURING PERIOD *
------------- ------------- ---------------
07/01/04 -
07/01/04 12/31/04 12/31/04
------------- ------------- ---------------

Actual (0.65% return)....................................... $1,000.00 $1,006.50 $2.12
Hypothetical (5% annual return before expenses)............. $1,000.00 $1,023.03 $2.14
</Table>

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

* Expenses are equal to the Fund's annualized expense ratio of 0.42%
multiplied by the average account value over the period, multiplied by
184/365 (to reflect the one-half year period).

Active Assets Money Trust
PORTFOLIO OF INVESTMENTS - DECEMBER 31, 2004 (UNAUDITED)

<Table>
<Caption>
ANNUALIZED
PRINCIPAL YIELD
AMOUNT IN ON DATE OF MATURITY
THOUSANDS DESCRIPTION PURCHASE DATE VALUE
- ----------------------------------------------------------------------------------------------------------

Commercial Paper (67.7%)
Asset-Backed - Auto (8.0%)
$ 132,916 DaimlerChrysler Revolving Auto Conduit
LLC..................................... 2.18-2.28% 01/11/05-01/12/05 $ 132,834,019
645,000 FCAR Owner Trust.......................... 2.01-2.39 01/05/05-02/17/05 643,495,611
350,000 New Center Asset Trust.................... 2.22-2.38 01/27/05-02/10/05 349,196,792
600,000 New Center Asset Trust Series A1.......... 2.08-2.39 01/03/05-01/27/05 599,664,542
---------------
1,725,190,964
---------------
Asset-Backed - Corporate (0.2%)
50,000 CIESCO, LLC............................... 2.42 03/03/05 49,795,819
---------------
Asset-Backed - Mortgage (0.2%)
50,000 Mortgage Interest Networking Trust
Series A1+ P1........................... 2.19 01/21/05 49,939,444
---------------
Finance - Automotive (0.5%)
100,000 Toyota Motor Credit Corp. ................ 2.27 02/03/05 99,792,833
---------------
Finance - Consumer (1.5%)
49,075 American Express Credit Corp. ............ 2.26 01/05/05 49,062,677
200,000 Household Finance Corp. .................. 2.24-2.26 01/11/05-01/25/05 199,788,833
71,575 HSBC Finance Corp. ....................... 2.35 01/26/05 71,458,691
---------------
320,310,201
---------------
Financial Conglomerates (4.8%)
1,030,975 General Electric Capital Corp. ........... 1.94-2.26 01/10/05-06/30/05 1,028,103,979
---------------
International Banks (47.4%)
250,000 ABN AMRO N.A. Finance, Inc. .............. 2.31 01/13/05 249,807,500
140,500 ANZ (DE) Inc. ............................ 2.27-2.47 02/01/05-04/07/05 140,040,789
458,375 BNP Paribas Finance, Inc. ................ 2.19-2.36 01/24/05-02/16/05 457,342,113
850,000 Barclays U.S. Funding Corp. .............. 2.25-2.29 01/27/05-02/22/05 848,160,687
415,425 CBA (Delaware) Finance Inc. .............. 1.99-2.60 01/07/05-05/17/05 414,245,738
850,000 Calyon North America, Inc................. 2.28-2.38 02/17/05-02/23/05 847,283,236
100,000 Canadian Imperial Holdings Inc. .......... 2.39 02/25/05 99,636,389
50,000 Danske Corp. ............................. 2.27 02/01/05 49,902,694
251,550 Deutsche Bank Financial LLC............... 2.33 01/20/05-01/25/05 251,177,547
478,675 Dexia Delaware LLC........................ 2.37-2.43 02/14/05-03/14/05 477,002,769
1,055,100 HBOS Treasury Services plc................ 2.24-2.43 01/18/05-03/14/05 1,053,000,968
50,000 ING (U.S.) Funding LLC.................... 2.29 01/11/05 49,968,194
250,000 Natexis Banques Populaires U.S.
Finance Co. LLC......................... 2.33 01/21/05 249,677,778
144,175 Nordea North America Inc. ................ 2.00-2.33 01/12/05-02/23/05 143,897,547
1,000,000 Rabobank USA Financial Corp. ............. 1.93-2.37 01/27/05-02/28/05 997,840,278
695,000 Royal Bank of Canada...................... 1.97-2.28 01/14/05-02/04/05 693,961,639
</Table>

See Notes to Financial Statements
5

Active Assets Money Trust
PORTFOLIO OF INVESTMENTS - DECEMBER 31, 2004 (UNAUDITED) continued

$ 851,275 Royal Bank of Scotland plc................ 2.26-2.39% 01/26/05-03/04/05 $ 849,345,024
400,000 Societe Generale N.A., Inc. .............. 2.34-2.38 02/10/05-03/04/05 398,591,250
525,000 Swedbank.................................. 2.07-2.34 01/04/05-02/24/05 524,128,958
613,500 UBS Finance (Delaware) LLC................ 2.22-2.39 01/05/05-02/28/05 612,320,132
796,950 Westpac Capital Corp. .................... 2.11-2.48 02/14/05-04/11/05 793,564,591
---------------
10,200,895,821
---------------
Investment Banks/Brokers (3.3%)
650,000 Citigroup Global Markets Holdings Inc. ... 2.23-2.29 01/26/05-02/07/05 648,739,222
72,825 Goldman Sachs Group, Inc. (The)........... 2.33 01/12/05 72,773,153
---------------
721,512,375
---------------
Major Banks (1.8%)
46,100 Bank of America Corp. .................... 2.23 02/07/05 45,994,815
333,450 Citicorp.................................. 2.15-2.26 01/05/05-02/02/05 332,994,332
---------------
378,989,147
---------------
Total Commercial Paper (Cost $14,574,530,583).............................. 14,574,530,583
---------------
U.S. Government & Agency Obligations (15.9%)
658,550 Federal Home Loan Banks................... 1.95-2.57 03/11/05-06/03/05 654,684,834
386,550 Federal National Mortgage Assoc........... 1.72-2.04 01/05/05-05/16/05 385,378,686
2,008,807 Freddie Mac............................... 1.41-2.69 01/04/05-07/26/05 1,999,186,795
400,000 U.S. Treasury Bills....................... 1.97-2.00 04/07/05-04/14/05 397,825,306
---------------
Total U.S. Government & Agency Obligations (Cost $3,437,075,621)........... 3,437,075,621
---------------
Certificates of Deposit (11.4%)
500,000 Branch Banking & Trust Co., N.C. ......... 2.17-2.34 01/10/05-01/24/05 500,000,000
100,000 Chase Manhattan Bank (USA), N.A. ......... 2.33 01/25/05 100,000,000
1,050,000 First Tennessee Bank, N.A. ............... 2.23-2.37 01/31/05-02/18/05 1,050,000,000
450,000 Washington Mutual Bank, FA................ 2.34-2.35 01/19/05-01/31/05 450,000,000
350,000 Wells Fargo Bank, N.A. ................... 2.35-2.42 01/07/05-01/26/05 350,000,000
---------------
Total Certificates of Deposit (Cost $2,450,000,000)........................ 2,450,000,000
---------------
</Table>

See Notes to Financial Statements
6

Active Assets Money Trust
PORTFOLIO OF INVESTMENTS - DECEMBER 31, 2004 (UNAUDITED) continued

Short-Term Bank Notes (4.9%)
$ 900,000 Bank of America, N.A. .................... 1.92-2.29% 01/18/05-02/10/05 $ 900,000,000
150,000 Standard Federal Bank, N.A. .............. 2.36 02/08/05 150,000,000
---------------
Total Short-Term Bank Notes (Cost $1,050,000,000).......................... 1,050,000,000
---------------
</Table>

<Table>

Total Investments (Cost $21,511,606,204) (a).................... 99.9% 21,511,606,204

Other Assets in Excess of Liabilities........................... 0.1 12,581,717
----- ---------------
Net Assets...................................................... 100.0% $21,524,187,921
===== ===============
</Table>

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

<Table>

(a) Cost is the same for federal income tax purposes.
</Table>

7
See Notes to Financial Statements

Active Assets Money Trust
FINANCIAL STATEMENTS

Statement of Assets and Liabilities
December 31, 2004 (unaudited)

<Table>

Assets:
Investments in securities, at value
(cost $21,511,606,204).................................... $21,511,606,204
Cash........................................................ 15,477
Receivable for:
Shares of beneficial interest sold...................... 12,896,278
Interest................................................ 6,998,528
Prepaid expenses and other assets........................... 274,499
---------------
Total Assets............................................ 21,531,790,986
---------------
Liabilities:
Payable for:
Investment advisory fee................................. 4,076,439
Distribution fee........................................ 1,918,863
Administration fee...................................... 959,432
Accrued expenses and other payables......................... 648,331
---------------
Total Liabilities....................................... 7,603,065
---------------
Net Assets.............................................. $21,524,187,921
===============
Composition of Net Assets:
Paid-in-capital............................................. $21,524,122,004
Accumulated undistributed net investment income............. 65,917
---------------
Net Assets.............................................. $21,524,187,921
===============
Net Asset Value Per Share,
21,524,163,803 shares outstanding (unlimited shares
authorized of $.01 par value)............................... $1.00
===============
</Table>

See Notes to Financial Statements
8

Active Assets Money Trust
FINANCIAL STATEMENTS continued

Statement of Operations
For the six months ended December 31, 2004 (unaudited)

<Table>

Net Investment Income:
Interest Income............................................. $189,475,972
------------
Expenses
Investment advisory fee..................................... 27,666,255
Distribution fee............................................ 11,207,274
Transfer agent fees and expenses............................ 4,301,931
Administration fee.......................................... 1,877,752
Insurance expenses.......................................... 595,886
Custodian fees.............................................. 430,414
Trustees' fees and expenses................................. 146,441
Shareholder reports and notices............................. 127,433
Registration fees........................................... 122,300
Professional fees........................................... 42,075
Other....................................................... 41,594
------------
Total Expenses.......................................... 46,559,355
------------
Net Investment Income....................................... $142,916,617
============
</Table>

See Notes to Financial Statements
9

Active Assets Money Trust
FINANCIAL STATEMENTS continued

Statement of Changes in Net Assets

<Table>
<Caption>
FOR THE SIX FOR THE YEAR
MONTHS ENDED ENDED
DECEMBER 31, 2004 JUNE 30, 2004
----------------- ---------------
(unaudited)

Increase (Decrease) in Net Assets:
Operations:
Net investment income....................................... $ 142,916,617 $ 152,178,285
Net realized gain........................................... -- 41,056
--------------- ---------------
Net Increase............................................ 142,916,617 152,219,341
--------------- ---------------
Dividends and Distributions to Shareholders from:
Net investment income....................................... (142,914,706) (152,179,374)
Net realized gain........................................... -- (41,056)
--------------- ---------------
Total Dividends and Distributions....................... (142,914,706) (152,220,430)
--------------- ---------------

Net decrease from transactions in shares of beneficial
interest.................................................. (130,600,160) (1,622,872,506)
--------------- ---------------
Net Decrease............................................ (130,598,249) (1,622,873,595)
Net Assets:
Beginning of period......................................... 21,654,786,170 23,277,659,765
--------------- ---------------
End of Period
(Including accumulated undistributed net investment income
of $65,917 and $64,006, respectively)....................... $21,524,187,921 $21,654,786,170
=============== ===============
</Table>

See Notes to Financial Statements
10

Active Assets Money Trust
NOTES TO FINANCIAL STATEMENTS - DECEMBER 31, 2004 (UNAUDITED)

1. Organization and Accounting Policies

Active Assets Money Trust (the "Fund") is registered under the Investment
Company Act of 1940, as amended (the "Act"), as a diversified, open-end
management investment company. The Fund's investment objective is high current
income, preservation of capital and liquidity. The Fund was organized as a
Massachusetts business trust on March 30, 1981 and commenced operations on July
7, 1981.

The following is a summary of significant accounting policies:

A. Valuation of Investments -- Portfolio securities are valued at amortized
cost, which approximates market value.

B. Accounting for Investments -- Security transactions are accounted for on the
trade date (date the order to buy or sell is executed). Realized gains and
losses on security transactions are determined by the identified cost method.
Discounts are accreted and premiums are amortized over the life of the
respective securities. Interest income is accrued daily.

C. Repurchase Agreements -- The Fund may invest directly with institutions in
repurchase agreements. The Fund's custodian receives the collateral, which is
marked-to-market daily to determine that the value of the collateral does not
decrease below the repurchase price plus accrued interest.

D. Federal Income Tax Policy -- It is the Fund's policy to comply with the
requirements of the Internal Revenue Code applicable to regulated investment
companies and to distribute substantially all of its taxable income to its
shareholders. Accordingly, no federal income tax provision is required.

E. Dividends and Distributions to Shareholders -- The Fund records dividends and
distributions to shareholders as of the close of each business day.

F. Use of Estimates -- The preparation of financial statements in accordance
with generally accepted accounting principles requires management to make
estimates and assumptions that affect the reported amounts and disclosures.
Actual results could differ from those estimates.

2. Investment Advisory/Administration Agreements

Effective November 1, 2004, pursuant to an Investment Advisory Agreement with
Morgan Stanley Investment Advisors Inc. (the "Investment Adviser"), the Fund
pays the Investment Adviser an advisory fee, accrued daily and payable monthly,
by applying the following annual rates to the net assets of the Fund determined
as of the close of each business day: 0.45% to the portion of the daily net
assets not exceeding $250 million; 0.375% to the portion of the daily net assets
exceeding

Active Assets Money Trust
NOTES TO FINANCIAL STATEMENTS - DECEMBER 31, 2004 (UNAUDITED) continued

$250 million but not exceeding $750 million; 0.325% to the portion of the daily
net assets exceeding $750 million but not exceeding $1.25 billion; 0.30% to the
portion of the daily net assets exceeding $1.25 billion but not exceeding $1.5
billion; 0.275% to the portion of the daily net assets exceeding $1.5 billion
but not exceeding $1.75 billion; 0.25% to the portion of the daily net assets
exceeding $1.75 billion but not exceeding $2.25 billion; 0.225% to the portion
of the daily net assets exceeding $2.25 billion but not exceeding $2.75 billion;
0.20% to the portion of the daily net assets exceeding $2.75 billion but not
exceeding $15 billion; 0.199% to the portion of the daily net assets exceeding
$15 billion but not exceeding $17.5 billion; 0.198% to the portion of the daily
net assets exceeding $17.5 billion but not exceeding $25.0 billion; 0.197% to
the portion of daily net assets exceeding $25.0 billion but not exceeding $30
billion; and 0.196% to the portion of the daily net assets exceeding $30
billion.

Effective November 1, 2004, pursuant to an Administration Agreement with Morgan
Stanley Services Company Inc. (the "Administrator"), an affiliate of the
Investment Adviser, the Fund pays an administration fee, accrued daily and
payable monthly, by applying the annual rate of 0.05% to the Fund's daily net
assets.

Prior to November 1, 2004, the Fund had retained the Investment Adviser to
provide administrative services and to manage the investment of the Fund's
assets pursuant to an investment management agreement pursuant to which the Fund
paid the Investment Adviser a monthly management fee, accrued daily and payable
monthly, by applying the following annual rates to the net assets of the Fund
determined as of the close of each business day: 0.50% to the portion of the
daily net assets not exceeding $500 million; 0.425% to the portion of the daily
net assets exceeding $500 million but not exceeding $750 million; 0.375% to the
portion of the daily net assets exceeding $750 million but not exceeding $1
billion; 0.35% to the portion of the daily net assets exceeding $1 billion but
not exceeding $1.5 billion; 0.325% to the portion of the daily net assets
exceeding $1.5 billion but not exceeding $2 billion; 0.30% to the portion of the
daily net assets exceeding $2 billion but not exceeding $2.5 billion; 0.275% to
the portion of the daily net assets exceeding $2.5 billion but not exceeding $3
billion; 0.25% to the portion of the daily net assets exceeding $3 billion but
not exceeding $15 billion; 0.249% to the portion of the daily net assets
exceeding $15 billion but not exceeding $17.5 billion; 0.248% to the portion of
the daily net assets exceeding $17.5 billion but not exceeding $25 billion;
0.247% to the portion of daily net assets exceeding $25 billion but not
exceeding $30 billion; and 0.246% to the portion of the daily net assets
exceeding $30 billion.

Active Assets Money Trust
NOTES TO FINANCIAL STATEMENTS - DECEMBER 31, 2004 (UNAUDITED) continued

3. Plan of Distribution

Morgan Stanley Distributors Inc. (the "Distributor"), an affiliate of the
Investment Adviser and Administrator, is the distributor of the Fund's shares
and in accordance with a Plan of Distribution (the "Plan") pursuant to Rule
12b-1 under the Act, finances certain expenses in connection with the promotion
of sales of Fund shares.

Reimbursements for these expenses are made in monthly payments by the Fund to
the Distributor, which will in no event exceed an amount equal to a payment at
the annual rate of 0.15% of the Fund's average daily net assets during the
month. Expenses incurred by the Distributor pursuant to the Plan in any fiscal
year will not be reimbursed by the Fund through payments accrued in any
subsequent fiscal year. For the six months ended December 31, 2004, the
distribution fee was accrued at the annual rate of 0.10%.

4. Security Transactions and Transactions with Affiliates

The cost of purchases and proceeds from sales/maturities of portfolio securities
for the six months ended December 31, 2004, aggregated $62,734,276,260 and
$63,029,768,837, respectively.

Morgan Stanley Trust, an affiliate of the Investment Adviser, Administrator and
Distributor, is the Fund's transfer agent.

The Fund has an unfunded noncontributory defined benefit pension plan covering
certain independent Trustees of the Fund who will have served as independent
Trustees for at least five years at the time of retirement. Benefits under this
plan are based on factors which include years of service and compensation.
Aggregate pension costs for the six months ended December 31, 2004, included in
Trustees' fees and expenses in the Statement of Operations amounted to $3,719.
At December 31, 2004, the Fund had an accrued pension liability of $61,825 which
is included in accrued expenses in the Statement of Assets and Liabilities. On
December 2, 2003, the Trustees voted to close the plan to new participants and
eliminate the future benefits growth due to increases to compensation after July
31, 2003.

Effective April 1, 2004, the Fund began an unfunded Deferred Compensation Plan
(the "Compensation Plan") which allows each independent Trustee to defer payment
of all, or a portion, of the fees he receives for serving on the Board of
Trustees. Each eligible Trustee generally may elect to have the deferred amounts
credited with a return equal to the total return on one or more of the Morgan
Stanley funds that are offered as investment options under the Compensation
Plan. Appreciation/depreciation and distributions received from these
investments are recorded with an offsetting increase/decrease in the deferred
compensation obligation and do not affect the net asset value of the Fund.

Active Assets Money Trust
NOTES TO FINANCIAL STATEMENTS - DECEMBER 31, 2004 (UNAUDITED) continued

5. Shares of Beneficial Interest

Transactions in shares of beneficial interest, at $1.00 per share, were as
follows:

<Table>
<Caption>
FOR THE SIX FOR THE YEAR
MONTHS ENDED ENDED
DECEMBER 31, 2004 JUNE 30, 2004
----------------- ---------------
(unaudited)

Shares sold................................................. 41,563,737,166 76,548,881,077
Shares issued in reinvestment of dividends and
distributions............................................. 142,521,769 151,806,090
--------------- ---------------
41,706,258,935 76,700,687,167
Shares redeemed............................................. (41,836,859,095) (78,323,559,673)
--------------- ---------------
Net decrease in shares outstanding.......................... (130,600,160) (1,622,872,506)
=============== ===============
</Table>

6. Legal Matters

The Investment Adviser, certain affiliates of the Investment Adviser, certain
officers of such affiliates and certain investment companies advised by the
Investment Adviser or its affiliates, including the Fund, are named as
defendants in a number of similar class action complaints which were recently
consolidated. This consolidated action also names as defendants certain
individual Trustees and Directors of the Morgan Stanley funds. The consolidated
amended complaint generally alleges that defendants, including the Fund,
violated their statutory disclosure obligations and fiduciary duties by failing
properly to disclose (i) that the Investment Adviser and certain affiliates of
the Investment Adviser allegedly offered economic incentives to brokers and
others to recommend the funds advised by the Investment Adviser or its
affiliates to investors rather than funds managed by other companies, and (ii)
that the funds advised by the Investment Adviser or its affiliates, including
the Fund, allegedly paid excessive commissions to brokers in return for their
efforts to recommend these funds to investors. The complaint seeks, among other
things, unspecified compensatory damages, rescissionary damages, fees and costs.
The defendants have moved to dismiss the action and intend to otherwise
vigorously defend it. While the Fund believes that it has meritorious defenses,
the ultimate outcome of this matter is not presently determinable at this early
stage of the litigation, and no provision has been made in the Fund's financial
statements for the effect, if any, of this matter.

Active Assets Money Trust
FINANCIAL HIGHLIGHTS

Selected ratios and per share data for a share of beneficial interest
outstanding throughout each period:

<Table>
<Caption>
FOR THE SIX FOR THE YEAR ENDED JUNE 30,
MONTHS ENDED ----------------------------------------------------
DECEMBER 31, 2004 2004 2003 2002 2001 2000
----------------- -------- -------- -------- -------- --------
(unaudited)

Selected Per Share Data:

Net asset value, beginning of period........ $ 1.00 $ 1.00 $ 1.00 $ 1.00 $ 1.00 $ 1.00
------ ------ ------ ------ ------ ------

Net income from investment operations....... 0.006 0.007 0.011 0.023 0.056 0.054

Less dividends from net investment income... (0.006) (0.007)+ (0.011)+ (0.023)+ (0.056)+ (0.054)
------ ------ ------ ------ ------ ------

Net asset value, end of period.............. $ 1.00 $ 1.00 $ 1.00 $ 1.00 $ 1.00 $ 1.00
====== ====== ====== ====== ====== ======

Total Return................................ 0.65%(1) 0.68% 1.13% 2.33% 5.76% 5.50%

Ratios to Average Net Assets:
Expenses.................................... 0.42%(2) 0.41% 0.41% 0.40% 0.41% 0.42%

Net investment income....................... 1.28%(2) 0.67% 1.12% 2.32% 5.58% 5.38%

Supplemental Data:
Net assets, end of period, in millions...... $21,524 $21,655 $23,278 $25,038 $26,212 $20,972
</Table>

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

<Table>

(1) Not annualized.
(2) Annualized.
+ Includes capital gain distribution of less than $0.001.
</Table>

See Notes to Financial Statements
15

TRUSTEES

Michael Bozic
Charles A. Fiumefreddo
Edwin J. Garn
Wayne E. Hedien
James F. Higgins
Dr. Manuel H. Johnson
Joseph J. Kearns
Michael E. Nugent
Fergus Reid

OFFICERS

Charles A. Fiumefreddo
Chairman of the Board

Mitchell M. Merin
President

Ronald E. Robison
Executive Vice President and Principal Executive Officer

Joseph J. McAlinden
Vice President

Barry Fink
Vice President

Amy R. Doberman
Vice President

Carsten Otto
Chief Compliance Officer

Stefanie V. Chang
Vice President

Francis J. Smith
Treasurer and Chief Financial Officer

Thomas F. Caloia
Vice President

Mary E. Mullin
Secretary

TRANSFER AGENT

Morgan Stanley Trust
Harborside Financial Center, Plaza Two
Jersey City, New Jersey 07311

INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

Deloitte & Touche LLP
Two World Financial Center
New York, New York 10281

INVESTMENT ADVISER

Morgan Stanley Investment Advisors Inc.
1221 Avenue of the Americas
New York, New York 10020

The financial statements included herein have been taken from the records of the
Fund without examination by the independent auditors and accordingly they do not
express an opinion thereon.

This report is submitted for the general information of shareholders of the
Fund. For more detailed information about the Fund, its fees and expenses and
other pertinent information, please read its Prospectus. The Fund's Statement of
Additional Information contains additional information about the Fund, including
its trustees. It is available, without charge, by calling (800) 869-NEWS.

This report is not authorized for distribution to prospective investors in the
Fund unless preceded or accompanied by an effective Prospectus. Read the
Prospectus carefully before investing.

Investments and services offered through Morgan Stanley DW Inc., member SIPC.
Morgan Stanley Distributors Inc., member NASD.

[MORGAN STANLEY LOGO]

MORGAN STANLEY FUNDS

Active Assets
Money Trust

Semiannual Report
December 31, 2004

[MORGAN STANLEY LOGO]

RA05-00112P-Y12/04

Item 2. Code of Ethics.