SELIGMAN NEW JERSEY TAX EXEMPT FUND INC
N-30D, 1996-05-20
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================================================================================
TO THE SHAREHOLDERS
--------------------------------------------------------------------------------

We are pleased to update you on Seligman New Jersey Tax-Exempt Fund at its
mid-year, March 31, 1996. During the past six months, total dividends for Class
A shares were $0.193 per share. Net asset value of Class A shares was $7.55 per
share at March 31, down from $7.59 at September 30, 1995. For Class D shares,
total dividends were $0.164 per share. Net asset value of Class D shares was
$7.63 per share at March 31, down from $7.67 at September 30, 1995. A capital
gain distribution of $0.004 per share was paid on November 17, 1995, to Class A
and D shareholders of record November 13, 1995.

     Turning to the economy, the Federal Reserve Board began lowering the
federal funds rate -- the interest rate charged for interbank loans -- in July
1995, in response to a slowdown in the rate of economic growth and a stable rate
of inflation. This less restrictive monetary policy encouraged the continuation
of the decline in long-term interest rates through 1995 and into 1996. During
the middle of the first quarter of 1996, however, the economy began to exhibit
signs of strength. Up to this point, the municipal bond market was rallying in
anticipation of an additional Fed easing of short-term interest rates. The
realization that a continued lowering of the federal funds rate was no longer
imminent caused long-term interest rates to spike sharply.

     Overall, municipal market psychology has been improving since the end of
1995. Tax reform legislation appears to have faded as an issue in the
presidential race, thereby easing the concerns that overshadowed the municipal
market in 1995. This, together with the higher yields available, has stimulated
demand. While new issue supply has slowed recently due to market conditions,
total first-quarter volume was 35% higher compared to last year's first quarter.

     In your Fund, your Manager views the current interest rate environment as
an opportunity to purchase long-term municipal bonds at levels not seen since
September 1995. While we believe that the increase in municipal yields is
temporary, the market may remain unsettled until participants are convinced that
the economy is not re-accelerating. Therefore, new purchases have been
concentrated in current coupon bonds, which are generally less volatile than
discount or zero coupon bonds during periods of uncertainty.

     Going forward, we believe the most likely outcome for 1996 is continued
moderate economic growth. However, in the event that the economy exceeds its
non-inflationary potential, we are confident that the Fed will act swiftly to
prevent the economy from growing at an unsustainable rate.

     For any additional information about Seligman New Jersey Tax-Exempt Fund,
or your investment in its shares, please write or call using the toll-free
telephone numbers listed on page 14.

By order of the Board of Directors,


/s/ WILLIAM C. MORRIS
William C. Morris
Chairman

                                  /s/ BRIAN T. ZINO
                                  Brian T. Zino
                                  President

May 3, 1996

                                                                               1
<PAGE>

================================================================================
SELIGMAN NEW JERSEY TAX-EXEMPT FUND, INC.
--------------------------------------------------------------------------------

                                     -------------------------------------------
HIGHLIGHTS  March 31, 1996                  CLASS A                 CLASS D
--------------------------------------------------------------------------------
  NET ASSETS (in millions)                   $69.4                    $1.3
--------------------------------------------------------------------------------
  YIELD*                                       4.24%                   3.67%
--------------------------------------------------------------------------------
  DIVIDENDS**                                 $0.193                  $0.164
--------------------------------------------------------------------------------
  CAPITAL GAIN DISTRIBUTION**                 $0.004                  $0.004
--------------------------------------------------------------------------------
  AVERAGE ANNUAL TOTAL RETURN
  One Year
    With sales charge/CDSL(1)                  1.34%                   4.47%
    Without sales charge/CDSL(2)               6.36                    5.47
  Five Years
    With sales charge(1)                       6.24                    n/a
    Without sales charge(2)                    7.26                    n/a
  Since Inception                       February 16, 1988       February 1, 1994
    With sales charge(1)                       6.85%                    n/a
    Without sales charge/CDSL(2)               7.50                     2.06%
--------------------------------------------------------------------------------
  NET ASSET VALUE PER SHARE                   $7.55                   $7.63
--------------------------------------------------------------------------------
  MAXIMUM OFFERING PRICE PER SHARE            $7.93                   $7.63
--------------------------------------------------------------------------------
  MOODY'S /S&P RATINGS+
  Aaa/AAA                                                 63%
  Aa/AA                                                   13
  A/A                                                     18
  Baa/BBB                                                  6
--------------------------------------------------------------------------------
  HOLDINGS BY MARKET SECTOR+
  Revenue Bonds                                           80%
  General Obligation Bonds                                20
--------------------------------------------------------------------------------
  WEIGHTED AVERAGE MATURITY (Years)                       21.2
--------------------------------------------------------------------------------

  *  Current yield representing the annualized yield for the 30-day period ended
     March 31, 1996.

 **  Represents per share amount paid or declared for the six months ended March
     31, 1996.

(1)  Represents the average compound rate of return per year over the specified
     period and reflects changes in price and assumes all distributions within
     the period are reinvested in additional shares; also reflects the effect of
     the 4.75% maximum initial sales charge or contingent deferred sales load
     ("CDSL") of 1%, if applicable.

(2)  Represents the rate of return as above, but does not reflect the effect of
     the 4.75% maximum initial sales charge or 1% CDSL.

  +  Percentages based on current market values of long-term holdings.

     Note: The yields have been computed in accordance with current SEC
     regulations and will vary, and the principal value of an investment will
     fluctuate. Shares, if redeemed, may be worth more or less than their
     original cost. A small portion of the Fund's income dividends may be
     subject to applicable state and local taxes, and to the federal alternative
     minimum tax. Past performance is not indicative of future investment
     results.

2
<PAGE>

================================================================================
PORTFOLIO OF INVESTMENTS                                          March 31, 1996
--------------------------------------------------------------------------------
<TABLE>
<CAPTION>
   FACE                                                                                          RATINGS           MARKET
  AMOUNT                                  MUNICIPAL BONDS                                      MOODY'S/S&P+         VALUE
  ------                                  ---------------                                      ------------         -----
<C>                                                                                              <C>             <C>        
$2,500,000   Brick Township Municipal Utilities Authority, NJ Rev., 6 1/2% due 12/1/2012.....    Aaa/AAA         $ 2,682,800
 1,000,000   Delran Sewerage Authority, NJ Subordinated Sewer Rev., 7 1/2% due 3/1/2013......    Aaa/AAA           1,092,090
 1,000,000   Hamilton Township Municipal Utilities Authority, NJ Rev., 6% due 8/15/2017          Aaa/AAA           1,015,700
 3,000,000   Howell Township, NJ G.O.'s, 6.80% due 1/1/2014..................................    Aaa/AAA           3,263,250
 1,250,000   Logan Township, NJ School District Certificates of Participation
               (Pacificorp Capital, Inc.), 7% due 6/15/2014..................................    Aaa/AAA           1,348,012
 1,500,000   Marlboro Township Municipal Utilities Authority Monmouth County, NJ Water Rev.,
               6% due 12/1/2018..............................................................    Aaa/AAA           1,518,225
 3,000,000   Mercer County, NJ Improvement Authority Rev. (Resource Recovery Project),
               6.70% due 4/1/2013*...........................................................    Aaa/AAA           3,024,000
 3,000,000   Morris County, NJ G.O.'s, 5% due 7/15/2011......................................    Aaa/AAA           2,863,890
 1,000,000   New Jersey Building Authority State Building Rev., 7.20% due 6/15/2013..........     Aa/AA-           1,068,770
 2,750,000   New Jersey Building Authority State Building Rev., 5% due 6/15/2018.............     Aa/AA-           2,461,195
 2,900,000   New Jersey Economic Development Authority Sewage Facilities Rev.
               (Anheuser-Busch Project), 5.85% due 12/1/2030*`...............................     A1/AA-           2,736,063
 1,000,000   New Jersey Economic Development Authority Water Facilities Rev.
               (Hackensack Water Co. Project), 7% due 10/1/2017*.............................      NR/A            1,027,360
 1,000,000   New Jersey Economic Development Authority Water Facilities Rev.
               (Hackensack Water Co. Project), 7% due 1/1/2019...............................    Aaa/AAA           1,039,370
 1,000,000   New Jersey Economic Development Authority Water Facilities Rev. 
               (Middlesex Water Co. Project), 5.20% due 10/1/2022............................    Aaa/AAA             910,490
 3,500,000   New Jersey Economic Development Authority Water Facilities Rev. 
               (New Jersey-American Water Co., Inc. Project), 5 1/2% due 6/1/2023*...........    Aaa/AAA           3,279,850
 2,500,000   New Jersey Educational Facilities Financing Authority Rev. 
               (Princeton University), 6% due 7/1/2024.......................................    Aaa/AAA           2,525,650
 1,495,000   New Jersey Health Care Facilities Financing Authority Rev. 
               (Chilton Memorial Hospital), 5% due 7/1/2013..................................      A/A             1,317,947
 1,000,000   New Jersey Health Care Facilities Financing Authority Rev. 
               (St. Clare's Riverside Medical Center), 7 3/4% due 7/1/2014...................    Aaa/AAA           1,069,030
 2,000,000   New Jersey Health Care Facilities Financing Authority Rev. 
               (St. Clare's Riverside Medical Center), 5 3/4% due 7/1/2014...................    Aaa/AAA           1,959,980
 2,000,000   New Jersey Health Care Facilities Financing Authority Rev. 
               (Hackensack Medical Center), 6 5/8% due 7/1/2017..............................    Aaa/AAA           2,126,620
 1,000,000   New Jersey Health Care Facilities Financing Authority Rev. 
               (Holy Name Hospital), 6 3/4% due 7/1/2020.....................................    Aaa/AAA           1,048,670
 2,500,000   New Jersey Health Care Facilities Financing Authority Rev. 
               (The Medical Center at Princeton), 7% due 7/1/2022............................    Aaa/AAA           2,710,725
 2,500,000   New Jersey Health Care Facilities Financing Authority Rev. 
               (Englewood Hospital & Medical Center), 6 3/4% due 7/1/2024....................    Baa/BBB           2,551,550
   985,000   New Jersey Housing & Mortgage Finance Agency (Home Mortgage Purchase Rev.),
               7 7/8% due 10/1/2016..........................................................    Aaa/AAA           1,023,740
   220,000   New Jersey Housing & Mortgage Finance Agency (Home Buyer Rev.),
               7.65% due 10/1/2016...........................................................    Aaa/AAA             229,640
</TABLE>

----------
*    Interest income earned from this security is subject to the federal
     alternative minimum tax.
+    Ratings have not been audited by Deloitte & Touche LLP.

     See notes to financial statements.

                                                                               3
<PAGE>

================================================================================
PORTFOLIO OF INVESTMENTS (continued)                              March 31, 1996
--------------------------------------------------------------------------------
<TABLE>
<CAPTION>
   FACE                                                                                          RATINGS           MARKET
  AMOUNT                                  MUNICIPAL BONDS                                      MOODY'S/S&P+         VALUE
  ------                                  ---------------                                      ------------         -----
<C>                                                                                              <C>             <C>        
$1,000,000   New Jersey Housing & Mortgage Finance Agency (Home Buyer Rev.),
               5 3/8% due 4/1/2025*..........................................................    Aaa/AAA          $  912,030
   545,000   New Jersey Housing & Mortgage Finance Agency (Home Buyer Rev.),
               7.70% due 10/1/2029*..........................................................    Aaa/AAA             565,950
 1,325,000   New Jersey Wastewater Treatment Trust Loan Rev., 7 1/4% due 5/15/2006...........     Aa/AA            1,406,753
 1,000,000   New Jersey Wastewater Treatment Trust Loan Rev., 7 3/8% due 5/15/2007...........    Aaa/AAA           1,073,290
 1,625,000   New Jersey Wastewater Treatment Trust Loan Rev., 7 1/4% due 5/15/2007...........     Aa/AA            1,722,305
 2,000,000   Oradell School District, NJ Certificates of Participation, 7.20% due 10/1/2009..    Aaa/AAA           2,219,960
 1,000,000   Paterson, NJ Water System G.O.'s, 7 1/8% due 7/1/2015...........................    Aaa/AAA           1,051,270
 3,000,000   Port Authority of New York & New Jersey Consolidated Rev., 5 3/4% due 6/15/2030.    A1/AA-            2,929,560
 2,000,000   Puerto Rico Highway & Transportation Authority Highway Rev., 5 1/2% due 7/1/2036    Baa1/A            1,840,100
 3,500,000   Salem County, NJ Improvement Authority Rev. (Correctional Facility
               & Courthouse Annex), 5.70% due 5/1/2017.......................................    Aaa/AAA           3,449,145
 2,500,000   Salem County, NJ Pollution Control Financing Authority Waste Disposal Rev.
               (E. I. duPont de Nemours & Co.), 6 1/8% due 7/15/2022*........................    Aa3/AA-           2,515,850
 1,750,000   South Jersey Port Corporation, NJ Marine Terminal Rev., 6 7/8% due 1/1/2020.....     NR/A+            1,806,368
 2,500,000   University of Medicine & Dentistry of New Jersey, 7.20% due 12/1/2019...........      A/AA            2,778,275
                                                                                                                 -----------
Total Municipal Bonds (Cost $68,147,974)--99.3%...........................................................        70,165,473
Variable Rate Demand Notes (Cost $1,000,000)--1.4%........................................................         1,000,000
Other Assets Less Liabilities--(0.7)%.....................................................................          (515,421)
                                                                                                                 -----------
NET ASSETS--100.0%........................................................................................       $70,650,052
                                                                                                                 ===========
</TABLE>

----------
*    Interest income earned from this security is subject to the federal
     alternative minimum tax.
+    Ratings have not been audited by Deloitte & Touche LLP.

     See notes to financial statements.

4
<PAGE>

================================================================================
STATEMENT OF ASSETS AND LIABILITIES.                              March 31, 1996
--------------------------------------------------------------------------------

<TABLE>
<CAPTION>
<S>                                                                        <C>              <C>
ASSETS:
Investments, at value:
  Long-term holdings (cost $68,147,974) .............................      $70,165,473
  Short-term holdings (cost $1,000,000) .............................        1,000,000      $71,165,473
                                                                           -----------
Cash ................................................................                           269,770

Interest receivable .................................................                         1,361,889
Receivable for Capital Stock sold ...................................                            38,750
Expenses prepaid to shareholder service agent .......................                             6,344
Other ...............................................................                             6,562
                                                                                            -----------
Total Assets ........................................................                        72,848,788
                                                                                            -----------

LIABILITIES:
Payable for securities purchased ....................................                         1,820,600
Dividends payable ...................................................                           140,038
Payable for Capital Stock repurchased ...............................                           124,708
Accrued expenses, taxes, and other ..................................                           113,390
                                                                                            -----------
Total Liabilities ...................................................                         2,198,736
                                                                                            -----------
Net Assets ..........................................................                       $70,650,052
                                                                                            ===========

COMPOSITION OF NET ASSETS:
Capital Stock, at par ($.001 par value; 50,000,000 shares authorized;
  9,357,905 shares outstanding):
  Class A ...........................................................                       $     9,189
  Class D ...........................................................                               169
Additional paid-in capital ..........................................                        66,991,371
Undistributed net realized gain .....................................                         1,631,824
Net unrealized appreciation of investments ..........................                         2,017,499
                                                                                            -----------
Net Assets ..........................................................                       $70,650,052
                                                                                            ===========
NET ASSET VALUE PER SHARE:
Class A ($69,360,245/9,188,868 shares) ..............................                             $7.55
                                                                                            ===========
Class D ($1,289,807/169,037 shares) .................................                             $7.63
                                                                                            ===========
</TABLE>

----------
See notes to financial statements.

                                                                               5
<PAGE>

================================================================================
STATEMENT OF OPERATIONS                  For the six months ended March 31, 1996
--------------------------------------------------------------------------------

<TABLE>
<CAPTION>
<S>                                                            <C>              <C>
INVESTMENT INCOME:
Interest ...................................................                    $2,223,617

EXPENSES:
Management fee..............................................   $   184,947
Distribution and service fees...............................        85,456
Shareholder account services ...............................        46,967
Auditing and legal fees.....................................        17,484
Custody and related services ...............................        16,925
Directors' fees and expenses................................        11,945
Shareholder reports and communications......................         5,780
Registration................................................         4,735
Miscellaneous ..............................................         3,598
                                                               -----------
Total expenses..............................................                       377,837
                                                                                ----------
Net investment income ......................................                     1,845,780

NET REALIZED AND UNREALIZED GAIN (LOSS) ON INVESTMENTS:
Net realized gain on investments............................     1,640,248
Net change in unrealized appreciation of investments .......    (1,933,295)
                                                               -----------
Net loss on investments ....................................                      (293,047)
                                                                                ----------
Increase in net assets from operations......................                    $1,552,733
                                                                                ==========
</TABLE>

----------
See notes to financial statements.

6
<PAGE>

================================================================================
STATEMENT OF CHANGES IN NET ASSETS
--------------------------------------------------------------------------------

<TABLE>
<CAPTION>
                                                                                         SIX MONTHS         YEAR
                                                                                            ENDED           ENDED
                                                                                           3/31/96         9/30/95
                                                                                         -----------     -----------
<S>                                                                                      <C>             <C>        
OPERATIONS:
Net investment income...............................................................     $ 1,845,780     $ 3,889,418
Net realized gain on investments....................................................       1,640,248          33,365
Net change in unrealized appreciation of investments................................      (1,933,295)      2,800,005
                                                                                         -----------     -----------
Increase in net assets from operations..............................................       1,552,733       6,722,788
                                                                                         -----------     -----------
DISTRIBUTIONS TO SHAREHOLDERS:
Net investment income:
   Class A..........................................................................      (1,818,419)     (3,838,302)
   Class D..........................................................................         (27,361)        (51,116)
Net realized gain on investments:
   Class A..........................................................................         (38,743)     (1,010,909)
   Class D..........................................................................            (665)        (13,739)
                                                                                         -----------     -----------
Decrease in net assets from distributions...........................................      (1,885,188)     (4,914,066)
                                                                                         -----------     -----------
</TABLE>

<TABLE>
<CAPTION>
                                                                    SHARES
                                                           -----------------------
                                                           SIX MONTHS      YEAR
                                                             ENDED        ENDED
                                                            3/31/96      9/30/95
                                                           --------     ----------
<S>                                                        <C>          <C>              <C>               <C>        
CAPITAL SHARE TRANSACTIONS:
Net proceeds from sale of shares:
   Class A .............................................    218,808        548,270         1,685,946         4,058,926
   Class D..............................................     22,256         63,760           172,994           466,899
Shares issued in payment of dividends:
   Class A .............................................    134,069        305,485         1,030,840         2,251,536
   Class D..............................................      2,247          4,801            17,479            35,924
Exchanged from associated Funds:
   Class A .............................................     48,936        512,716           376,667         3,727,736
   Class D..............................................      7,301          1,613            56,910            12,373
Shares issued in payment of gain distributions:
   Class A .............................................      3,678        109,013            28,281           742,377
   Class D..............................................         61          1,519               471            10,467
                                                           --------     ----------       -----------       -----------
Total...................................................    437,356      1,547,177         3,369,588        11,306,238
                                                           --------     ----------       -----------       -----------
Cost of shares repurchased:
   Class A .............................................   (824,969)    (1,428,147)       (6,371,970)      (10,436,724)
   Class D..............................................     (9,796)       (48,118)          (76,252)         (359,695)
Exchanged into associated Funds:
   Class A .............................................    (81,860)      (345,862)         (626,230)       (2,493,426)
   Class D..............................................     (8,080)          (316)          (63,232)           (2,400)
                                                           --------     ----------       -----------       -----------
Total...................................................   (924,705)    (1,822,443)       (7,137,684)      (13,292,245)
                                                           --------     ----------       -----------       -----------
Decrease in net assets from capital share transactions .   (487,349)      (275,266)       (3,768,096)       (1,986,007)
                                                           ========     ==========       -----------       -----------
Decrease in net assets............................................................        (4,100,551)         (177,285)
NET ASSETS:
Beginning of period...............................................................        74,750,603        74,927,888
                                                                                         -----------       -----------
End of period ....................................................................       $70,650,052       $74,750,603
                                                                                         ===========       ===========
</TABLE>

----------
See notes to financial statements.

                                                                               7
<PAGE>

================================================================================
NOTES TO FINANCIAL STATEMENTS
--------------------------------------------------------------------------------

1. Seligman New Jersey Tax-Exempt Fund, Inc. (the "Fund") offers two classes of
shares. All shares existing prior to February 1, 1994, were classified as Class
A shares. Class A shares are sold with an initial sales charge of up to 4.75%
and a continuing service fee of up to 0.25% on an annual basis. Class D shares
are sold without an initial sales charge but are subject to a distribution fee
of up to 0.75% and a service fee of up to 0.25% on an annual basis, and
contingent deferred sales load ("CDSL") of 1% imposed on certain redemptions
made within one year of purchase. The two classes of shares represent interests
in the same portfolio of investments, have the same rights and are generally
identical in all respects except that each class bears its separate distribution
and certain class expenses and has exclusive voting rights with respect to any
matter to which a separate vote of any class is required.

2. Significant accounting policies followed, all in conformity with generally
accepted accounting principles, are given below:

a.   All tax-exempt securities and other short-term holdings maturing in more
     than 60 days are valued based upon quotations provided by an independent
     pricing service or, in their absence, at fair value determined in
     accordance with procedures approved by the Board of Directors. Short-term
     holdings maturing in 60 days or less are generally valued at amortized
     cost.

b.   There is no provision for federal income or excise tax. The Fund has
     elected to be taxed as a regulated investment company and intends to
     distribute substantially all taxable net income and net gain realized.
     Dividends are declared daily and paid monthly.

c.   Investment transactions are recorded on trade dates. Identified cost of
     investments sold is used for both financial statement and federal income
     tax purposes. Interest income is recorded on the accrual basis. The Fund
     amortizes original issue discounts and premiums paid on purchases of
     portfolio securities. Discounts other than original issue discounts are not
     amortized.

d.   All income, expenses (other than class-specific expenses), and realized and
     unrealized gains or losses are allocated daily to each class of shares
     based upon the relative value of the shares of each class. Class-specific
     expenses, which include distribution and service fees and any other items
     that are specifically attributed to a particular class, are charged
     directly to such class. For the six months ended March 31, 1996,
     distribution and service fees were the only class-specific expenses.

e.   The treatment for financial statement purposes of distributions made during
     the year from net investment income or net realized gains may differ from
     their ultimate treatment for federal income tax purposes. These differences
     are caused primarily by differences in the timing of the recognition of
     certain components of income, expense, and capital gain for federal income
     tax purposes. Where such differences are permanent in nature, they are
     reclassified in the components of net assets based on their ultimate
     characterization for federal income tax purposes. Any such
     reclassifications will have no effect on net assets, results of operations
     or net asset value per share of the Fund.

3. Purchases and sales of portfolio securities, excluding short-term
investments, for the six months ended March 31, 1996, amounted to $12,944,350
and $14,499,608, respectively.

     At March 31, 1996, the cost of investments for federal income tax purposes
was substantially the same as the cost for financial reporting purposes, and the
tax basis gross unrealized appreciation and depreciation of investments amounted
to $2,940,452 and $922,953, respectively.

4. J. & W. Seligman & Co. Incorporated (the "Manager") manages the affairs of
the Fund and provides the necessary personnel and facilities. Compensation of
all officers of the Fund, all directors of the Fund who are employees or
consultants of the Manager, and all personnel of the Fund and the Manager is
paid by the Manager. The Manager's fee, calculated daily and payable monthly, is
equal to 0.50% per annum of the Fund's average daily net assets.

8
<PAGE>

================================================================================

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

     Seligman Financial Services, Inc. (the "Distributor"), agent for the
distribution of the Fund's shares and an affiliate of the Manager, received
concessions of $7,969 from the sale of Class A shares, after commissions of
$59,132 paid to dealers.

     The Fund has an Administration, Shareholder Services and Distribution Plan
(the "Plan") with respect to Class A shares under which service organizations
can enter into agreements with the Distributor and receive a continuing fee of
up to 0.25% on an annual basis, payable quarterly, of the average daily net
assets of the Class A shares attributable to the particular service
organizations for providing personal services and/or the maintenance of
shareholder accounts. The Distributor charges such fees to the Fund pursuant to
the Plan. For the six months ended March 31, 1996, fees paid aggregated $78,981,
or 0.22% per annum of the average daily net assets of Class A shares.

     The Fund has a Plan with respect to Class D shares under which service
organizations can enter into agreements with the Distributor and receive a
continuing fee for providing personal services and/or the maintenance of
shareholder accounts of up to 0.25% on an annual basis of the average daily net
assets of the Class D shares for which the organizations are responsible, and
fees for providing other distribution assistance of up to 0.75% on an annual
basis of such average daily net assets. Such fees are paid monthly by the Fund
to the Distributor pursuant to the Plan. For the six months ended March 31,
1996, fees paid amounted to $6,475, or 1% per annum of the average daily net
assets of Class D shares.

     The Distributor is entitled to retain any CDSL imposed on certain
redemptions of Class D shares occurring within one year of purchase. For the six
months ended March 31, 1996, such charges amounted to $31.

     Seligman Services, Inc., an affiliate of the Manager, is eligible to
receive commissions from certain sales of Fund shares, as well as distribution
and service fees pursuant to the Plan. For the six months ended March 31, 1996,
Seligman Services, Inc. received commissions of $391 from sales of shares of the
Fund. Seligman Services, Inc. also received distribution and service fees of
$4,308, pursuant to the Plan.

     Seligman Data Corp., which is owned by certain associated investment
companies, charged at cost $46,967 for shareholder account services.

     Certain officers and directors of the Fund are officers or directors of the
Manager, the Distributor, Seligman Services, Inc., and/or Seligman Data Corp.

     Fees of $4,000 were incurred by the Fund for the legal services of Sullivan
& Cromwell, a member of which firm is a director of the Fund.

     The Fund has a compensation arrangement under which directors who receive
fees may elect to defer receiving such fees. Interest is accrued on the deferred
balances. The cost of such fees and interest is included in directors' fees and
expenses, and the accumulated balance thereof at March 31, 1996, of $33,869 is
included in other liabilities. Deferred fees and related accrued interest are
not deductible for federal income tax purposes until such amounts are paid.

                                                                               9
<PAGE>

================================================================================
FINANCIAL HIGHLIGHTS
--------------------------------------------------------------------------------

The Fund's financial highlights are presented below. The per share operating
performance data is designed to allow investors to trace the operating
performance, on a per share basis, from the Fund's beginning net asset value to
the ending net asset value so that they can understand what effect the
individual items have on their investment assuming it was held throughout the
period. Generally, the per share amounts are derived by converting the actual
dollar amounts incurred for each item as disclosed in the financial statements
to their equivalent per share amounts using average shares outstanding.

     The total return based on net asset value measures the Fund's performance
assuming investors purchased shares at net asset value as of the beginning of
the period, reinvested dividends and capital gains paid at net asset value, and
then sold their shares at the net asset value per share on the last day of the
period. The total return computations do not reflect any sales charges investors
may incur in purchasing or selling shares of the Fund. The total returns for
periods of less than one year are not annualized.

<TABLE>
<CAPTION>
                                                             CLASS A                                          CLASS D
                               ----------------------------------------------------------------  --------------------------------
                               SIX MONTHS                 YEAR ENDED SEPTEMBER 30                SIX MONTHS     YEAR      2/1/94*
                                 ENDED      ---------------------------------------------------     ENDED       ENDED       TO
                                3/31/96       1995       1994       1993       1992       1991     3/31/96     9/30/95    9/30/94
                                -------     -------    -------    -------    -------    -------    -------     -------    -------
<S>                             <C>         <C>        <C>        <C>        <C>        <C>         <C>         <C>       <C> 
PER SHARE OPERATING
  PERFORMANCE:
Net asset value, beginning
  of period ..................    $7.59       $7.40      $8.24      $7.74      $7.49      $7.01      $7.67       $7.48      $8.14
                                -------     -------    -------    -------    -------    -------    -------     -------    -------
Net investment income ........      .19         .39        .41        .42        .44        .44        .16         .33        .23
Net realized and unrealized
  investment gain (loss) .....     (.04)        .29       (.74)       .61        .27        .51       (.04)        .29       (.66)
                                -------     -------    -------    -------    -------    -------    -------     -------    -------
Increase (decrease) from
  investment operations ......      .15         .68       (.33)      1.03        .71        .95        .12         .62       (.43)
Dividends paid or declared ...     (.19)       (.39)      (.41)      (.42)      (.44)      (.44)      (.16)       (.33)      (.23)
Distributions from
  net gain realized ..........       --        (.10)      (.10)      (.11)      (.02)      (.03)        --        (.10)        --
                                -------     -------    -------    -------    -------    -------    -------     -------    -------
Net increase (decrease) in
  net asset value ............     (.04)        .19       (.84)       .50        .25        .48       (.04)        .19       (.66)
                                -------     -------    -------    -------    -------    -------    -------     -------    -------
Net asset value, end of period    $7.55       $7.59      $7.40      $8.24      $7.74      $7.49      $7.63       $7.67      $7.48
                                =======     =======    =======    =======    =======    =======    =======     =======    =======
TOTAL RETURN BASED ON
  NET ASSET VALUE ............     2.03%       9.77%     (4.25)%    14.02%      9.70%     13.97%      1.64%       8.79%     (5.47)%
RATIOS/SUPPLEMENTAL DATA:
Expenses to average net assets     1.01%+      1.01%       .90%       .86%       .85%       .81%      1.79%+      1.89%      1.75%+
Net investment income to
  average net assets .........     5.01%+      5.29%      5.24%      5.37%      5.74%      6.02%      4.23%+      4.45%      4.37%+
Portfolio turnover ...........    18.06%       4.66%     12.13%     15.90%     27.13%     14.64%     18.06%       4.66%     12.13%++
Net assets, end of period
  (000's omitted) ............  $69,360     $73,561    $73,942    $82,447    $74,256    $65,044     $1,290      $1,190       $986
</TABLE>

----------
See footnotes on page 11.

10
<PAGE>

================================================================================

--------------------------------------------------------------------------------
<TABLE>
<CAPTION>
                                                             CLASS A                                          CLASS D
                               ----------------------------------------------------------------  --------------------------------
                               SIX MONTHS                 YEAR ENDED SEPTEMBER 30                SIX MONTHS     YEAR      2/1/94*
                                 ENDED      ---------------------------------------------------     ENDED       ENDED       TO
                                3/31/96       1995       1994       1993       1992       1991     3/31/96     9/30/95    9/30/94
                                -------     -------    -------    -------    -------    -------    -------     -------    -------
<S>                                         <C>        <C>        <C>        <C>        <C>                     <C>       <C> 
RATIOS/SUPPLEMENTAL DATA (Cont'd.):
Without management fee waiver:**

Net investment income per share..              $.39      $.40       $.40       $.42       $.42                   $.33       $.22
Expenses to average net assets...              1.06%     1.07%      1.11%      1.10%      1.11%                  1.94%      1.87%+
Net investment income to
   average net assets............              5.24%     5.07%      5.12%      5.49%      6.01%                  4.40%      4.25%+
</TABLE>

----------
*    Commencement of offering of Class D shares.
**   The Manager, at its discretion, waived a portion of its fees for the
     periods presented.
 + Annualized.
++   For the year ended September 30, 1994.

See notes to financial statements.

                                                                              11
<PAGE>

================================================================================
REPORT OF INDEPENDENT AUDITORS
--------------------------------------------------------------------------------

The Board of Directors and Shareholders,
Seligman New Jersey Tax-Exempt Fund, Inc.:

We have audited the accompanying statement of assets and liabilities, including
the portfolio of investments, of Seligman New Jersey Tax-Exempt Fund, Inc. as of
March 31, 1996, the related statements of operations for the six months then
ended and of changes in net assets for the six months then ended and for the
year ended September 30, 1995, and the financial highlights for each of the
periods presented. These financial statements and financial highlights are the
responsibility of the Fund's management. Our responsibility is to express an
opinion on these financial statements and financial highlights based on our
audits.

We conducted our audits in accordance with generally accepted auditing
standards. Those standards require that we plan and perform the audit to obtain
reasonable assurance about whether the financial statements and financial
highlights are free of material misstatement. An audit includes examining, on a
test basis, evidence supporting the amounts and disclosures in the financial
statements. Our procedures included confirmation of securities owned as of March
31, 1996 by correspondence with the Fund's custodian and brokers; where replies
were not received from brokers, we performed other auditing procedures. An audit
also includes assessing the accounting principles used and significant estimates
made by management, as well as evaluating the overall financial statement
presentation. We believe that our audits provide a reasonable basis for our
opinion.

In our opinion, such financial statements and financial highlights present
fairly, in all material respects, the financial position of Seligman New Jersey
Tax-Exempt Fund, Inc. as of March 31, 1996, the results of its operations, the
changes in its net assets, and the financial highlights for the respective
stated periods, in conformity with generally accepted accounting principles.

DELOITTE & TOUCHE LLP
New York, New York
May 3, 1996

12
<PAGE>

================================================================================
BOARD OF DIRECTORS
--------------------------------------------------------------------------------

Fred E. Brown
Director and Consultant,
  J. & W. Seligman & Co. Incorporated

John R. Galvin (2)
Dean, Fletcher School of Law and Diplomacy
  at Tufts University
Director, USLIFE Corporation

Alice S. Ilchman (3)
President, Sarah Lawrence College
Trustee, Committee for Economic Development
Director, NYNEX
Chairman, The Rockefeller Foundation

Frank A. McPherson (2)
Chairman and CEO, Kerr-McGee Corporation
Director, Kimberly-Clark Corporation
Director, Baptist Medical Center

John E. Merow
Partner, Sullivan & Cromwell, Law Firm
Director, Commonwealth Aluminum Corporation

Betsy S. Michel (2)
Director or Trustee,
  Various Organizations

William C. Morris (1)
Chairman
Chairman of the Board and President,
  J. & W. Seligman & Co. Incorporated
Chairman, Carbo Ceramics Inc.
Director, Kerr-McGee Corporation

James C. Pitney (3)
Partner, Pitney, Hardin, Kipp & Szuch, Law Firm
Director, Public Service Enterprise Group

James Q. Riordan (3)
Director, The Brooklyn Union Gas Company
Trustee, Committee for Economic Development
Director, Dow Jones & Co., Inc.
Director, Public Broadcasting Service

Ronald T. Schroeder (1)
Managing Director,
  J. & W. Seligman & Co. Incorporated

Robert L. Shafer (3)
Vice President, Pfizer Inc.
Director, USLIFE Corporation

James N. Whitson (2)
Executive Vice President and Director,
  Sammons Enterprises, Inc.
Director, C-SPAN
Director, Red Man Pipe and Supply Company

Brian T. Zino (1)
President
Managing Director,
  J. & W. Seligman & Co. Incorporated

----------
Member: (1) Executive Committee
        (2) Audit Committee
        (3) Director Nominating Committee

                                                                              13
<PAGE>

================================================================================
EXECUTIVE OFFICERS
--------------------------------------------------------------------------------

William C. Morris
Chairman

Brian T. Zino
President

Thomas G. Moles
Vice President

Lawrence P. Vogel
Vice President

Thomas G. Rose
Treasurer

Frank J. Nasta
Secretary

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

Manager
J. & W. Seligman & Co.
  Incorporated
100 Park Avenue
New York, NY 10017

General Counsel
Sullivan & Cromwell

Independent Auditors
Deloitte & Touche LLP

General Distributor
Seligman Financial Services, Inc.
100 Park Avenue
New York, NY 10017

Shareholder Service Agent
Seligman Data Corp.
100 Park Avenue
New York, NY 10017

Important Telephone Numbers
(800) 221-2450   Shareholder
                 Services

(800) 622-4597   24-Hour Automated
                 Telephone Access
                 Service

14
<PAGE>





                        SELIGMAN FINANCIAL SERVICES, INC.
                                 an affiliate of

                                     [LOGO]

                             J. & W. SELIGMAN & CO.
                                  INCORPORATED
                                ESTABLISHED 1864
                       100 Park Avenue, New York, NY 10017

This report is intended only for the information of shareholders or those who
have received the offering prospectus covering shares of Capital Stock of
Seligman New Jersey Tax-Exempt Fund, Inc., which contains information about the
sales charges, management fee, and other costs. Please read the prospectus
carefully before investing or sending money.


                                                                     TECNJ3 3/96




================================================================================
                                 MID-YEAR REPORT


                        -------------------------------
                                    SELIGMAN
                                   NEW JERSEY
                                   TAX-EXEMPT
                                   FUND, INC.
                        -------------------------------



                                 March 31, 1996


                                     [LOGO]


--------------------------------------------------------------------------------
                            Providing Tax-Free Income
                                   Since 1988



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