NUVEEN TAX EXEMPT UNIT TRUST SERIES 821
497, 1995-08-28
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<PAGE>
NUVEEN  Tax-Exempt Unit Trusts
     NUVEEN
     CONNECTICUT
     TRUST 276
              (CONNECTICUT TRADITIONAL TRUST 276)
 
            Estimated Current Return
            5.21% to 5.42%
            as of 08/24/95
 
            Estimated Long Term Return
            5.36% to 5.58%
             35,000 units in a
             diversified $3,500,000
             portfolio of tax-exempt
             bonds
                  Cusip:
                  67094E 766 Monthly Payment Option
                  67094E 774 Quarterly Payment Option
                  67094E 782 Semi-Annual Payment Option
 
                  Registered in Connecticut
                    John Nuveen & Co. Incorporated
                    Investment Bankers
 
<TABLE>
<S>                           <C>
Chicago:                      Atlanta
333 W. Wacker Dr.             Austin
Chicago, Illinois 60606       Boca Raton
Telephone: 312.917.7700       Boston
                              Columbus
New York:                     Dallas/Ft. Worth
Swiss Bank Tower              Irvine
10 East 50th Street           Philadelphia
New York, New York 10022      Phoenix
Telephone: 212.207.2000       San Francisco
                              Seattle
                              Tampa
                              Washington, D.C.
</TABLE>
 
<PAGE>
--------------------------------------------------------------------------------
 
NUVEEN TAX-EXEMPT UNIT TRUST--CONNECTICUT TRADITIONAL TRUST 276
SCHEDULE OF INVESTMENTS
DATE OF DEPOSIT AUGUST 25, 1995
--------------------------------------------------------------------------------
 
   
<TABLE>
<CAPTION>
                                                                                                             Ratings
                                                                                    Optional         -----------------------
  Aggregate            Name of Issuer and Title of Issue Represented               Redemption        Standard
  Principal               by Sponsor's Contracts to Purchase Bonds                 Provisions        & Poor's       Moody's
  <C>       <C> <S>                                                              <C>                 <C>           <C>
  --------------------------------------------------------------------------------------------------------------------------
  $  500,000    State of Connecticut Health and Educational Facilities             2005 at 101          AAA           Aaa
                  Authority, Revenue Bonds, Kent School Issue, Series B,
                  5.40% Due 7/1/23. (MBIA Insured.)
     335,000    State of Connecticut Health and Educational Facilities             2003 at 102          AAA           Aaa
                  Authority, Revenue Bonds, Lawrence and Memorial Hospital
                  Issue, Series D, 5.00% Due 7/1/22. (Original issue
                  discount bonds delivered on or about December 29, 1993 at
                  a price of 94.491% of principal amount.)(MBIA Insured.)
     210,000    State of Connecticut, Health and Educational Facilities            2003 at 102          AAA           Aaa
                  Authority, Revenue Bonds, Saint Francis Hospital and
                  Medical Center Issue, Series C, 5.00% Due 7/1/23. (FGIC
                  Insured.)
     500,000    State of Connecticut, Special Tax Obligation Bonds,                2003 at 101          AAA           Aaa
                  Transportation Infrastructure Purposes, 1993 Series C,               1/2
                  5.00% Due 10/1/13. (FGIC Insured.)
     455,000    Town of Cheshire, Connecticut, General Obligation Bonds,           2005 at 102          --            Aa
                  Issue of 1995, 5.625% Due 8/1/14.
     500,000    South Central Connecticut Regional Water Authority, Water          2003 at 102          AAA           Aaa
                  System Revenue Bonds, Eleventh Series, 5.75% Due 8/1/12.
                  (FGIC Insured.)
     500,000    City of Stamford, Connecticut, General Obligation Bonds,           2004 at 102          AAA           Aaa
                  Issue of 1995, 5.50% Due 3/15/15.
     500,000    Commonwealth of Puerto Rico, Public Improvement Bonds of           2005 at 101          AAA           Aaa
                  1995 (General Obligation Bonds.),                                    1/2
                250M-5.375% Due 7/1/22, (Original issue discount bonds
                  delivered on or about May 4, 1995 at a price of 93.916% of
                  principal amount.)
                250M-5.75% Due 7/1/24. (MBIA Insured.)
  ----------
  $3,500,000
  ----------
  ----------
</TABLE>
    
 
<PAGE>
--------------------------------------------------------------------------------
UNIT PRICE, ESTIMATED CURRENT RETURN AND ESTIMATED LONG TERM RETURN DEPEND ON
AMOUNT PURCHASED AND PAYMENT OPTION    The sales charges/volume discounts below
apply on all concurrent purchases of any Nuveen trust units, unless any such
purchases are made by a class of investors for which a separate sales charge is
applicable as described more fully in the Prospectus. Estimated Current Return
equals net income divided by offering price. Estimated Long Term Return
represents an average of the yields to maturity (or call) of the Bonds in the
Trust adjusted to reflect expenses and sales charges.
--------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                                                                          Estimated Current Return (2)
                                                              -----------------------------------------------------
          AMOUNT PURCHASED                         Public
-------------------------------------  Sales      Offering          Monthly         Quarterly       Semi-Annual
     Units              Dollars        Charge     Price (1)         Payment          Payment          Payment
----------------  -------------------  ------    -----------     -------------    -------------    -------------
<S>               <C>                  <C>       <C>         <C>                <C>              <C>
50-499                 $5,000-$49,999   4.90 %   $     98.94          5.21%            5.24%            5.26%
500-999                 50,000-99,999   4.75           98.78          5.22             5.25             5.27
1,000-2,499           100,000-249,999   4.50           98.52          5.23             5.27             5.29
2,500-4,999           250,000-499,999   4.25           98.27          5.25             5.28             5.30
5,000-9,999           500,000-999,999   3.50           97.50          5.29             5.32             5.34
10,000-24,999     1,000,000- 2,499,999  3.00           97.00          5.32             5.35             5.37
25,000-49,999     2,500,000- 4,999,999  2.50           96.50          5.34             5.38             5.40
50,000 and over    5,000,000 and over   2.00           96.01          5.37             5.40             5.42
</TABLE>
 
--------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                                                                         Estimated Long Term Return (3)
                                                              -----------------------------------------------------
          AMOUNT PURCHASED                         Public
-------------------------------------  Sales      Offering          Monthly         Quarterly       Semi-Annual
     Units              Dollars        Charge     Price (1)         Payment          Payment          Payment
----------------  -------------------  ------    -----------     -------------    -------------    -------------
<S>               <C>                  <C>       <C>         <C>                <C>              <C>
50-499                 $5,000-$49,999   4.90 %   $     98.94          5.36%            5.39%            5.41%
500-999                 50,000-99,999   4.75           98.78          5.37             5.40             5.42
1,000-2,499           100,000-249,999   4.50           98.52          5.39             5.42             5.43
2,500-4,999           250,000-499,999   4.25           98.27          5.40             5.43             5.45
5,000-9,999           500,000-999,999   3.50           97.50          5.44             5.47             5.49
10,000-24,999     1,000,000- 2,499,999  3.00           97.00          5.47             5.50             5.52
25,000-49,999     2,500,000- 4,999,999  2.50           96.50          5.50             5.53             5.55
50,000 and over    5,000,000 and over   2.00           96.01          5.53             5.56             5.58
</TABLE>
 
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
 
(1) As of the business day prior to the Date of Deposit. Units are offered at
    the Public Offering Price plus accrued interest.
(2) All figures as of the business day prior to Date of Deposit. The estimated
    current return for purchases made on such date will be as shown, as long as
    the portfolio size and composition remain the same.
(3) In contrast to Estimated Current Return, Estimated Long Term Return reflects
    the amortization of premium or accretion of discount, if any, on the bonds
    in the Trust's portfolio.
 
--------------------------------------------------------------------------------
 
INTEREST DISTRIBUTIONS TO UNITHOLDERS   Unitholders may elect to have interest
distributions made on a monthly, quarterly, or semi-annual basis. Record Dates
are May 1 and November 1 for semi-annual distributions; February 1, May 1,
August 1 and November 1 for quarterly distributions; and the first of each month
for monthly distributions. Details of interest distributions per unit under the
various plans appear in the following table based upon estimated net annual
interest income at the Date of Deposit:
--------------------------------------------------------------------------------
 
   
<TABLE>
<CAPTION>
                                                                                                          Normal
                                                                                                      Distributions
Connecticut Traditional Trust                     1995                             1996                 per Year +
<S>                                     <C>            <C>            <C>            <C>            <C>
----------------------------------------------------------------------------------------------------  --------------
Record Date*..........................       10/1           11/1            2/1            5/1
Distribution Date.....................      10/15          11/15           2/15           5/15
--------------------------------------------------------------------------------------------------------------------
Monthly Distribution Plan.............  $   .5155(1)                                                  $  5.1558
                                                          --------  $.4296 every month  --------
Quarterly Distribution Plan...........  $   .5155(1)   $   .4323(2)   $  1.2969      $  1.2969        $  5.1878
Semi-Annual Distribution Plan.........  $   .5155(1)   $   .4338(3)                  $  2.6028        $  5.2068
--------------------------------------------------------------------------------------------------------------------
<FN>
  * Record Dates for semi-annual distributions are May 1 and November 1; for quarterly distributions, they are February 1, May 1,
    August 1 and November 1. Record Dates for monthly distributions are the first day of each month.
(1) The first distribution will be paid to all Unitholders, regardless of the distribution plan selected. Such distribution may
    be more or less than a regular monthly distribution.
(2) The second distribution under the quarterly distribution plan represents a 1-month distribution; subsequent quarterly
    distributions will be regular 3-month distributions.
(3) The second distribution under the semi-annual distribution plan represents a 1-month distribution; subsequent semi-annual
    distributions will be regular 6-month distributions.
</TABLE>
    
 
+ Interest for Unitholders of this series began to accrue as of the Date of
Deposit. Units purchased on the Date of Deposit will have $.07 of accrued
interest that will be added to the Public Offering Price on the Settlement Date.
After provision for expenses of the Fund, the daily rate of accrual from the
Date of Deposit to the first Record Date is $.01432 per unit per day.
Consequently, on the first Record Date (10/01/95), accrued interest will total
$0.5155 per unit for the 36-day period. All interest accrued from the Date of
Deposit to the first Record Date, less expenses, will be distributed on the
first Distribution Date to Unitholders of Record as of the first Record Date.
The first payment to all Unitholders of Record on 10/01/95 is $.5155 per unit.
After the first Record Date daily rates of accrual are:
              Monthly - $0.01432              Quarterly - $0.01441
                             Semi-Annual - $0.01446
This daily rate of accrual, and the annual distributions shown above, will
remain the same as long as the portfolio size and composition remain the same.
 
--------------------------------------------------------------------------------
 
                                                          821
<PAGE>
-------------------------------------------------------
 
AVERAGE PORTFOLIO LIFE   The average maturity of portfolio bonds is 22.5 years.
The first bond is scheduled to mature in August, 2012, with the last bond
maturity being July, 2024.
 
-------------------------------------------------------
 
QUALITY OF PORTFOLIO AS RATED BY
STANDARD & POOR'S CORPORATION
OR MOODY'S INVESTORS SERVICES
-------------------------------------------------------
 
<TABLE>
<S>                       <C>                    <C>
Rating                    Percent of Portfolio
Category                  Par Value
--------------------------------------------------------------------
AAA                           87%
AA                            13
                             ---
                             100%
</TABLE>
 
-------------------------------------------------------
 
CALL PROTECTION   Bonds are first subject to optional redemption by the issuers
in the years and at the prices shown under the Redemption Provisions column in
the Schedule of Investments. Unless otherwise stated, in subsequent years, bonds
are redeemable at declining prices, but not usually below par value. Some issues
or some portions of issues may also be subject to sinking fund redemption or
extraordinary redemption without premium prior to the dates shown.
 
-------------------------------------------------------
 
NO CHARGE FOR REDEMPTION   The Trustee, United States Trust Company of New York,
will redeem units at net asset value. In addition, John Nuveen & Co.
Incorporated intends to maintain a secondary market for this Nuveen Tax-Exempt
Unit Trust. Inasmuch as all securities investments are subject to market price
fluctuation, net asset value at the time of redemption could be more or less
than the initial investment.
 
-------------------------------------------------------
 
REINVESTMENT OPTIONS   Specify automatic reinvestment of trust income, with no
sales charge, to earn compounded dividends with Nuveen mutual funds.
 
-------------------------------------------------------
 
UNITS OF THE TRUST ARE NOT DEPOSITS OR OBLIGATIONS OF, OR GUARANTEED OR ENDORSED
BY, ANY BANK AND ARE NOT FEDERALLY INSURED OR OTHERWISE PROTECTED BY THE FEDERAL
DEPOSIT INSURANCE CORPORATION, THE FEDERAL RESERVE BOARD OR ANY OTHER AGENCY AND
INVOLVE INVESTMENT RISK, INCLUDING THE POSSIBLE LOSS OF PRINCIPAL.
 
-------------------------------------------------------
 
FOR A PROSPECTUS CONTAINING MORE COMPLETE INFORMATION, INCLUDING CHARGES AND
EXPENSES, ON THIS NUVEEN TAX-EXEMPT UNIT TRUST AND ANY OTHER NUVEEN FUND, CALL
YOUR BROKER . . . OR NUVEEN AT
 
                                 1-800-257-8787
 
READ THE PROSPECTUS CAREFULLY BEFORE YOU INVEST OR SEND MONEY.
<PAGE>
NUVEEN  Tax-Exempt Unit Trusts
     NUVEEN
     VIRGINIA
     TRUST 303
              (VIRGINIA TRADITIONAL TRUST 303)
 
            Estimated Current Return
            5.50% to 5.72%
            as of 08/24/95
 
            Estimated Long Term Return
            5.59% to 5.82%
             35,000 units in a
             diversified $3,500,000
             portfolio of tax-exempt
             bonds
                  Cusip:
                  6706L5 796 Monthly Payment Option
                  6706L5 804 Quarterly Payment Option
                  6706L5 812 Semi-Annual Payment Option
 
                  Registered in Virginia
                    John Nuveen & Co. Incorporated
                    Investment Bankers
 
<TABLE>
<S>                           <C>
Chicago:                      Atlanta
333 W. Wacker Dr.             Austin
Chicago, Illinois 60606       Boca Raton
Telephone: 312.917.7700       Boston
                              Columbus
New York:                     Dallas/Ft. Worth
Swiss Bank Tower              Irvine
10 East 50th Street           Philadelphia
New York, New York 10022      Phoenix
Telephone: 212.207.2000       San Francisco
                              Seattle
                              Tampa
                              Washington, D.C.
</TABLE>
 
<PAGE>
--------------------------------------------------------------------------------
 
NUVEEN TAX-EXEMPT UNIT TRUST--VIRGINIA TRADITIONAL TRUST 303
SCHEDULE OF INVESTMENTS
DATE OF DEPOSIT AUGUST 25, 1995
--------------------------------------------------------------------------------
 
   
<TABLE>
<CAPTION>
                                                                                                             Ratings
                                                                                    Optional         -----------------------
  Aggregate            Name of Issuer and Title of Issue Represented               Redemption        Standard
  Principal               by Sponsor's Contracts to Purchase Bonds                 Provisions        & Poor's       Moody's
  <C>       <C> <S>                                                              <C>                 <C>           <C>
  --------------------------------------------------------------------------------------------------------------------------
  $  500,000    Metropolitan Washington Airports Authority (District of            2003 at 102          AAA           Aaa
                  Columbia and Virginia), Airport System Revenue and
                  Refunding Bonds, Series 1993A, 5.25% Due 10/1/22. (MBIA
                  Insured.)
     500,000    Commonwealth of Puerto Rico, Public Improvement Bonds of           2005 at 101          AAA           Aaa
                  1995 (General Obligation Bonds.), 5.75% Due 7/1/24. (MBIA            1/2
                  Insured.)
     500,000    Commonwealth Transportation Board, Commonwealth of Virginia,       2004 at 101          AA            Aa
                  Transportation Revenue Bonds, Series 1995A (Northern
                  Virginia Transportation District Program), 6.375% Due
                  5/15/20.
     250,000    Industrial Development Authority of the City of Chesapeake,        2003 at 102          AA-           Aa3
                  Virginia, Port Facilities Refunding Revenue Bonds, Series
                  1993 (Cargill, Incorporated Project), 5.875% Due 3/1/13.
     500,000    Industrial Development Authority of Fairfax County,                No Optional          AA-           Aa
                  Virginia, Hospital Revenue Refunding Bonds (Inova Health            Call
                  System Hospitals Project), Series 1993A, 5.00% Due
                  8/15/23. (Original issue discount bonds delivered on or
                  about November 3, 1993 at a price of 94.807% of principal
                  amount.)
     250,000    Loudoun County Sanitation Authority (Virginia), Water and          2004 at 102          AAA           Aaa
                  Sewer System Revenue Bonds, Series 1994A, 5.25% Due
                  1/1/30. (Original issue discount bonds delivered on or
                  about March 30, 1994 at a price of 89.671% of principal
                  amount.)(MBIA Insured.)
     500,000    City of Norfolk, Virginia, Water Revenue Bonds, Series 1993,       2003 at 102          AAA           Aaa
                  5.375% Due 11/1/23. (AMBAC Insured.)
     500,000    Norfolk Redevelopment and Housing Authority (Virginia),            2005 at 102          AA            Aa
                  Educational Facility Bonds (State Board for Community
                  Colleges-Tidewater Community College Downtown Campus),
                  Series of 1995, 5.875% Due 11/1/15.
  ----------
  $3,500,000
  ----------
  ----------
</TABLE>
    
 
<PAGE>
--------------------------------------------------------------------------------
UNIT PRICE, ESTIMATED CURRENT RETURN AND ESTIMATED LONG TERM RETURN DEPEND ON
AMOUNT PURCHASED AND PAYMENT OPTION    The sales charges/volume discounts below
apply on all concurrent purchases of any Nuveen trust units, unless any such
purchases are made by a class of investors for which a separate sales charge is
applicable as described more fully in the Prospectus. Estimated Current Return
equals net income divided by offering price. Estimated Long Term Return
represents an average of the yields to maturity (or call) of the Bonds in the
Trust adjusted to reflect expenses and sales charges.
--------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                                                                          Estimated Current Return (2)
                                                              -----------------------------------------------------
          AMOUNT PURCHASED                         Public
-------------------------------------  Sales      Offering          Monthly         Quarterly       Semi-Annual
     Units              Dollars        Charge     Price (1)         Payment          Payment          Payment
----------------  -------------------  ------    -----------     -------------    -------------    -------------
<S>               <C>                  <C>       <C>         <C>                <C>              <C>
50-499                 $5,000-$49,999   4.90 %   $     97.42          5.50%            5.53%            5.55%
500-999                 50,000-99,999   4.75           97.27          5.51             5.54             5.56
1,000-2,499           100,000-249,999   4.50           97.02          5.52             5.55             5.57
2,500-4,999           250,000-499,999   4.25           96.76          5.54             5.57             5.59
5,000-9,999           500,000-999,999   3.50           96.01          5.58             5.61             5.63
10,000-24,999     1,000,000- 2,499,999  3.00           95.52          5.61             5.64             5.66
25,000-49,999     2,500,000- 4,999,999  2.50           95.03          5.64             5.67             5.69
50,000 and over    5,000,000 and over   2.00           94.54          5.67             5.70             5.72
</TABLE>
 
--------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                                                                         Estimated Long Term Return (3)
                                                              -----------------------------------------------------
          AMOUNT PURCHASED                         Public
-------------------------------------  Sales      Offering          Monthly         Quarterly       Semi-Annual
     Units              Dollars        Charge     Price (1)         Payment          Payment          Payment
----------------  -------------------  ------    -----------     -------------    -------------    -------------
<S>               <C>                  <C>       <C>         <C>                <C>              <C>
50-499                 $5,000-$49,999   4.90 %   $     97.42          5.59%            5.63%            5.65%
500-999                 50,000-99,999   4.75           97.27          5.60             5.64             5.66
1,000-2,499           100,000-249,999   4.50           97.02          5.62             5.65             5.67
2,500-4,999           250,000-499,999   4.25           96.76          5.63             5.67             5.69
5,000-9,999           500,000-999,999   3.50           96.01          5.67             5.71             5.73
10,000-24,999     1,000,000- 2,499,999  3.00           95.52          5.70             5.74             5.76
25,000-49,999     2,500,000- 4,999,999  2.50           95.03          5.73             5.77             5.79
50,000 and over    5,000,000 and over   2.00           94.54          5.76             5.80             5.82
</TABLE>
 
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
 
(1) As of the business day prior to the Date of Deposit. Units are offered at
    the Public Offering Price plus accrued interest.
(2) All figures as of the business day prior to Date of Deposit. The estimated
    current return for purchases made on such date will be as shown, as long as
    the portfolio size and composition remain the same.
(3) In contrast to Estimated Current Return, Estimated Long Term Return reflects
    the amortization of premium or accretion of discount, if any, on the bonds
    in the Trust's portfolio.
 
--------------------------------------------------------------------------------
 
INTEREST DISTRIBUTIONS TO UNITHOLDERS   Unitholders may elect to have interest
distributions made on a monthly, quarterly, or semi-annual basis. Record Dates
are May 1 and November 1 for semi-annual distributions; February 1, May 1,
August 1 and November 1 for quarterly distributions; and the first of each month
for monthly distributions. Details of interest distributions per unit under the
various plans appear in the following table based upon estimated net annual
interest income at the Date of Deposit:
--------------------------------------------------------------------------------
 
   
<TABLE>
<CAPTION>
                                                                                                          Normal
                                                                                                      Distributions
Virginia Traditional Trust                        1995                             1996                 per Year +
<S>                                     <C>            <C>            <C>            <C>            <C>
----------------------------------------------------------------------------------------------------  --------------
Record Date*..........................       10/1           11/1            2/1            5/1
Distribution Date.....................      10/15          11/15           2/15           5/15
--------------------------------------------------------------------------------------------------------------------
Monthly Distribution Plan.............  $   .5353(1)                                                  $  5.3559
                                                          --------  $.4461 every month  --------
Quarterly Distribution Plan...........  $   .5353(1)   $   .4488(2)   $  1.3464      $  1.3464        $  5.3879
Semi-Annual Distribution Plan.........  $   .5353(1)   $   .4503(3)                  $  2.7018        $  5.4069
--------------------------------------------------------------------------------------------------------------------
<FN>
  * Record Dates for semi-annual distributions are May 1 and November 1; for quarterly distributions, they are February 1, May 1,
    August 1 and November 1. Record Dates for monthly distributions are the first day of each month.
(1) The first distribution will be paid to all Unitholders, regardless of the distribution plan selected. Such distribution may
    be more or less than a regular monthly distribution.
(2) The second distribution under the quarterly distribution plan represents a 1-month distribution; subsequent quarterly
    distributions will be regular 3-month distributions.
(3) The second distribution under the semi-annual distribution plan represents a 1-month distribution; subsequent semi-annual
    distributions will be regular 6-month distributions.
</TABLE>
    
 
+ Interest for Unitholders of this series began to accrue as of the Date of
Deposit. Units purchased on the Date of Deposit will have $.07 of accrued
interest that will be added to the Public Offering Price on the Settlement Date.
After provision for expenses of the Fund, the daily rate of accrual from the
Date of Deposit to the first Record Date is $.01487 per unit per day.
Consequently, on the first Record Date (10/01/95), accrued interest will total
$0.5353 per unit for the 36-day period. All interest accrued from the Date of
Deposit to the first Record Date, less expenses, will be distributed on the
first Distribution Date to Unitholders of Record as of the first Record Date.
The first payment to all Unitholders of Record on 10/01/95 is $.5353 per unit.
After the first Record Date daily rates of accrual are:
              Monthly - $0.01487              Quarterly - $0.01496
                             Semi-Annual - $0.01501
This daily rate of accrual, and the annual distributions shown above, will
remain the same as long as the portfolio size and composition remain the same.
 
--------------------------------------------------------------------------------
 
                                                          821
<PAGE>
-------------------------------------------------------
 
AVERAGE PORTFOLIO LIFE   The average maturity of portfolio bonds is 26.1 years.
The first bond is scheduled to mature in March, 2013, with the last bond
maturity being January, 2030.
 
-------------------------------------------------------
 
QUALITY OF PORTFOLIO AS RATED BY
STANDARD & POOR'S CORPORATION
OR MOODY'S INVESTORS SERVICES
-------------------------------------------------------
 
<TABLE>
<S>                       <C>                    <C>
Rating                    Percent of Portfolio
Category                  Par Value
--------------------------------------------------------------------
AAA                           50%
AA                            50
                             ---
                             100%
</TABLE>
 
-------------------------------------------------------
 
CALL PROTECTION   Bonds are first subject to optional redemption by the issuers
in the years and at the prices shown under the Redemption Provisions column in
the Schedule of Investments. Unless otherwise stated, in subsequent years, bonds
are redeemable at declining prices, but not usually below par value. Some issues
or some portions of issues may also be subject to sinking fund redemption or
extraordinary redemption without premium prior to the dates shown.
 
-------------------------------------------------------
 
NO CHARGE FOR REDEMPTION   The Trustee, United States Trust Company of New York,
will redeem units at net asset value. In addition, John Nuveen & Co.
Incorporated intends to maintain a secondary market for this Nuveen Tax-Exempt
Unit Trust. Inasmuch as all securities investments are subject to market price
fluctuation, net asset value at the time of redemption could be more or less
than the initial investment.
 
-------------------------------------------------------
 
REINVESTMENT OPTIONS   Specify automatic reinvestment of trust income, with no
sales charge, to earn compounded dividends with Nuveen mutual funds.
 
-------------------------------------------------------
 
UNITS OF THE TRUST ARE NOT DEPOSITS OR OBLIGATIONS OF, OR GUARANTEED OR ENDORSED
BY, ANY BANK AND ARE NOT FEDERALLY INSURED OR OTHERWISE PROTECTED BY THE FEDERAL
DEPOSIT INSURANCE CORPORATION, THE FEDERAL RESERVE BOARD OR ANY OTHER AGENCY AND
INVOLVE INVESTMENT RISK, INCLUDING THE POSSIBLE LOSS OF PRINCIPAL.
 
-------------------------------------------------------
 
FOR A PROSPECTUS CONTAINING MORE COMPLETE INFORMATION, INCLUDING CHARGES AND
EXPENSES, ON THIS NUVEEN TAX-EXEMPT UNIT TRUST AND ANY OTHER NUVEEN FUND, CALL
YOUR BROKER . . . OR NUVEEN AT
 
                                 1-800-257-8787
 
READ THE PROSPECTUS CAREFULLY BEFORE YOU INVEST OR SEND MONEY.
<PAGE>
NUVEEN  Tax-Exempt Unit Trusts
     NUVEEN
     MASSACHUSETTS
     INSURED
     TRUST 129
 
            Estimated Current Return
            First
            Year: 5.37% to 5.59%
            Subsequent
            Years: 5.42% to 5.63%
            as of 08/24/95
 
            Estimated Long Term Return
            5.54% to 5.76%
             35,000 units in a
             diversified $3,500,000
             portfolio of tax-exempt
             bonds rated "AAA"
                  Cusip:
                  670947 464 Monthly Payment Option
                  670947 472 Quarterly Payment Option
                  670947 480 Semi-Annual Payment Option
 
                  Registered in Massachusetts
                    John Nuveen & Co. Incorporated
                    Investment Bankers
 
<TABLE>
<S>                           <C>
Chicago:                      Atlanta
333 W. Wacker Dr.             Austin
Chicago, Illinois 60606       Boca Raton
Telephone: 312.917.7700       Boston
                              Columbus
New York:                     Dallas/Ft. Worth
Swiss Bank Tower              Irvine
10 East 50th Street           Philadelphia
New York, New York 10022      Phoenix
Telephone: 212.207.2000       San Francisco
                              Seattle
                              Tampa
                              Washington, D.C.
</TABLE>
 
<PAGE>
--------------------------------------------------------------------------------
 
NUVEEN TAX-EXEMPT UNIT TRUST--INSURED, MASSACHUSETTS INSURED TRUST 129
SCHEDULE OF INVESTMENTS
DATE OF DEPOSIT AUGUST 25, 1995
--------------------------------------------------------------------------------
 
   
<TABLE>
<CAPTION>
                                                                                                             Ratings
                                                                                    Optional         -----------------------
  Aggregate            Name of Issuer and Title of Issue Represented               Redemption        Standard
  Principal               by Sponsor's Contracts to Purchase Bonds                 Provisions        & Poor's       Moody's
  <C>       <C> <S>                                                              <C>                 <C>           <C>
  --------------------------------------------------------------------------------------------------------------------------
  $  500,000    The Commonwealth of Massachusetts, General Obligation Bonds,       2005 at 101          AAA           Aaa
                  Consolidated Loan of 1995, Series B, 5.50% Due 7/1/14.
     250,000    Massachusetts Bay Transportation Authority, General                2005 at 102          AAA           Aaa
                  Transportation System Bonds, 1995 Series A, 5.75% Due
                  3/1/25. (General Obligation Bonds.)
     250,000    Massachusetts Health and Educational Facilities Authority,         2005 at 102          AAA           Aaa
                  Revenue Bonds, Harvard University Issue, Series P, 5.625%
                  Due 11/1/28.
     500,000    Massachusetts Health and Educational Facilities Authority,         2005 at 102          AAA           Aaa
                  Revenue Bonds, Newton-Wellesley Hospital Issue, Series E,
                  6.00% Due 7/1/25. (When issued.)
     500,000    Massachusetts Health and Educational Facilities Authority,         2004 at 102          AAA           Aaa
                  Revenue Bonds, Smith College Issue, Series D, 5.75% Due
                  7/1/24.
     500,000    Massachusetts Municipal Wholesale Electric Company, Power          2004 at 102          AAA           Aaa
                  Supply System Revenue Bonds, 1994 Series B, 5.00% Due
                  7/1/13.
     500,000    Massachusetts Water Resources Authority, General Revenue           2004 at 101          AAA           Aaa
                  Bonds, 1994 Series A, 6.00% Due 8/1/24.                              1/2
     500,000    Commonwealth of Puerto Rico, Public Improvement Bonds of           2005 at 101          AAA           Aaa
                  1995 (General Obligation Bonds.), 5.375% Due 7/1/22.                 1/2
                  (Original issue discount bonds delivered on or about May
                  4, 1995 at a price of 93.916% of principal amount.)
  ----------
  $3,500,000
  ----------
  ----------
</TABLE>
    
 
<PAGE>
--------------------------------------------------------------------------------
UNIT PRICE, ESTIMATED CURRENT RETURN AND ESTIMATED LONG TERM RETURN DEPEND ON
AMOUNT PURCHASED AND PAYMENT OPTION    The sales charges/volume discounts below
apply on all concurrent purchases of any Nuveen trust units, unless any such
purchases are made by a class of investors for which a separate sales charge is
applicable as described more fully in the Prospectus. Estimated Current Return
equals net income divided by offering price. Estimated Long Term Return
represents an average of the yields to maturity (or call) of the Bonds in the
Trust adjusted to reflect expenses and sales charges.
--------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                                                                              Estimated Current Return (2)
          AMOUNT PURCHASED                         Public      -----------------------------------------------------------
-------------------------------------  Sales      Offering         Monthly           Quarterly            Semi-Annual
     Units              Dollars        Charge     Price (1)        Payment            Payment               Payment
----------------  -------------------  ------    -----------   ---------------    ---------------    ---------------------
<S>               <C>                  <C>       <C>           <C>       <C>      <C>       <C>      <C>       <C>
50-499                 $5,000-$49,999   4.90 %   $     99.11     (5.37%)  5.42%     (5.40%)  5.45%     (5.42%)  5.47%
500-999                 50,000-99,999   4.75           98.95     (5.38)   5.42      (5.41)   5.46      (5.43)   5.48
1,000-2,499           100,000-249,999   4.50           98.69     (5.39)   5.44      (5.43)   5.47      (5.45)   5.49
2,500-4,999           250,000-499,999   4.25           98.43     (5.41)   5.45      (5.44)   5.49      (5.46)   5.51
5,000-9,999           500,000-999,999   3.50           97.67     (5.45)   5.50      (5.48)   5.53      (5.50)   5.55
10,000-24,999     1,000,000- 2,499,999  3.00           97.17     (5.48)   5.52      (5.51)   5.56      (5.53)   5.58
25,000-49,999     2,500,000- 4,999,999  2.50           96.67     (5.51)   5.55      (5.54)   5.59      (5.56)   5.61
50,000 and over    5,000,000 and over   2.00           96.17     (5.53)   5.58      (5.57)   5.61      (5.59)   5.63
</TABLE>
 
--------------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                                                                         Estimated Long Term Return (3)
                                                              -----------------------------------------------------
          AMOUNT PURCHASED                         Public
-------------------------------------  Sales      Offering          Monthly         Quarterly       Semi-Annual
     Units              Dollars        Charge     Price (1)         Payment          Payment          Payment
----------------  -------------------  ------    -----------     -------------    -------------    -------------
<S>               <C>                  <C>       <C>         <C>                <C>              <C>
50-499                 $5,000-$49,999   4.90 %   $     99.11          5.54%            5.57%            5.59%
500-999                 50,000-99,999   4.75           98.95          5.55             5.58             5.60
1,000-2,499           100,000-249,999   4.50           98.69          5.57             5.60             5.62
2,500-4,999           250,000-499,999   4.25           98.43          5.58             5.61             5.63
5,000-9,999           500,000-999,999   3.50           97.67          5.63             5.66             5.67
10,000-24,999     1,000,000- 2,499,999  3.00           97.17          5.66             5.68             5.70
25,000-49,999     2,500,000- 4,999,999  2.50           96.67          5.68             5.71             5.73
50,000 and over    5,000,000 and over   2.00           96.17          5.71             5.74             5.76
</TABLE>
 
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
 
(1) As of the business day prior to the Date of Deposit. Units are offered at
    the Public Offering Price plus accrued interest.
(2) All figures as of the business day prior to the Date of Deposit. Figures in
    brackets represent the current return. The first year's estimated current
    returns are slightly lower than those for subsequent years because a portion
    of the monies received in the first year only will be treated as a return of
    principal due to the inclusion in the portfolio of "when issued" or other
    Bonds having delivery dates after the date of settlement for a purchase made
    on the Date of Deposit.
(3) In contrast to Estimated Current Return, Estimated Long Term Return reflects
    the amortization of premium or accretion of discount, if any, on the bonds
    in the Trust's portfolio.
 
--------------------------------------------------------------------------------
 
INTEREST DISTRIBUTIONS TO UNITHOLDERS   Unitholders may elect to have interest
distributions made on a monthly, quarterly, or semi-annual basis. Record Dates
are May 1 and November 1 for semi-annual distributions; February 1, May 1,
August 1 and November 1 for quarterly distributions; and the first of each month
for monthly distributions. Details of interest distributions per unit under the
various plans appear in the following table based upon estimated net annual
interest income at the Date of Deposit:
--------------------------------------------------------------------------------
 
   
<TABLE>
<CAPTION>
                                                                                                          Normal
                                                                                                      Distributions
Massachusetts Insured Trust                       1995                             1996                 per Year +
<S>                                     <C>            <C>            <C>            <C>            <C>
----------------------------------------------------------------------------------------------------  --------------
Record Date*..........................       10/1           11/1            2/1            5/1
Distribution Date.....................      10/15          11/15           2/15           5/15
--------------------------------------------------------------------------------------------------------------------
Monthly Distribution Plan.............  $   .5367(1)                                                  $  5.3679
                                                          --------  $.4473 every month  --------
Quarterly Distribution Plan...........  $   .5367(1)   $   .4497(2)   $  1.3491      $  1.3491        $  5.3999
Semi-Annual Distribution Plan.........  $   .5367(1)   $   .4515(3)                  $  2.7090        $  5.4189
--------------------------------------------------------------------------------------------------------------------
<FN>
  * Record Dates for semi-annual distributions are May 1 and November 1; for quarterly distributions, they are February 1, May 1,
    August 1 and November 1. Record Dates for monthly distributions are the first day of each month.
(1) The first distribution will be paid to all Unitholders, regardless of the distribution plan selected. Such distribution may
    be more or less than a regular monthly distribution.
(2) The second distribution under the quarterly distribution plan represents a 1-month distribution; subsequent quarterly
    distributions will be regular 3-month distributions.
(3) The second distribution under the semi-annual distribution plan represents a 1-month distribution; subsequent semi-annual
    distributions will be regular 6-month distributions.
</TABLE>
    
 
+ Interest for Unitholders of this series began to accrue as of the Date of
Deposit. Units purchased on the Date of Deposit will have $.07 of accrued
interest that will be added to the Public Offering Price on the Settlement Date.
After provision for expenses of the Fund, the daily rate of accrual from the
Date of Deposit to the first Record Date is $.01491 per unit per day.
Consequently, on the first Record Date (10/01/95), accrued interest will total
$0.5367 per unit for the 36-day period. All interest accrued from the Date of
Deposit to the first Record Date, less expenses, will be distributed on the
first Distribution Date to Unitholders of Record as of the first Record Date.
The first payment to all Unitholders of Record on 10/01/95 is $.5367 per unit.
After the first Record Date daily rates of accrual are:
              Monthly - $0.01491              Quarterly - $0.01499
                             Semi-Annual - $0.01505
This daily rate of accrual, and the annual distributions shown above, will
remain the same as long as the portfolio size and composition remain the same.
 
--------------------------------------------------------------------------------
 
                                                          821
<PAGE>
-------------------------------------------------------
 
AVERAGE PORTFOLIO LIFE   The average maturity of portfolio bonds is 26.1 years.
The first bond is scheduled to mature in July, 2013, with the last bond maturity
being November, 2028.
 
-------------------------------------------------------
 
BONDS INSURED BY MBIA   Each bond in this Nuveen Insured series has been
insured* by the Municipal Bond Investors Assurance Corporation, which guarantees
timely payments of principal and interest. Premium payments have been fully paid
by the Date of Deposit.
 
-------------------------------------------------------
 
CALL PROTECTION   Bonds are first subject to optional redemption by the issuers
in the years and at the prices shown under the Redemption Provisions column in
the Schedule of Investments. Unless otherwise stated, in subsequent years, bonds
are redeemable at declining prices, but not usually below par value. Some issues
or some portions of issues may also be subject to sinking fund redemption or
extraordinary redemption without premium prior to the dates shown.
 
-------------------------------------------------------
 
NO CHARGE FOR REDEMPTION   The Trustee, United States Trust Company of New York,
will redeem units at net asset value. In addition, John Nuveen & Co.
Incorporated intends to maintain a secondary market for this Nuveen Tax-Exempt
Unit Trust. Inasmuch as all securities investments are subject to market price
fluctuation, net asset value at the time of redemption could be more or less
than the initial investment.
 
-------------------------------------------------------
 
REINVESTMENT OPTIONS   Specify automatic reinvestment of trust income, with no
sales charge, to earn compounded dividends with Nuveen mutual funds.
 
-------------------------------------------------------
 
UNITS OF THE TRUST ARE NOT DEPOSITS OR OBLIGATIONS OF, OR GUARANTEED OR ENDORSED
BY, ANY BANK AND ARE NOT FEDERALLY INSURED OR OTHERWISE PROTECTED BY THE FEDERAL
DEPOSIT INSURANCE CORPORATION, THE FEDERAL RESERVE BOARD OR ANY OTHER AGENCY AND
INVOLVE INVESTMENT RISK, INCLUDING THE POSSIBLE LOSS OF PRINCIPAL.
 
-------------------------------------------------------
 
* Insurance relates specifically to the bonds and not to the units or to the
  market value of units. Terms of the insurance are more fully described in the
  prospectus. No representation is made as to the insurer's ability to meet its
  commitments. See Section 5 of the prospectus for details.
 
-------------------------------------------------------
 
FOR A PROSPECTUS CONTAINING MORE COMPLETE INFORMATION, INCLUDING CHARGES AND
EXPENSES, ON THIS NUVEEN TAX-EXEMPT UNIT TRUST AND ANY OTHER NUVEEN FUND, CALL
YOUR BROKER . . . OR NUVEEN AT
 
                                 1-800-257-8787
 
READ THE PROSPECTUS CAREFULLY BEFORE YOU INVEST OR SEND MONEY.


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