NUVEEN TAX FREE UNIT TRUST SERIES 956
497, 1997-08-18
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<PAGE>
                                                                          NUVEEN
   
NUVEEN VIRGINIA
TRADITIONAL UNIT TRUST 318                                                   956
    
 
- --------------------------------------------------------------------------------
 
   
<TABLE>
<S>                                                 <C>
ESTIMATED CURRENT RETURN:                           NUVEEN TAX-FREE UNIT TRUSTS:
4.87 - 5.07%                                        For the tax-sensitive, conservative investor.
ESTIMATED LONG-TERM RETURN:                         - Double Tax-Free
4.90 - 5.16%                                        - Dependable Income
DATE OF DEPOSIT: August 18, 1997                    - Diversified Portfolios
                                                    - Investment Grade Municipal Bonds
</TABLE>
    
 
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 FDIC OR
ANY OTHER FEDERAL AGENCY AND INVOLVE INVESTMENT RISK, INCLUDING THE POSSIBLE
LOSS OF PRINCIPAL.
 
- --------------------------------------------------------------------------------
 
QUICK FACTS ABOUT THIS UNIT TRUST
 
<TABLE>
<S>             <C>
Tax Status      Income is exempt from federal and state income
                taxes. Capital gains are taxable.
Total Principal $3,500,000 in 35,000 units
Average Life    25.4 years
Call Protection Earliest ordinary optional call is 2005
Minimum         $5,000 or 50 units, whichever is lower
Investment
Offering Price  $101.12 to $98.13 depending on the purchase amount
Cusip           6706LB 462 monthly payment plan
Numbers         6706LB 470 quarterly payment plan
                6706LB 488 semi-annual payment plan
Ratings of      As rated by Standard & Poor's, a division of The McGraw
Portfolio       Hill Companies
                or Moody's Investors Service, Inc.
                AAA               43%
                AA                57
                                  ---------
                                  100%
Registration    Registered in Virginia
</TABLE>
 
<TABLE>
<S>             <C>
Payment         Investors may choose to receive monthly, quarterly
Plans           or semi-annual interest payments.
Bond Calls      Most municipal bonds are subject to optional bond
                calls. Bonds are usually called at a premium price
                and generally not below par value.
Sales Charge    The sales charge is a one-time expense included in
                the Public Offering Price.
Letter          Investors may use a Letter of Intent to get
of Intent       reduced sales charges on purchases made over a
(LOI)           13-month period (and to take advantage of dollar
                cost averaging). Minimum LOI investment $50,000.
Redemptions     Units can be redeemed on any business day at no
                charge. Units are redeemed at their current market
                value.
Reinvestment    Interest income and returned principal can be
                reinvested with no sales charge into Nuveen tax-
                free mutual or money market funds. For more
                information obtain a prospectus.
</TABLE>
 
- --------------------------------------------------------------------------------
 
<TABLE>
<S>                          <C>
MATURITY DATES (Description of Chart)
2015-17                                            28.5%
2018-20                                            14.3%
2021-23                                            14.3%
2024-26                                            14.3%
2027+                                              28.6%
The earliest ordinary optional call date is 2005
 
YIELD COMPARISON AS OF 08/15/97*
  (Description of Yield Comparison Chart)
 
Nuveen UIT
     Yield                                         4.87%
     Tax Equivalent Yield                          8.05%
 
Treasury Bonds
     Yield                                         6.55%
     Tax Equivalent Yield                          6.95%
 
Corporate Bonds
</TABLE>
<PAGE>
<TABLE>
<S>                          <C>
     Yield                   7.33%
</TABLE>
 
 *COMPARES TRUST AS OF 08/15/97 WITH 30-YEAR TREASURY BONDS AND LEHMAN BROTHERS
  INVESTMENT GRADE LONG CORPORATE BOND INDEX AS OF 08/14/97. ASSUMES 39.5%
  FEDERAL AND STATE INCOME TAX RATE AND A 5.75% STATE INCOME TAX RATE. TREASURY
  BONDS ARE SUBJECT TO FEDERAL BUT NOT STATE INCOME TAXES; CORPORATE BONDS ARE
  GENERALLY SUBJECT TO BOTH. TREASURY BONDS, UNLIKE MUNICIPAL BONDS, ARE
  GUARANTEED BY THE U.S. GOVERNMENT.
<PAGE>
- --------------------------------------------------------------------------------
 
 BONDS THIS VIRGINIA TRADITIONAL UNIT TRUST CONTAINS
 
<TABLE>
<CAPTION>
                                                                                                        RATINGS
  PRINCIPAL                                                                              EARLIEST CALL ----------
    AMOUNT    BOND ISSUE                                                                 DATE AND PRICE S&P MOODY'S
 <C>        <S>                                                                          <C>           <C><C>
 ----------------------------------------------------------------------------------------------------------------
 $   500,000  Metropolitan Washington (D.C.) Airports Authority, Airport System Revenue                AA-   Aa3
              Bonds, Series 1997A, 5.375% Due 10/1/23.                                    2007 at 101
     500,000  Commonwealth Transportation Board, Commonwealth of Virginia, Transportation              AA   Aa2
              Program Revenue Bonds, Series 1997A (Oak Grove Connector, City of Chesa-
              peake), 5.25% Due 5/15/16.                                                  2007 at 101
     500,000  Chesapeake Bay Bridge and Tunnel District (Virginia), General Resolution                 AAA   Aaa
              Revenue Bonds, Refunding Series 1996, 5.25% Due 7/1/19. (MBIA Insured.)     2005 at 102
     500,000  Fairfax County Water Authority (Virginia), Water Refunding Revenue Bonds,                AA   Aa2
              Series 1997, 5.00% Due 4/1/29. (When issued.)                               2007 at 102
     500,000  City of Norfolk, Virginia, General Obligation Capital Improvement Bonds,                 AA   A1
              Series 1996, 5.25% Due 6/1/16. (Original issue discount bonds delivered on
              or about April 12, 1996 at a price of 94.073% of principal amount.)         2006 at 101
     500,000  Industrial Development Authority of The City of Norfolk (Virginia), Health               AAA   Aaa
              Care Revenue Bonds, Series 1997 (Bon Secours Health System), 5.25% Due
              8/15/26. (MBIA Insured.)                                                    2007 at 102
     500,000  Upper Occoquan Sewage Authority (Virginia), Regional Sewerage System                     AAA   Aaa
              Revenue Bonds, Series of 1995A, 4.75% Due 7/1/29. (Original issue discount
              bonds delivered on or about January 9, 1996 at a price of 91.422% of
              principal amount.)(MBIA Insured.)                                           2006 at 100
 ----------------------------------------------------------------------------------------------------------------
 $ 3,500,000  TOTAL         6 BONDS FROM VIRGINIA AND ONE BOND FROM THE DISTRICT OF COLUMBIA.
</TABLE>
 
- --------------------------------------------------------------------------------
 
HOW TO DETERMINE YOUR INCOME AND YIELD
 
HOW TO CALCULATE YOUR RETURN
 
<TABLE>
<S>                                                    <C>
The estimated current return is the net income         the sales charge, and returns are as of 08/15/97.
divided by the offering price. Estimated long-term     As of this date, Units are offered at the public
return is a measure of the return to the investor      offering price plus accrued interest to the
expected to be earned over the estimated life of       settlement date of $.04. Returns and prices will
the Unit Trust. The public offering prices, which      fluctuate.
include
</TABLE>
 
<TABLE>
<CAPTION>
                          Public                       Estimated Return (CURRENT/Long Term)
 Breakpoints             Offering     Sales      -------------------------------------------------
 Units / Dollars           Price      Charge      Monthly Plan   Quarterly Plan  Semi-Annual Plan
 <S>                   <C>            <C>        <C>     <C>     <C>     <C>     <C>     <C>   <C>  <C>
 50 / $5,000           $    101.12     4.90 %      4.87%   4.90%   4.90%   4.93%   4.92%   4.95 %
 500 / $50,000              100.97     4.75        4.88    4.90    4.91    4.93    4.93    4.95
 1,000 / $100,000           100.70     4.50        4.89    4.93    4.92    4.96    4.94    4.98
 2,500 / $250,000           100.44     4.25        4.90    4.94    4.93    4.97    4.95    4.99
 5,000 / $500,000            99.66     3.50        4.94    5.00    4.97    5.03    4.99    5.05
 10,000 / $1,000,000         99.14     3.00        4.97    5.04    5.00    5.07    5.02    5.09
 25,000 / $2,500,000         98.64     2.50        4.99    5.07    5.02    5.10    5.04    5.12
 50,000 / $5,000,000         98.13     2.00        5.02    5.11    5.05    5.14    5.07    5.16
</TABLE>
 
HOW TO DETERMINE YOUR
TAXABLE EQUIVALENT YIELD
 
The table shows the approximate yield an investor must get from a taxable
investment to match the estimated current return from this Unit Trust.
 
<TABLE>
<CAPTION>
                 Taxable Equivalent Yield (by tax
   UNIT TRUST                bracket)
     RETURN      32.0%   35.0%   39.5%      43.0%
 <C>             <S>     <C>     <C>     <C>       <C>
         4.87  % 7.16%   7.49%   8.05%      8.54 %
         4.88    7.18    7.51    8.07       8.56
         4.89    7.19    7.52    8.08       8.58
         4.90    7.21    7.54    8.10       8.60
         4.94    7.26    7.60    8.17       8.67
         4.97    7.31    7.65    8.21       8.72
         4.99    7.34    7.68    8.25       8.75
         5.02    7.38    7.72    8.30       8.81
</TABLE>
 
JOHN NUVEEN & CO. INCORPORATED
333 WEST WACKER DRIVE, CHICAGO, IL 60606
HOW TO CALCULATE YOUR INCOME
The table shows expected interest payments for monthly, quarterly and
semi-annual plans. Payments will remain relatively constant as long as the Unit
Trust's size, composition and expenses remain the same. The first record date is
10/01/97.
 
<TABLE>
<CAPTION>
                                                 Annual
                    First Payment   Payment      Income
 Payment Plan           Date       (per unit)  (per unit)
 <S>                <C>            <C>         <C>         <C>
 Initial payment
  (all plans)           10/15/97   $   .5878
 Monthly plan           11/15/97       .4101   $ 4.9242
 Quarterly plan         11/15/97       .4128
                         2/15/98      1.2384     4.9562
 Semi-annual plan       11/15/97       .4146
                         5/15/98      2.4876     4.9752
 EXAMPLE OF HOW TO CALCULATE YOUR ESTIMATED INCOME:
 $10,000       DIVIDED  BY 101.16 =  98.853
 investment       offering price     # of units
 (as of           and accrued        purchased
 08/15/97)        interest
 98.853       X   $4.9242        =   $486.77
 # of units       annual income      annual income
 purchased        per unit
                  (monthly plan)
</TABLE>
<PAGE>
   
NUVEEN CALIFORNIA                                                         NUVEEN
INSURED UNIT TRUST 291                                                       956
    
 
- --------------------------------------------------------------------------------
 
   
<TABLE>
<S>                                                 <C>
RATED: "AAA"                                        NUVEEN TAX-FREE UNIT TRUSTS:
All bonds in this Unit Trust are insured by MBIA    For the tax-sensitive, conservative investor.
Insurance Corporation. As a result, the bonds are   - Double Tax-Free
rated Aaa by Moody's Investors Service, Inc.        - Dependable Income
and/or AAA by Standard & Poor's, the highest        - Diversified Portfolios
rating given by each agency.                        - Top-Rated Municipal Bonds
ESTIMATED CURRENT RETURN:                           DATE OF DEPOSIT: August 18, 1997
4.86 - 5.06%
ESTIMATED LONG-TERM RETURN:
4.88 - 5.14%
</TABLE>
    
 
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 FDIC OR
ANY OTHER FEDERAL AGENCY AND INVOLVE INVESTMENT RISK, INCLUDING THE POSSIBLE
LOSS OF PRINCIPAL.
 
- --------------------------------------------------------------------------------
 
QUICK FACTS ABOUT THIS UNIT TRUST
 
<TABLE>
<S>             <C>
Tax Status      Income is exempt from federal and state income
                taxes. Capital gains are taxable.
Total Principal $3,500,000 in 35,000 units
Average Life    25.8 years
Call Protection Earliest ordinary optional call is 2005
Minimum         $5,000 or 50 units, whichever is lower
Investment
Offering Price  $100.60 to $97.62 depending on the purchase amount
Cusip           67065A 645 monthly payment plan
Numbers         67065A 652 quarterly payment plan
                67065A 660 semi-annual payment plan
Insurance       Individual bonds (not units) are fully insured by
                MBIA Insurance Corporation, which guarantees
                timely payment of interest and principal.
Registration    Registered in California
</TABLE>
 
<TABLE>
<S>             <C>
Payment         Investors may choose to receive monthly, quarterly
Plans           or semi-annual interest payments.
Bond Calls      Most municipal bonds are subject to optional bond
                calls. Bonds are usually called at a premium price
                and generally not below par value.
Sales Charge    The sales charge is a one-time expense included in
                the Public Offering Price.
Letter          Investors may use a Letter of Intent to get
of Intent       reduced sales charges on purchases made over a
(LOI)           13-month period (and to take advantage of dollar
                cost averaging). Minimum LOI investment $50,000.
Redemptions     Units can be redeemed on any business day at no
                charge. Units are redeemed at their current market
                value.
Reinvestment    Interest income and returned principal can be
                reinvested with no sales charge into Nuveen tax-
                free mutual or money market funds. For more
                information obtain a prospectus.
</TABLE>
 
- --------------------------------------------------------------------------------
 
<TABLE>
<S>                          <C>
MATURITY DATES (Description of Chart)
2019-20                                            28.6%
2021-22                                            17.9%
2023-24                                            14.3%
2025-26                                            24.9%
2027+                                              14.3%
The earliest ordinary optional call date is 2005
 
YIELD COMPARISON AS OF 08/15/97*
  (Description of Yield Comparison Chart)
 
Nuveen UIT
     Yield                                         4.86%
     Tax Equivalent Yield                          8.38%
 
Treasury Bonds
     Yield                                         6.55%
     Tax Equivalent Yield                          7.22%
 
Corporate Bonds
     Yield                   7.33%
</TABLE>
 
<PAGE>
 *COMPARES TRUST AS OF 08/15/97 WITH 30-YEAR TREASURY BONDS AND LEHMAN BROTHERS
  INVESTMENT GRADE LONG CORPORATE BOND INDEX AS OF 08/14/97. ASSUMES 42.0%
  FEDERAL AND STATE INCOME TAX RATE AND A 9.30% STATE INCOME TAX RATE. TREASURY
  BONDS ARE SUBJECT TO FEDERAL BUT NOT STATE INCOME TAXES; CORPORATE BONDS ARE
  GENERALLY SUBJECT TO BOTH. TREASURY BONDS, UNLIKE MUNICIPAL BONDS, ARE
  GUARANTEED BY THE U.S. GOVERNMENT.
 
CALL 1.800.257.8787 FOR A PROSPECTUS CONTAINING MORE COMPLETE INFORMATION
INCLUDING CHARGES AND EXPENSES.
READ THE PROSPECTUS CAREFULLY BEFORE INVESTING.
<PAGE>
- --------------------------------------------------------------------------------
 
 BONDS THIS CALIFORNIA INSURED UNIT TRUST CONTAINS
 
<TABLE>
<CAPTION>
                                                                                                        RATINGS
  PRINCIPAL                                                                              EARLIEST CALL ----------
    AMOUNT    BOND ISSUE                                                                 DATE AND PRICE S&P MOODY'S
 <C>        <S>                                                                          <C>           <C><C>
 ----------------------------------------------------------------------------------------------------------------
 $   500,000  State of California, Department of Water Resources, Central Valley Project, 2006 at 101.5 AAA   Aaa
              Water System Revenue Bonds, Series Q, 5.375% Due 12/1/27.
     125,000  Burbank Unified School District (Los Angeles County, California), General   No Optional  AAA   Aaa
              Obligation Bonds, 1997 Election, Series A, 0.00% Due 8/1/22. (Original          Call
              issue discount bonds will be delivered on or about August 21, 1997 at a
              price of 24.611% of principal amount.)(When issued.)
     500,000  Eastern Municipal Water District (California), Water and Sewer Revenue      2007 at 101  AAA   Aaa
              Refunding Certificates of Participation, Series 1997A, 5.25% Due 7/1/23.
     500,000  Los Angeles County Metropolitan Transportation Authority (California),      2005 at 100  AAA   Aaa
              Proposition C Sales Tax Revenue Bonds, Second Senior Bonds, Series 1995-A,
              5.00% Due 7/1/25. (Original issue discount bonds delivered on or about July
              26, 1995 at a price of 88.18% of principal amount.)
     500,000  Port of Oakland, California, Refunding Revenue Bonds, 1997 Series I, 5.60%  2007 at 102  AAA   Aaa
              Due 11/1/19.
     500,000  San Francisco State Building Authority (California), Lease Revenue Bonds    2006 at 102  AAA   Aaa
              (State Of California San Francisco Civic Center Complex), 1996 Series A,
              5.25% Due 12/1/21.
     500,000  San Jose-Santa Clara Clean Water Financing Authority (California), Sewer    2005 at 101  AAA   Aaa
              Revenue Series 1995A Bonds, 5.375% Due 11/15/20.
     375,000  Commonwealth of Puerto Rico, Public Improvement Bonds of 1997, 5.375% Due   2007 at 100  AAA   Aaa
              7/1/25. (Original issue discount bonds delivered on or about April 3, 1997
              at a price of 93.725% of principal amount.)(General Obligation Bonds.)
 ----------------------------------------------------------------------------------------------------------------
 $ 3,500,000  TOTAL         7 BONDS FROM CALIFORNIA AND ONE BOND FROM THE TERRITORY OF PUERTO RICO.
</TABLE>
 
- --------------------------------------------------------------------------------
 
HOW TO DETERMINE YOUR INCOME AND YIELD
 
HOW TO CALCULATE YOUR RETURN
 
<TABLE>
<S>                                                    <C>
The estimated current return is the net income         the sales charge, and returns are as of 08/15/97.
divided by the offering price. Estimated long-term     As of this date, Units are offered at the public
return is a measure of the return to the investor      offering price plus accrued interest to the
expected to be earned over the estimated life of       settlement date of $.04. Returns and prices will
the Unit Trust. The public offering prices, which      fluctuate.
include
</TABLE>
 
<TABLE>
<CAPTION>
                          Public                       Estimated Return (CURRENT/Long Term)
 Breakpoints             Offering     Sales      -------------------------------------------------
 Units / Dollars           Price      Charge      Monthly Plan   Quarterly Plan  Semi-Annual Plan
 <S>                   <C>            <C>        <C>     <C>     <C>     <C>     <C>     <C>   <C>  <C>
 50 / $5,000           $    100.60     4.90 %      4.86%   4.88%   4.89%   4.92%   4.91%   4.93 %
 500 / $50,000              100.44     4.75        4.86    4.89    4.90    4.93    4.92    4.94
 1,000 / $100,000           100.18     4.50        4.88    4.91    4.91    4.95    4.93    4.96
 2,500 / $250,000            99.92     4.25        4.89    4.93    4.92    4.97    4.94    4.97
 5,000 / $500,000            99.14     3.50        4.93    4.98    4.96    5.02    4.98    5.03
 10,000 / $1,000,000         98.63     3.00        4.95    5.02    4.99    5.06    5.01    5.07
 25,000 / $2,500,000         98.12     2.50        4.98    5.06    5.01    5.10    5.03    5.11
 50,000 / $5,000,000         97.62     2.00        5.01    5.09    5.04    5.13    5.06    5.14
</TABLE>
 
HOW TO DETERMINE YOUR
TAXABLE EQUIVALENT YIELD
 
The table shows the approximate yield an investor must get from a taxable
investment to match the estimated current return from this Unit Trust.
 
<TABLE>
<CAPTION>
                 Taxable Equivalent Yield (by tax
   UNIT TRUST                bracket)
     RETURN      34.5%   37.5%   42.0%      45.0%
 <C>             <S>     <C>     <C>     <C>       <C>
         4.86  % 7.42%   7.78%   8.38%      8.84 %
         4.86    7.42    7.78    8.38       8.84
         4.88    7.45    7.81    8.41       8.87
         4.89    7.47    7.82    8.43       8.89
         4.93    7.53    7.89    8.50       8.96
         4.95    7.56    7.92    8.53       9.00
         4.98    7.60    7.97    8.59       9.05
         5.01    7.65    8.02    8.64       9.11
</TABLE>
 
JOHN NUVEEN & CO. INCORPORATED
333 WEST WACKER DRIVE, CHICAGO, IL 60606
HOW TO CALCULATE YOUR INCOME
The table shows expected interest payments for monthly, quarterly and
semi-annual plans. Payments will remain relatively constant as long as the Unit
Trust's size, composition and expenses remain the same. The first record date is
10/01/97.
 
<TABLE>
<CAPTION>
                                                 Annual
                    First Payment   Payment      Income
 Payment Plan           Date       (per unit)  (per unit)
 <S>                <C>            <C>         <C>         <C>
 Initial payment
  (all plans)           10/15/97   $   .5835
 Monthly plan           11/15/97       .4071   $ 4.8860
 Quarterly plan         11/15/97       .4098
                         2/15/98      1.2294     4.9180
 Semi-annual plan       11/15/97       .4113
                         5/15/98      2.4678     4.9370
 EXAMPLE OF HOW TO CALCULATE YOUR ESTIMATED INCOME:
 $10,000       DIVIDED  BY 100.64 =  99.364
 investment       offering price     # of units
 (as of           and accrued        purchased
 08/15/97)        interest
 99.364       X   $4.8860        =   $485.49
 # of units       annual income      annual income
 purchased        per unit
                  (monthly plan)
</TABLE>


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