NUVEEN TAX EXEMPT UNIT TRUST SERIES 831
497, 1995-10-23
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<PAGE>
NUVEEN  Tax-Exempt Unit Trusts
     NUVEEN
     NATIONAL
     INSURED
     TRUST 306
 
            Estimated Current Return
            5.21% to 5.42%
            as of 10/19/95
 
            Estimated Long Term Return
            5.27% to 5.55%
             100,000 units in a
             diversified $10,000,000
             portfolio of tax-exempt
             bonds rated "AAA"
                  Cusip:
                  6710A4 371 Monthly Payment Option
                  6710A4 389 Quarterly Payment Option
                  6710A4 397 Semi-Annual Payment Option
 
                  Registered in all states
                    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, NATIONAL INSURED TRUST 306
SCHEDULE OF INVESTMENTS
DATE OF DEPOSIT OCTOBER 20, 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    California Statewide Communities Development Authority,            2003 at 102          AAA           Aaa
                  Certificates of Participation (Sisters of Charity of
                  Leavenworth Health Services Corporation), 5.00% Due
                  12/1/23. (Original issue discount bonds delivered on or
                  about February 2, 1994 at a price of 92.625% of principal
                  amount.)
   1,000,000    Imperial Irrigation District, California, Certificates of          2004 at 102          AAA           Aaa
                  Participation (1994 Electric System Project), 6.00% Due
                  11/1/15.
   1,000,000    Chicago Metropolitan Housing Development Corporation               2004 at 100          AAA           Aaa
                  (Chicago, Illinois), Housing Development Revenue Refunding
                  Bonds (FHA-Insured Mortgage Loan-Section 8 Assisted
                  Project-Academy Square), Series 1993A, 5.60% Due 10/1/25.
   1,000,000    Illinois Health Facilities Authority, Revenue Bonds, Series        2003 at 102          AAA           Aaa
                  1993 (Rush-Presbyterian-St. Luke's Medical Center
                  Obligated Group), 5.50% Due 11/15/25.
   1,000,000    City of Bloomington, Indiana, Monroe County, Indiana,              2005 at 102          AAA           Aaa
                  Waterworks Revenue Bonds of 1995, 5.80% Due 1/1/20.
   1,000,000    City of Cedar Rapids, Iowa, Pollution Control Revenue              2003 at 102          AAA           Aaa
                  Refunding Bonds (Iowa Electric Light and Power Company
                  Project), Series 1993, 5.50% Due 11/1/23.
   1,000,000    Woodbury County, Iowa, Health System Revenue Refunding Bonds       2005 at 102          AAA           Aaa
                  (St. Luke's Obligated Group), Series 1995A, 5.50% Due
                  9/1/16. (When issued.)
   1,000,000    Massachusetts Bay Transportation Authority, General                2004 at 102          AAA           Aaa
                  Transportation System Bonds, 1994 Series B Bonds, 5.875%
                  Due 3/1/19. (General Obligation Bonds.)
     500,000    Dormitory Authority of the State of New York, State                2005 at 102          AAA           Aaa
                  University Educational Facilities Revenue Bonds, Series
                  1995A, 6.00% Due 5/15/25.
     500,000    New York City, New York, Municipal Water Finance Authority,        2005 at 101          AAA           Aaa
                  Water and Sewer System Revenue Bonds, Fiscal 1996 Series
                  A, 6.00% Due 6/15/25.
   1,000,000    Sabine River Authority of Texas, Collateralized Pollution          2003 at 102          AAA           Aaa
                  Control Revenue Refunding Bonds (Texas Utilities Electric
                  Company Project), Series 1993B Bonds, 5.85% Due 5/1/22.
     500,000    Washington Public Power Supply System, Nuclear Project No. 3       No Optional          AAA           Aaa
                  Refunding Revenue Bonds, Series 1993C, 0.00% Due 7/1/18.            Call
                  (Original issue discount bonds delivered on or about
                  September 23, 1993 at a price of 24.553% of principal
                  amount.)
  ----------
  $10,000,000
  ----------
  ----------
</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 a compounding factor, 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 %   $     99.55          5.21%            5.24%            5.26%
500-999                 50,000-99,999   4.75           99.39          5.22             5.25             5.27
1,000-2,499           100,000-249,999   4.50           99.13          5.23             5.26             5.28
2,500-4,999           250,000-499,999   4.25           98.87          5.24             5.28             5.29
5,000-9,999           500,000-999,999   3.50           98.10          5.28             5.32             5.34
10,000-24,999     1,000,000- 2,499,999  3.00           97.60          5.31             5.34             5.36
25,000-49,999     2,500,000- 4,999,999  2.50           97.10          5.34             5.37             5.39
50,000 and over    5,000,000 and over   2.00           96.60          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 %   $     99.55          5.27%            5.31%            5.33%
500-999                 50,000-99,999   4.75           99.39          5.27             5.31             5.33
1,000-2,499           100,000-249,999   4.50           99.13          5.30             5.34             5.36
2,500-4,999           250,000-499,999   4.25           98.87          5.31             5.35             5.37
5,000-9,999           500,000-999,999   3.50           98.10          5.37             5.41             5.43
10,000-24,999     1,000,000- 2,499,999  3.00           97.60          5.41             5.45             5.47
25,000-49,999     2,500,000- 4,999,999  2.50           97.10          5.45             5.49             5.51
50,000 and over    5,000,000 and over   2.00           96.60          5.49             5.53             5.55
</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.
 
- --------------------------------------------------------------------------------
 
REINVESTMENT OPTIONS   Specify automatic reinvestment of trust income, with no
sales charge, to earn compounded dividends with Nuveen mutual funds.
- --------------------------------------------------------------------------------
 
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
                                          1995                                  1996                                 per Year +
<S>                                     <C>            <C>            <C>            <C>            <C>            <C>
- -------------------------------------------------------------------------------------------------------------      --------------
Record Date*..........................       12/1            2/1            5/1            8/1           11/1
Distribution Date.....................      12/15           2/15           5/15           8/15          11/15
- ---------------------------------------------------------------------------------------------------------------------------------
Monthly Distribution Plan.............  $   .5899(1)                                                               $  5.1836
                                                             --------    $.4317 every month    --------
Quarterly Distribution Plan...........  $   .5899(1)   $   .8688(2)   $  1.3032      $  1.3032      $  1.3032      $  5.2156
Semi-Annual Distribution Plan.........  $   .5899(1)                  $  2.1810(3)                  $  2.6172      $  5.2346
- ---------------------------------------------------------------------------------------------------------------------------------
</TABLE>
 
  * 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.
    Distribution Dates under each distribution plan are the fifteenth day of the
    month in which the respective Record Date occurred.
(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
    2-month distribution; subsequent quarterly distributions will be regular
    3-month distributions.
(3) The second distribution under the semi-annual distribution plan represents a
    5-month distribution; subsequent semi-annual distributions will be regular
    6-month distributions.
+ 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 $.01439 per unit per day.
Consequently, on the first Record Date (12/01/95), accrued interest will total
$0.5899 per unit for the 41-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 12/01/95 is $.5899 per unit.
After the first Record Date daily rates of accrual are:
              Monthly - $0.01439              Quarterly - $0.01448
                             Semi-Annual - $0.01454
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.
 
- --------------------------------------------------------------------------------
<PAGE>
- -------------------------------------------------------
 
DIVERSIFICATION OF PORTFOLIO INCOME
There are 12 Tax-exempt bond issues in this trust; this diversified portfolio
yields current income from issuers in 7 states .
 
<TABLE>
<S>                    <C>        <C>        <C>                    <C>        <C>
- -------------------------------------------------------
                         Percent                                      Percent
                        of Total                                     of Total
                          Income                                       Income
- -------------------------------------------------------
California                  15.7  %          Massachusetts               10.9  %
Iowa                        20.3             New York                    11.1
Illinois                    20.5             Texas                       10.8
Indiana                     10.7
</TABLE>
 
- -------------------------------------------------------
AVERAGE PORTFOLIO LIFE   The average maturity of portfolio bonds is 25.8 years.
The first bond is scheduled to mature in November, 2015, with the last bond
maturity being November, 2025.
 
- -------------------------------------------------------
BONDS INSURED BY MBIA   Each bond in this Nuveen Insured series has been
insured* by the MBIA Insurance 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 Optional 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.
 
- -------------------------------------------------
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.
 
- -------------------------------------------------------
FOR A PROSPECTUS CONTAINING MORE COMPLETE INFORMATION, INCLUDING CHARGES, RISKS
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.
831
<PAGE>
NUVEEN  Tax-Exempt Unit Trusts
     NUVEEN
      COLORADO
     INSURED
     TRUST 61
 
            Estimated Current Return
            4.94% to 5.15%
            as of 10/19/95
 
            Estimated Long Term Return
            5.03% to 5.32%
             35,000 units in a
             diversified $3,500,000
             portfolio of tax-exempt
             bonds rated "AAA"
                  Cusip:
                  6706E9 341 Monthly Payment Option
                  6706E9 358 Quarterly Payment Option
                  6706E9 366 Semi-Annual Payment Option
 
                  Registered in Colorado
                    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, COLORADO INSURED TRUST 61
SCHEDULE OF INVESTMENTS
DATE OF DEPOSIT OCTOBER 20, 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    City of Aurora, Colorado, General Obligation Water Refunding       2003 at 100          AAA           Aaa
                  Bonds, Series 1993, 4.75% Due 11/1/14. (Original issue
                  discount bonds delivered on or about October 25, 1993 at a
                  price of 94.899% of principal amount.)
     500,000    City of Colorado Springs, Colorado, Utilities System               2004 at 100          AAA           Aaa
                  Improvement and Refunding Revenue Bonds, Series 1994A,
                  5.125% Due 11/15/23.
     500,000    City and County of Denver, Colorado, Airport System Revenue        2005 at 102          AAA           Aaa
                  Bonds, Series 1995A, 5.70% Due 11/15/25.
     500,000    Mesa County, Colorado, Revenue Bonds, Series 1994 (Sisters         2003 at 102          AAA           Aaa
                  of Charity of Leavenworth Health Services Corporation),
                  5.00% Due 12/1/23. (Original issue discount bonds
                  delivered on or about February 2, 1994 at a price of
                  94.00% of principal amount.)
     500,000    Metro Wastewater Reclamation District, Colorado, Sewer             2003 at 100          AAA           Aaa
                  Refunding Bonds, Series 1993B, 4.75% Due 4/1/12. (Original
                  issue discount bonds delivered on or about December 29,
                  1993 at a price of 94.39% of principal amount.)
     500,000    Morgan County, Colorado, Pollution Control Refunding Revenue       2003 at 101          AAA           Aaa
                  Bonds, 1993 Series A (Public Service Company of Colorado
                  Project), 5.50% Due 6/1/12.
     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 a compounding factor, 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 %   $     99.80          4.94%            4.98%            4.99%
500-999                 50,000-99,999   4.75           99.64          4.95             4.98             5.00
1,000-2,499           100,000-249,999   4.50           99.38          4.96             5.00             5.02
2,500-4,999           250,000-499,999   4.25           99.12          4.98             5.01             5.03
5,000-9,999           500,000-999,999   3.50           98.35          5.02             5.05             5.07
10,000-24,999     1,000,000- 2,499,999  3.00           97.85          5.04             5.07             5.09
25,000-49,999     2,500,000- 4,999,999  2.50           97.34          5.07             5.10             5.12
50,000 and over    5,000,000 and over   2.00           96.85          5.09             5.13             5.15
</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 %   $     99.80          5.03%            5.07%            5.09%
500-999                 50,000-99,999   4.75           99.64          5.04             5.08             5.10
1,000-2,499           100,000-249,999   4.50           99.38          5.06             5.10             5.12
2,500-4,999           250,000-499,999   4.25           99.12          5.08             5.12             5.14
5,000-9,999           500,000-999,999   3.50           98.35          5.14             5.18             5.20
10,000-24,999     1,000,000- 2,499,999  3.00           97.85          5.18             5.22             5.24
25,000-49,999     2,500,000- 4,999,999  2.50           97.34          5.22             5.26             5.28
50,000 and over    5,000,000 and over   2.00           96.85          5.26             5.30             5.32
</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
                                          1995                                  1996                                 per Year +
<S>                                     <C>            <C>            <C>            <C>            <C>            <C>
- -------------------------------------------------------------------------------------------------------------      --------------
Record Date*..........................       12/1            2/1            5/1            8/1           11/1
Distribution Date.....................      12/15           2/15           5/15           8/15          11/15
- ---------------------------------------------------------------------------------------------------------------------------------
Monthly Distribution Plan.............  $   .5617(1)                                                               $  4.9335
                                                             --------    $.4110 every month    --------
Quarterly Distribution Plan...........  $   .5617(1)   $   .8274(2)   $  1.2411      $  1.2411      $  1.2411      $  4.9655
Semi-Annual Distribution Plan.........  $   .5617(1)                  $  2.0760(3)                  $  2.4912      $  4.9845
- ---------------------------------------------------------------------------------------------------------------------------------
</TABLE>
 
  * 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.
    Distribution Dates under each distribution plan are the fifteenth day of the
    month in which the respective Record Date occurred.
(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
    2-month distribution; subsequent quarterly distributions will be regular
    3-month distributions.
(3) The second distribution under the semi-annual distribution plan represents a
    5-month distribution; subsequent semi-annual distributions will be regular
    6-month distributions.
+ 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 $.01370 per unit per day.
Consequently, on the first Record Date (12/01/95), accrued interest will total
$0.5617 per unit for the 41-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 12/01/95 is $.5617 per unit.
After the first Record Date daily rates of accrual are:
              Monthly - $0.01370              Quarterly - $0.01379
                             Semi-Annual - $0.01384
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.
 
- --------------------------------------------------------------------------------
 
                                                          831
<PAGE>
- -------------------------------------------------------
 
AVERAGE PORTFOLIO LIFE   The average maturity of portfolio bonds is 23.6 years.
The first bond is scheduled to mature in April, 2012, with the last bond
maturity being November, 2025.
 
- -------------------------------------------------------
 
BONDS INSURED BY MBIA   Each bond in this Nuveen Insured series has been
insured* by the MBIA Insurance 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 Optional 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, The Chase Manhattan Bank, N.A., 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.
 
- -------------------------------------------------------
 
FOR A PROSPECTUS CONTAINING MORE COMPLETE INFORMATION, INCLUDING CHARGES, RISKS
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
      PENNSYLVANIA
     INSURED
     TRUST 204
 
            Estimated Current Return
            First
            Year: 5.08% to 5.29%
            Subsequent
            Years: 5.10% to 5.31%
            as of 10/19/95
 
            Estimated Long Term Return
            5.13% to 5.41%
             35,000 units in a
             diversified $3,500,000
             portfolio of tax-exempt
             bonds rated "AAA"
                  Cusip:
                  6706H8 340 Monthly Payment Option
                  6706H8 357 Quarterly Payment Option
                  6706H8 365 Semi-Annual Payment Option
 
                  Registered in Pennsylvania
                    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, PENNSYLVANIA INSURED TRUST 204
SCHEDULE OF INVESTMENTS
DATE OF DEPOSIT OCTOBER 20, 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    Pennsylvania Higher Educational Facilities Authority               2005 at 102          AAA           Aaa
                  (Commonwealth of Pennsylvania), Saint Joseph's University
                  Revenue Bonds, Series of 1995, 5.875% Due 7/15/25.
     500,000    Pennsylvania Higher Educational Facilities Authority               2004 at 100          AAA           Aaa
                  (Commonwealth of Pennsylvania), Revenue Bonds, State
                  System of Higher Education, Series J, 5.625% Due 6/15/19.
     500,000    Pennsylvania Intergovernmental Cooperation Authority,              2003 at 100          AAA           Aaa
                  Special Tax Revenue Bonds (City of Philadelphia Funding
                  Program), Series of 1993, 5.60% Due 6/15/15.
     300,000    State Public School Authority (Commonwealth of                     2005 at 100          AAA           Aaa
                  Pennsylvania), College Revenue Bonds (Westmoreland County
                  Community College Project), Series F of 1995, 5.50% Due
                  10/15/15. (When issued.)
     400,000    County of Berks, Pennsylvania, General Obligation Bonds,           2005 at 100          AAA           Aaa
                  Series of 1995, 5.85% Due 11/15/18.
     500,000    Lehigh County (Pennsylvania) General Purpose Authority,            2005 at 102          AAA           Aaa
                  Hospital Revenue Bonds (Lehigh Valley Hospital, Inc.),
                  Series A of 1995, 5.875% Due 7/1/15.
     500,000    Philadelphia Authority for Industrial Development                  2003 at 102          AAA           Aaa
                  (Pennsylvania), Project Revenue Refunding Bonds (PGH
                  Development Corporation), Series of 1993, 5.25% Due
                  7/1/17. (Original issue discount bonds delivered on or
                  about August 18, 1993 at a price of 93.005% of principal
                  amount.)
     100,000    City of Philadelphia, Pennsylvania, Water and Wastewater           2003 at 102          AAA           Aaa
                  Revenue Bonds, Series 1993, 5.25% Due 6/15/23. (Original
                  issue discount bonds delivered on or about August 26, 1993
                  at a price of 92.499% of principal amount.)
     200,000    Municipal Authority of Westmoreland County (Westmoreland           No Optional          AAA           Aaa
                  County, Pennsylvania), Municipal Service Revenue Bonds,             Call
                  Series of 1995A, 0.00% Due 8/15/20. (Original issue
                  discount bonds delivered on or about July 27, 1995 at a
                  price of 21.928% 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 a compounding factor, 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 %   $     99.60     (5.08%)  5.10%     (5.12%)  5.13%     (5.13%)  5.15%
500-999                 50,000-99,999   4.75           99.44     (5.09)   5.11      (5.12)   5.14      (5.14)   5.16
1,000-2,499           100,000-249,999   4.50           99.18     (5.10)   5.12      (5.14)   5.15      (5.16)   5.17
2,500-4,999           250,000-499,999   4.25           98.92     (5.12)   5.13      (5.15)   5.17      (5.17)   5.19
5,000-9,999           500,000-999,999   3.50           98.16     (5.16)   5.17      (5.19)   5.21      (5.21)   5.23
10,000-24,999     1,000,000- 2,499,999  3.00           97.65     (5.18)   5.20      (5.22)   5.23      (5.24)   5.25
25,000-49,999     2,500,000- 4,999,999  2.50           97.15     (5.21)   5.23      (5.24)   5.26      (5.26)   5.28
50,000 and over    5,000,000 and over   2.00           96.65     (5.24)   5.25      (5.27)   5.29      (5.29)   5.31
</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 %   $     99.60          5.13%            5.15%            5.18%
500-999                 50,000-99,999   4.75           99.44          5.13             5.16             5.18
1,000-2,499           100,000-249,999   4.50           99.18          5.16             5.19             5.21
2,500-4,999           250,000-499,999   4.25           98.92          5.17             5.20             5.22
5,000-9,999           500,000-999,999   3.50           98.16          5.24             5.27             5.29
10,000-24,999     1,000,000- 2,499,999  3.00           97.65          5.28             5.31             5.33
25,000-49,999     2,500,000- 4,999,999  2.50           97.15          5.32             5.35             5.37
50,000 and over    5,000,000 and over   2.00           96.65          5.36             5.39             5.41
</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
                                          1995                                  1996                                 per Year +
<S>                                     <C>            <C>            <C>            <C>            <C>            <C>
- -------------------------------------------------------------------------------------------------------------      --------------
Record Date*..........................       12/1            2/1            5/1            8/1           11/1
Distribution Date.....................      12/15           2/15           5/15           8/15          11/15
- ---------------------------------------------------------------------------------------------------------------------------------
Monthly Distribution Plan.............  $   .5781(1)                                                               $  5.0788
                                                             --------    $.4230 every month    --------
Quarterly Distribution Plan...........  $   .5781(1)   $   .8514(2)   $  1.2771      $  1.2771      $  1.2771      $  5.1108
Semi-Annual Distribution Plan.........  $   .5781(1)                  $  2.1360(3)                  $  2.5632      $  5.1298
- ---------------------------------------------------------------------------------------------------------------------------------
</TABLE>
 
  * 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.
    Distribution Dates under each distribution plan are the fifteenth day of the
    month in which the respective Record Date occurred.
(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
    2-month distribution; subsequent quarterly distributions will be regular
    3-month distributions.
(3) The second distribution under the semi-annual distribution plan represents a
    5-month distribution; subsequent semi-annual distributions will be regular
    6-month distributions.
+ 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 $.01410 per unit per day.
Consequently, on the first Record Date (12/01/95), accrued interest will total
$0.5781 per unit for the 41-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 12/01/95 is $.5781 per unit.
After the first Record Date daily rates of accrual are:
              Monthly - $0.01410              Quarterly - $0.01419
                             Semi-Annual - $0.01424
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.
 
- --------------------------------------------------------------------------------
 
                                                          831
<PAGE>
- -------------------------------------------------------
 
AVERAGE PORTFOLIO LIFE   The average maturity of portfolio bonds is 22.9 years.
The first bond is scheduled to mature in June, 2015, with the last bond maturity
being July, 2025.
 
- -------------------------------------------------------
 
BONDS INSURED BY MBIA   Each bond in this Nuveen Insured series has been
insured* by the MBIA Insurance 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 Optional 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, The Chase Manhattan Bank, N.A., 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.
 
- -------------------------------------------------------
 
FOR A PROSPECTUS CONTAINING MORE COMPLETE INFORMATION, INCLUDING CHARGES, RISKS
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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