<PAGE>   1
                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549
                                    FORM 10-Q

(Mark One)
[X] QUARTERLY REPORT PURSUANT TO SECTION 13 or 15(d) OF THE
SECURITIES EXCHANGE ACT OF 1934


For the quarterly period ended          June 30, 1998

                                       or

[ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
SECURITIES EXCHANGE ACT OF 1934


For the transition period from ________________ to _________________


Commission File Number:             1-5273-1


                                Sterling Bancorp
             (Exact name of registrant as specified in its charter)


       New York                                                 13-2565216
(State or other jurisdiction of                             (I.R.S. Employer
incorporation or organization)                                Identification)


430 Park Avenue, New York, N.Y.                                  10022-3505
(Address of principal executive offices)                          (Zip Code)


                                  212-826-8000
              (Registrant's telephone number, including area code)


                                       N/A
        (Former name, former address and former fiscal year, if changed
                               since last report)


    Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.
                         [X] Yes  [] No


    As of June 30, 1998 there were 8,259,191 shares of common stock, $1.00 par
value, outstanding.
<PAGE>   2
                                STERLING BANCORP




<TABLE>
<CAPTION>
PART I FINANCIAL INFORMATION                                                                           Page
<S>                                                                                                  <C>
        Item 1. Financial Statements (Unaudited)

               Consolidated Financial Statements                                                         3
               Notes to Consolidated Financial Statements                                                8

        Item 2. Management's Discussion and Analysis of Financial
                       Condition and Results of Operations

               Business                                                                                 10
               Results for the Three Months                                                             10
               Results for the Six Months                                                               12
               Balance Sheet Analysis                                                                   14
               Capital                                                                                  17
               Average Balance Sheets                                                                   18
               Rate/Volume Analysis                                                                     20
               Regulatory Capital and Ratios                                                            22

        Item 3. Quantitative and Qualitative Disclosures About
                       Market Risk

               Asset/Liability Management                                                               23
               Interest Rate Sensitivity                                                                26

PART II OTHER INFORMATION


        Item 4. Submission of Matter to a
                      Vote of Security-Holders                                                          27

        Item 6. Exhibits and Reports on Form 8-K                                                        28



SIGNATURES                                                                                              28
</TABLE>




                                        2
<PAGE>   3
                        STERLING BANCORP AND SUBSIDIARIES
                           Consolidated Balance Sheets

<TABLE>
<CAPTION>
                                                                        June 30,            December 31,
ASSETS                                                                    1998                   1997
                                                                          ----                   ----
<S>                                                                 <C>                   <C>
Cash and due from banks                                             $   52,082,079        $   40,065,863
Interest-bearing deposits with other banks                                 315,000             3,010,000
Investment securities
   Available for sale (at estimated market value)                      119,584,844           148,921,006
   Held to maturity (estimated market value
     $210,096,638 and $236,009,925, respectively)                      209,916,399           236,030,004
                                                                    --------------        --------------
            Total investment securities                                329,501,243           384,951,010
                                                                    --------------        --------------

Loans, net of unearned discounts                                       546,330,332           558,481,845
Less allowance for credit losses                                         8,825,911             8,677,610
                                                                    --------------        --------------
            Loans, net                                                 537,504,421           549,804,235
                                                                    --------------        --------------
Customers' liability under acceptances                                   1,365,801             1,125,654
Excess cost over equity in net assets of the
   banking subsidiary                                                   21,158,440            21,158,440
Premises and equipment, net                                              6,898,592             7,330,062
Accrued interest receivable                                              3,737,692             4,147,008
Other assets                                                             8,366,918             8,387,386
                                                                    --------------        --------------
                                                                    $  960,930,186        $1,019,979,658
                                                                    ==============        ==============

LIABILITIES AND SHAREHOLDERS' EQUITY
Deposits
   Noninterest-bearing deposits                                     $  253,472,704        $  312,461,489
   Interest-bearing deposits                                           402,459,838           418,946,491
                                                                    --------------        --------------
            Total deposits                                             655,932 542           731,407,980
Federal funds purchased and securities
   sold under agreements to repurchase                                  68,384,115           106,752,546
Commercial paper                                                        36,648,100            24,070,600
Other short-term borrowings                                             20,551,068            19,891,252
Acceptances outstanding                                                  1,365,801             1,125,654
Due to factoring clients                                                30,027,652            30,798,610
Accrued expenses and other liabilities                                   8,932,886            11,560,450
                                                                    --------------        --------------
                                                                       821,842,164           925,607,092
Long-term debt - FHLB                                                   41,400,000             1,750,000
                                                                    --------------        --------------
            Total liabilities                                          863,242,164           927,357,092
                                                                    --------------        --------------

Commitments and contingent liabilities


Shareholders' equity
   Preferred stock, $5 par value. Authorized 644,389 shares
      Series B ($20 liquidation value), issued 1,230 shares                 24,600                24,600
      Series D ($10 liquidation value), issued 243,929 and
        246,213 shares, respectively                                     2,439,290             2,462,130
                                                                    --------------        --------------
                                                                         2,463,890             2,486,730


   Common stock, $1 par value. Authorized 20,000,000 shares;
      issued 8,303,784 and 8,262,500 shares, respectively                8,303,784             8,262,500
   Capital surplus                                                      45,242,940            44,775,759
   Retained earnings                                                    43,961,444            39,590,806
   Accumulated other comprehensive income, net of tax
      Net unrealized appreciation on securities
          available for sale                                               246,151               197,374
                                                                    --------------        --------------
                                                                       100,218,209            95,313,169
   Less
      Common shares in treasury at cost,
       44,593 shares                                                       441,257               441,257
      Unearned compensation                                              2,088,930             2,249,346
                                                                    --------------        --------------
            Total shareholders' equity                                  97,688,022            92,622,566
                                                                    --------------        --------------
                                                                    $  960,930,186        $1,019,979,658
                                                                    ==============        ==============
</TABLE>

See Notes to Consolidated Financial Statements.

                                       3
<PAGE>   4
                        STERLING BANCORP AND SUBSIDIARIES
                        Consolidated Statements of Income


<TABLE>
<CAPTION>
                                                         Three Months Ended                     Six Months Ended
                                                              June 30,                               June 30,
                                                       1998               1997               1998               1997
                                                       ----               ----               ----               ----
<S>                                                <C>                <C>                <C>                <C>
INTEREST INCOME
   Loans                                           $12,661,785        $11,406,455        $24,921,704        $22,489,977
   Investment securities:
      Available for sale                             1,920,525          1,083,128          3,798,660          2,400,645
      Held to maturity                               3,241,675          4,000,246          7,078,801          7,783,102
   Federal funds sold                                  217,946             15,628            356,585             89,741
   Deposits with other banks                            30,732             64,821            105,403            123,128
                                                   -----------        -----------        -----------        -----------
            Total interest income                   18,072,663         16,570,278         36,261,153         32,886,593
                                                   -----------        -----------        -----------        -----------

INTEREST EXPENSE
   Deposits                                          4,166,160          3,501,499          8,570,887          6,820,229
   Federal funds purchased
      and securities sold under agreements
      to repurchase                                    869,540          1,258,601          2,086,989          2,350,677
   Commercial paper                                    387,785            314,769            748,816            645,462
   Other short-term borrowings                         252,646            159,510            497,078            305,579
   Long-term debt                                      525,746            284,638            730,010            615,984
                                                   -----------        -----------        -----------        -----------
            Total interest expense                   6,201,877          5,519,017         12,633,780         10,737,931
                                                   -----------        -----------        -----------        -----------
Net interest income                                 11,870,786         11,051,261         23,627,373         22,148,662
Provision for credit losses                          1,267,333            610,000          2,111,333          1,381,000
                                                   -----------        -----------        -----------        -----------
Net interest income after provision
   for credit losses                                10,603,453         10,441,261         21,516,040         20,767,662
                                                   -----------        -----------        -----------        -----------

NONINTEREST INCOME
   Factoring income                                  1,277,325          1,005,938          2,310,977          2,096,138
   Mortgage banking income                           1,014,288            835,991          1,848,115          1,528,689
   Service charges on deposit accounts                 750,364            474,794          1,424,952            984,714
   Letter of credit commissions                        388,916            359,980            660,618            600,059
   Trust fees                                          237,793             30,221            427,288            223,168
   Other income                                        507,615            314,923            979,676            702,468
                                                   -----------        -----------        -----------        -----------
            Total noninterest income                 4,176,301          3,021,847          7,651,626          6,135,236
                                                   -----------        -----------        -----------        -----------

NONINTEREST EXPENSES
   Salaries                                          4,607,415          4,144,517          9,015,079          8,288,115
   Employee benefits                                   970,318            926,715          1,976,663          1,814,332
                                                   -----------        -----------        -----------        -----------
            Total personnel expenses                 5,577,733          5,071,232         10,991,742         10,102,447
   Occupancy expense, net                              796,586            742,864          1,589,384          1,475,643
   Equipment expense                                   631,267            535,702          1,221,898          1,101,093
   Other expenses                                    2,428,667          2,327,142          4,750,896          4,903,812
                                                   -----------        -----------        -----------        -----------
            Total noninterest expenses               9,434,253          8,676,940         18,553,920         17,582,995
                                                   -----------        -----------        -----------        -----------
Income before income taxes                           5,345,501          4,786,168         10,613,746          9,319,903
Provision for income taxes                           2,232,029          2,153,052          4,497,309          4,224,311
                                                   -----------        -----------        -----------        -----------

Net income                                         $ 3,113,472        $ 2,633,116        $ 6,116,437        $ 5,095,592
                                                   ===========        ===========        ===========        ===========

Average number of common shares outstanding
   Basic                                             8,279,458          7,791,977          8,253,079          7,758,583
   Diluted                                           8,691,472          8,611,812          8,629,857          8,577,852
Per average common share
   Basic                                                  $.37               $.33               $.74               $.65
   Diluted                                                 .36                .31                .71                .61
Dividends per common share                                 .11                .09                .21                .18
</TABLE>

See Notes to Consolidated Financial Statements.

                                        4
<PAGE>   5
                        STERLING BANCORP AND SUBSIDIARIES
                 Consolidated Statements of Comprehensive Income









<TABLE>
<CAPTION>
                                                    Three Months Ended                     Six Months Ended
                                                          June 30,                              June 30,
                                                   1998              1997                1998               1997
                                                   ----              ----                ----               ----
<S>                                            <C>                <C>                <C>                <C>
Net income                                     $ 3,113,472        $ 2,633,116        $ 6,116,437        $ 5,095,592

Other comprehensive income, net of tax:
      Unrealized holding gains/(losses)
       arising during the period                   124,704            170,636             48,777            (65,280)
                                               -----------        -----------        -----------        -----------


Comprehensive income                           $ 3,238,176        $ 2,803,752        $ 6,165,214        $ 5,030,312
                                               ===========        ===========        ===========        ===========

</TABLE>

See Notes to Consolidated Financial Statements.

                                        5
<PAGE>   6
                        STERLING BANCORP AND SUBSIDIARIES
           Consolidated Statements of Changes in Shareholders' Equity


<TABLE>
<CAPTION>
                                                            Six Months Ended
                                                                June 30,
                                                        1998                 1997
                                                        ----                 ----
<S>                                                 <C>                  <C>
PREFERRED STOCK
   Balance at January 1                             $  2,486,730         $  2,506,600
   Conversions of Series D shares                        (22,840)             (17,300)
                                                    ------------         ------------
   Balance at June 30                               $  2,463,890         $  2,489,300
                                                    ============         ============

COMMON STOCK
   Balance at January 1                             $  8,262,500         $  7,725,533
   Conversions of subordinated debentures                     --              133,920
   Conversions of preferred shares
      into common shares                                   2,284                1,730
   Options exercised                                      39,000                5,500
                                                    ------------         ------------
   Balance at June 30                               $  8,303,784         $  7,866,683
                                                    ============         ============

CAPITAL SURPLUS
   Balance at January 1                             $ 44,775,759         $ 38,619,434
   Conversions of subordinated debentures                     --            1,540,080
   Conversions of preferred shares
      into common shares                                  20,556               15,570
   Options exercised                                     446,625               54,250
                                                    ------------         ------------
   Balance at June 30                               $ 45,242,940         $ 40,229,334
                                                    ============         ============

RETAINED EARNINGS
   Balance at January 1                             $ 39,590,806         $ 31,648,806
   Net income                                          6,116,437            5,095,592
   Cash dividends paid - common shares                (1,718,753)          (1,386,117)
                        - preferred shares               (27,046)             (21,489)
                                                    ------------         ------------
   Balance at June 30                               $ 43,961,444         $ 35,336,792
                                                    ============         ============

ACCUMULATED OTHER COMPREHENSIVE INCOME
   Balance at January 1                             $    197,374         $     90,001
                                                    ------------         ------------
   Unrealized holding gains/(losses) arising
      during the period:
        Before tax                                        90,161             (121,886)
        Tax benefit                                       41,384               56,606
                                                    ------------         ------------
           Net of tax                                     48,777              (65,280)
                                                    ------------         ------------
   Balance at June 30                               $    246,151         $     24,721
                                                    ============         ============

TREASURY STOCK
   Balance at January 1 and June 30                 $   (441,257)        $   (418,959)
                                                    ============         ============


UNEARNED COMPENSATION
   Balance at January 1                             $ (2,249,346)        $ (2,993,980)
   Amortization of unearned compensation                 160,416              196,824
                                                    ------------         ------------
   Balance at June 30                               $ (2,088,930)        $ (2,797,156)
                                                    ============         ============

TOTAL SHAREHOLDERS' EQUITY
   Balance at January 1                             $ 92,622,566         $ 77,177,435
   Net changes during the period                       5,065,456            5,553,280
                                                    ------------         ------------
   Balance at June 30                               $ 97,688,022         $ 82,730,715
                                                    ============         ============
</TABLE>

See Notes to Consolidated Financial Statements.

                                        6
<PAGE>   7
                        STERLING BANCORP AND SUBSIDIARIES
                      Consolidated Statements of Cash Flows

<TABLE>
<CAPTION>
                                                                                Six Months Ended
                                                                                    June 30,
                                                                            1998                  1997
                                                                            ----                  ----
<S>                                                                    <C>                   <C>
OPERATING ACTIVITIES
  Net income                                                           $   6,116,437         $   5,095,592
  Adjustments to reconcile net income to net cash
      provided by operating activities:
        Provision for credit losses                                        2,111,333             1,381,000
        Depreciation and amortization of premises and equipment              737,378               581,341
        Deferred income tax (provision)                                     (127,946)             (183,706)
        Net change in loans held for sale                                 (3,862,571)           (2,018,020)
        Amortization of unearned compensation                                160,416               196,824
        Amortization of premiums on securities                             1,075,253               656,936
        Accretion of discounts on securities                                (290,324)              (75,907)
        Decrease in accrued interest receivable                              409,316               500,814
        Decrease in due to factored clients                                 (770,958)           12,994,222
        Decrease in other liabilities                                     (2,627,564)           (2,626,803)
        Other, net                                                        (1,855,999)           (1,912,711)
                                                                       -------------         -------------

              Net cash provided by operating activities                    1,074,771            14,589,582
                                                                       -------------         -------------

INVESTING ACTIVITIES
  Purchase of premises and equipment                                        (305,908)           (2,294,346)
   Net decrease in interest-bearing deposits
      with other banks                                                     2,695,000                    --
   Net decrease in Federal funds sold                                             --             3,000,000
   Net decrease in loans                                                  16,014,084             1,882,322
   Proceeds from prepayments, redemptions or maturities
      of securities - held to maturity                                    35,015,256            16,862,986
   Purchases of securities - held to maturity                             (9,794,814)          (31,850,173)
   Purchases of securities - available for sale                         (214,745,892)           (5,452,844)
   Proceeds from prepayments, redemptions or maturities
      of securities - available for sale                                 244,280,446            27,838,649
                                                                       -------------         -------------
              Net cash provided by investing activities                   73,158,172             9,986,594
                                                                       -------------         -------------

FINANCING ACTIVITIES
   Net decrease in noninterest-bearing deposits                          (58,988,785)          (11,695,472)
   Net (decrease)increase in interest-bearing deposits                   (16,486,653)              415,431
   Net (decrease)increase in Federal funds purchased and
      securities sold under agreements to repurchase                     (38,368,431)            4,500,154
   Net increase(decrease) in commercial paper
      and other short-term borrowings                                     13,237,316           (29,990,919)
   Increase(Decrease) in other long-term debt                             39,650,000              (250,000)
   Proceeds from exercise of stock options                                   485,625                59,750
   Cash dividends paid on common and preferred stock                      (1,745,799)           (1,407,395)
                                                                       -------------         -------------
              Net cash used in financing activities                      (62,216,727)          (38,368,451)
                                                                       -------------         -------------
Net increase (decrease) in cash and due from banks                        12,016,216           (13,792,275)
Cash and due from banks - beginning of period                             40,065,863            54,512,462
                                                                       -------------         -------------
Cash and due from banks - end of period                                $  52,082,079         $  40,720,187
                                                                       =============         =============

Supplemental schedule of non-cash financing activities:
   Debenture and preferred stock conversions                           $      22,840         $   1,673,782
Supplemental disclosure of cash flow information:
   Interest paid                                                       $  12,992,642         $  12,375,149
   Income taxes paid                                                       3,868,832             1,630,749
</TABLE>

See Notes to Consolidated Financial Statements.

                                        7
<PAGE>   8
                        STERLING BANCORP AND SUBSIDIARIES
                   Notes to Consolidated Financial Statements


   1.         The consolidated financial statements include the accounts of
              Sterling Bancorp ("the parent company") and its subsidiaries,
              principally Sterling National Bank and its subsidiaries ("the
              Bank"), after elimination of material intercompany transactions.
              The term "the Company" refers to Sterling Bancorp and its
              subsidiaries. The consolidated financial statements as of and for
              the interim periods ended June 30, 1998 and 1997 are unaudited;
              however, in the opinion of management, all adjustments, consisting
              of normal recurring accruals, necessary for a fair presentation of
              such periods have been made. Certain reclassifications have been
              made to the 1997 financial statements to conform to current
              presentation. The interim financial statements should be read in
              conjunction with the Company's annual report on Form 10-K for the
              year ended December 31, 1997.

   2.         For purposes of reporting cash flows, cash and cash equivalents
              include cash and due from banks.

   3.         The Company's outstanding Preferred Shares as of June 30, 1998
              comprise 1,230 Series B shares (of 4,389 Series B shares
              authorized) and 244,691 Series D shares (of 300,000 Series D
              shares authorized). Each Series B share is entitled to cumulative
              dividends at the rate of $0.10 per year, to one vote per share and
              upon liquidation or redemption to an amount equal to accrued and
              unpaid dividends to the date of redemption or liquidation plus an
              amount which is $20 in the case of involuntary liquidation and $28
              otherwise. Each Series D share (all of such shares are owned by
              the Company's Employee Stock Ownership Trust) is entitled to
              dividends at the rate of $0.6125 per year, is convertible into one
              Common Share, and is entitled to a liquidation preference of $10
              (together with accrued dividends). All preferred shares are
              entitled to one vote per share (voting with the Common Shares
              except as otherwise required by law).

   4.         SFAS No. 128, "Earnings per Share," which superseded Accounting
              Principles Board Opinion No. 15, "Earnings per Share," established
              standards for computing, presenting and disclosing earnings per
              share ("EPS"). SFAS No. 128 required the presentation of basic
              earnings per share and, for entities with complex capital
              structures, diluted earnings per share. Basic earnings per share
              is computed by dividing income available to common stockholders by
              the weighted average number of common shares outstanding for the
              period. Diluted earnings per share reflects the potential dilution
              that could occur if securities or other contracts to issue common
              stock were exercised or converted into common stock or resulted in
              the issuance of common stock that then shared in the earnings of
              the Company.

                  The Company has applied the provisions of SFAS No. 128 for the
              year ended December 31, 1997 and, in conformity with the
              provisions of SFAS No. 128, has restated prior-period EPS data
              presented in this report. Adoption of SFAS No. 128 has resulted in
              modest changes in EPS data from previously reported amounts.

                                        8
<PAGE>   9
                        STERLING BANCORP AND SUBSIDIARIES
                   Notes to Consolidated Financial Statements


   5.         In June 1997, the Financial Accounting Standards Board issued
              Statement of Financial Accounting Standards No. 130, "Reporting
              Comprehensive Income" ("SFAS 130"). SFAS 130 established standards
              for reporting and display of comprehensive income and its
              components (revenues, expenses, gains and losses) in a full set of
              general-purpose financial statements. It does not address issues
              of recognition or measurement of comprehensive income and its
              components. SFAS 130 required that all items that are required to
              be recognized under accounting standards as components of
              comprehensive income be reported in a financial statement that is
              displayed with the same prominence as other financial statements.
              Under the requirements of SFAS 130, an enterprise must classify
              items of other comprehensive income by their nature in a financial
              statement and display the accumulated balance of other
              comprehensive income separately from retained earnings and
              additional paid-in capital in the equity section of a balance
              sheet. SFAS 130 is effective for fiscal years beginning after
              December 15, 1997 and requires reclassification of financial
              statements for earlier periods provided for comparative purposes.

                  The Company has applied the provisions of SFAS No. 130 as of
              January 1, 1998, and in conformity with the provisions of SFAS No.
              130, has restated prior-period amounts presented in this report.
              Adoption of SFAS No. 130 had no effect on previously reported
              amounts.

   6.         In June 1997, the Financial Accounting Standards Board issued
              Statement of Financial Accounting Standards No. 131, "Disclosure
              about Segments of an Enterprise and Related Information" ("SFAS
              131"). SFAS 131 establishes standards for the way that public
              business enterprises report information about operating segments
              in annual financial statements, requires that selected information
              about operating segments be reported in interim financial
              statements issued to shareholders, and establishes standards for
              related disclosures about an enterprise's products and services,
              geographic areas and major customers. As defined in SFAS 131,
              operating segments are components of an enterprise about which
              separate financial information is available that is evaluated
              regularly by the enterprise's chief operating decision maker in
              deciding how to allocate resources and in assessing performance.
              SFAS 131 supersedes "Statement of Financial Accounting Standards
              No. 14, "Financial Reporting for Segments of a Business," and
              amends Statement of Financial Accounting Standards No. 94,
              "Consolidation of All Majority-Owned Subsidiaries." SFAS 131 need
              not be applied to interim financial statements in the initial year
              of its application, but comparative information for interim
              periods in the initial year of application is to be reported in
              financial statements for interim periods in the second year of
              application. SFAS 131 is effective for financial statements for
              fiscal years beginning after December 15, 1997 and, accordingly,
              will be adopted by the Company for its fiscal year ending December
              31, 1998.

   7.         In February 1998, the Financial Accounting Standards Board issued
              Statement of Financial Accounting Standards No. 132, "Employers'
              Disclosures about Pensions and Other Postretirement Benefits"
              ("SFAS 132"). SFAS 132 standardizes the disclosure requirements
              for pensions and other postretirement benefits to the extent
              practicable. SFAS 132 provides information that assists users in
              (a) evaluating the employer's obligations under pension and other
              postretirement plans and the effects on the employer's prospects
              for future cash flows, (b) analyzing the quality of currently
              reported net income, and (c) estimating future reported net
              income. SFAS 132 addresses disclosure only. SFAS 132 is effective
              for fiscal years beginning after December 15, 1997, and, as
              appropriate, will be adopted in the financial statements of the
              Company for the year ended December 31, 1998.

                                        9
<PAGE>   10
                        STERLING BANCORP AND SUBSIDIARIES
           MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
                            AND RESULTS OF OPERATIONS



The following commentary presents management's discussion and analyses of the
consolidated results of operations and financial condition of Sterling Bancorp
(the "parent company"), a bank holding company as defined by the Bank Holding
Company Act of 1956, as amended, and its wholly-owned subsidiaries Sterling
Banking Corporation, Sterling Industrial Loan Association, and Sterling National
Bank (the "Bank"). The Bank, which is the principal subsidiary, owns all of the
outstanding shares of Sterling Factors Corporation ("Factors"), Sterling
National Mortgage Company, Inc.("SNMC-New York"), Sterling National Mortgage
Corp. ("SNMC-Virginia") and Sterling Real Estate Holding Company Inc. ("SREHC").
Throughout this discussion and analysis, the term "the Company" refers to
Sterling Bancorp and its subsidiaries. This discussion and analysis should be
read in conjunction with the Company's annual report on Form 10-K for the year
ended December 31, 1997. This report contains statements that constitute
forward-looking statements and are subject to certain risks and uncertainties
that could cause actual facts to differ materially from those presented in this
report. Readers are cautioned not to place undue reliance on these
forward-looking statements which speak only as of the date of this report.


COMPANY BUSINESS

The Company provides a full range of financial products and services, including
business and consumer loans, commercial and residential mortgage lending and
brokerage, asset-based financing, accounts receivable management services, trade
financing, equipment leasing, corporate and consumer deposits services, trust
and estate administration and, investment management services. The Company has
operations in New York and Virginia and conducts business throughout the United
States.

         There is intense competition in all areas in which the Company conducts
its business. In addition to competing with other banks, the Company competes in
certain areas of its business with other financial institutions. At June
30,1998, the Bank's year-to-date average earning assets (of which loans were 55%
and investment securities were 43%) represented approximately 96% of the
Company's year-to-date average earning assets.

         The Company regularly evaluates acquisition opportunities and conducts
due diligence activities in connection with possible acquisitions. As a result,
acquisition discussions and, in some cases negotiations, regularly take place
and future acquisitions could occur.


            Results for the three months ended June 30, 1998 and 1997

OVERVIEW

The Company reported net income for the three months ended June 30,1998 of $3.1
million, representing $0.36 per share, calculated on a diluted basis, compared
to $2.6 million, or $0.31 per share calculated on a diluted basis, for the like
period in 1997. This increase reflects continued growth in both net interest
income and noninterest income as explained below.

         Net interest income increased to $11.9 million for the second quarter
of 1998 compared with $11.1 million for the same period in 1997, principally due
to higher average earning asset outstandings. The net interest margin was 5.83%
for

                                       10
<PAGE>   11
the three months ended June 30, 1998 compared to 6.18% for the like 1997 period.
This decrease was due to a decrease in average yield on earning assets of 44
basis points partially offset by a 6 basis point decrease in the average cost of
funds.

         Noninterest income rose to $4.2 million for the three months ended June
30,1998 compared to $3.0 million for the like 1997 period principally due to
continued growth in fees from mortgage banking, factoring, trust and deposit
services.



INCOME STATEMENT ANALYSIS

Net Interest Income
Net interest income, which represents the difference between interest earned on
interest-earning assets and interest incurred on interest-bearing liabilities,
is the Company's primary source of earnings. Net interest income can be affected
by changes in market interest rates as well as the level and composition of
assets, liabilities and shareholders' equity. The increases (decreases) for the
components of quarterly interest income and interest expense, expressed in terms
of fluctuation in average volume and rate are shown on page 20. Information as
to the components of interest income and interest expense and average rates for
the quarter is provided in the Average Balance Sheets shown on page 18.

         Net interest income for the three months ended June 30,1998 increased
$820,000 to $11,871,000 from $11,051,000 for the comparable period in 1997.

         Total interest income aggregated $18,072,000 up $1,501,000 for the
second quarter of 1998 as compared to $16,571,000 for the same period of 1997.
The yield on interest-earning assets was 8.87% for the three months ended June
30, 1998 compared with 9.31% for the comparable period in 1997. The increase in
interest income was principally due to an increase in income earned on the
Company's loan portfolio as a result of management's strategy of increasing loan
outstandings as a percentage of total assets. The decrease in yield on earning
assets was due to lower yields on loans and investment securities.

         Interest earned on the loan portfolio for the three months ended June
30, 1998 amounted to $12,662,000 up $1,255,000 when compared to the like 1997
period. Average loan balances amounted to $495,613,000 up $64,860,000 from an
average of $430,753,000 in the prior year period. The increase in the average
loans, primarily in the Company's leasing, mortgage and in the short-term money
market component of commercial and industrial loan portfolio, accounted for the
increase in interest earned on loans. The decrease in the yield on the domestic
loan portfolio to 11.08% for the three months ended June 30,1998 from 11.34% for
the comparable 1997 period was attributable to a greater proportion of
short-term, lower-yielding loans within the portfolio.

         Interest earned on investment securities increased $79,000 to
$5,162,000 in the second quarter of 1998 principally due to higher average
outstandings partially offset by lower yields due to a flattening of the U.S.
Treasury yield curve.

         Interest expense increased $683,000 to $6,202,000 for the second
quarter of 1998 from $5,519,000 for the comparable period in 1997. The increase
in interest expense was due to higher average funds employed and higher average
rates paid for interest-bearing deposits.

                                       11
<PAGE>   12
         Interest expense on interest-bearing deposits increased $664,000 for
the three months ended June 30,1998 to $4,166,000 from $3,502,000 for the
comparable 1997 period due to increases in average outstandings and the cost of
funds. Average outstandings increased $60,590,000 to $417,257,000 in 1998 from
$356,667,000 in 1997. The average rate paid on interest-bearing deposits rose to
4.00% in 1998 compared to 3.94% in the comparable year ago period.

Provision for Credit Losses
Based on management's continuing evaluation of the loan portfolio (discussed
under "Asset Quality" below), and principally as the result of the growth in the
loan portfolios, the provision for credit losses increased to $1,267,000 up
$657,000 when compared to the same period last year.

Noninterest Income
Noninterest income increased $1,154,000 for the second quarter of 1998 when
compared with the like 1997 period primarily as a result of increased fees from
mortgage banking, factoring, trust and deposit services.

Noninterest Expense
Noninterest expenses increased $757,000 for the second quarter of 1998 when
compared with the like 1997 period primarily due to increased personnel expenses
incurred to support growing levels of business activity and continued
investments in the business franchise.

Provision for Income Taxes
The increase in the provision for income taxes was principally due to higher
pretax earnings partially offset by tax strategies implemented during 1997.


             Results for the six months ended June 30, 1998 and 1997

OVERVIEW

The Company reported net income for the six months ended June 30,1998 of $6.1
million, representing $0.71 per share, calculated on a diluted basis, compared
to $5.1 million, or $0.61 per share calculated on a diluted basis, for the like
period in 1997. This increase reflects continued growth in both net interest
income and noninterest income as explained below.

         Net interest income increased to $23.6 million for the first six months
of 1998 compared with $22.1 million for the same period in 1997, principally due
to higher average earning asset outstandings. The net interest margin was 5.83%
for the first six months of 1998 compared to 6.25% for the like 1997 period.
This decrease was due to a decrease in average yield on earning assets of 35
basis points and a 8 basis point increase in the average cost of funds.

         Noninterest income rose to $7.7 million for the six months ended June
30,1998 compared to $6.1 million for the like 1997 period principally due to
continued growth in fees from mortgage banking, factoring, trust and deposit
services.

                                       12
<PAGE>   13
INCOME STATEMENT ANALYSIS

Net Interest Income
Net interest income, which represents the difference between interest earned on
interest-earning assets and interest incurred on interest-bearing liabilities,
is the Company's primary source of earnings. Net interest income can be affected
by changes in market interest rates as well as the level and composition of
assets, liabilities and shareholders' equity. The increases (decreases) for the
components of interest income and interest expense for the first six months,
expressed in terms of fluctuation in average volume and rate are shown on page
21. Information as to the components of interest income and interest expense and
average rates for the first six months is provided in the Average Balance Sheets
shown on page 19.

         Net interest income for the six months ended June 30,1998 increased
$1,478,000 to $23,627,000 from $22,149,000 for the comparable period in 1997.

         Total interest income aggregated $36,261,000 up $3,374,000 for the
first half of 1998 as compared to $32,887,000 for the same period of 1997. The
yield on interest-earning assets was 8.96% for the first six months of 1998
compared with 9.31% for the comparable period in 1997. The increase in interest
income was principally due to an increase in income earned on the Company's loan
portfolio as a result of management's strategy of increasing loan outstandings
as a percentage of total assets. The decrease in yield on earning assets was due
to lower yields on loans and investment securities.

         Interest earned on the loan portfolio amounted to $24,922,000 up
$2,432,000 when compared to a year ago. Average loan balances amounted to
$490,337,000 up $61,338,000 from an average of $428,999,000 in the prior year
period. The increase in the average loans, primarily in the Company's leasing,
mortgage and in the short-term money market component of commercial and
industrial loan portfolio, accounted for the increase in interest earned on
loans. The decrease in the yield on the domestic loan portfolio to 11.15% for
the six months ended June 30,1998 from 11.37% for the comparable 1997 period was
attributable to a greater proportion of short-term, lower-yielding loans within
the portfolio.

         Interest earned on investment securities increased $693,000 to
$10,877,000 in 1998 principally due to higher average outstandings partially
offset by lower yields due to a flattening of the U.S. Treasury yield curve.

         Interest expense increased $1,896,000 to $12,634,000 for the first six
months of 1998 from $10,738,000 for the comparable period in 1997. The increase
in interest expense was due to higher average funds employed and higher average
rates paid for interest-bearing deposits.

         Interest expense on interest-bearing deposits increased $1,751,000 for
the six months ended June 30,1998 to $8,571,000 from $6,820,000 for the
comparable 1997 period due to increases in average outstandings and the cost of
funds. Average outstandings increased $67,983,000 to $423,336,000 in 1998 from
$355,353,000 in 1997. The average rate paid on interest-bearing deposits rose to
4.08% in 1998 compared to 3.87% in the comparable year ago period.

Provision for Credit Losses
Based on management's continuing evaluation of the loan portfolio (discussed
under "Asset Quality" below), and principally as the result of the growth in the
loan portfolios, the provision for credit losses increased to $2,111,000 up
$730,000 when compared to the same period last year.

                                       13
<PAGE>   14
Noninterest Income
Noninterest income increased $1,517,000 for the first six months of 1998 when
compared with the like 1997 period primarily as a result of increased fees from
mortgage banking, factoring, trust and deposit services.

Noninterest Expense
Noninterest expenses increased $971,000 for the second quarter of 1998 when
compared with the like 1997 period primarily due to increased personnel expenses
incurred to support growing levels of business activity and continued
investments in the business franchise.

Provision for Income Taxes
The increase in the provision for income taxes was principally due to higher
pretax earnings partially offset by tax strategies implemented during 1997.


BALANCE SHEET ANALYSIS

Securities
The Company's securities portfolios are comprised of principally U.S. Government
and U.S. Government corporation and agency guaranteed mortgage backed securities
along with other debt and equity securities. At June 30, 1998, the Company's
portfolio of securities totalled $329,501,000 of which U.S. Government and U.S.
Government corporation and agency guaranteed mortgage-backed securities having
an average life of approximately 4 years amounted to $308,633,000. The Company
has the intent and ability to hold to maturity securities classified as "held to
maturity". These securities are carried at cost, adjusted for amortization of
premiums and accretion of discounts. The gross unrealized gains and losses on
"held to maturity" securities were $1,367,000 and $1,187,000, respectively.
Securities classified as "available for sale" may be sold in the future, prior
to maturity. These securities are carried at market value. Net aggregate
unrealized gains or losses on these securities are included in a valuation
allowance account and are shown net of taxes, as a component of shareholders'
equity. "Available for sale" securities included gross unrealized gains of
$620,000 and gross unrealized losses of $182,000. Given the generally high
credit quality of the portfolio, management expects to realize all of its
investment upon the maturity of such instruments, and thus believes that any
market value impairment is temporary in nature.


Loan Portfolio
A key management objective is to maintain the quality of the loan portfolio.
This objective is achieved by maintaining high underwriting standards coupled
with regular evaluation of the creditworthiness of and the designation of
lending limits for each borrower. The portfolio strategies seek to avoid
concentrations by industry or loan size in order to minimize credit exposure and
to originate loans in markets with which it is familiar.

                                       14
<PAGE>   15
         The Company's commercial and industrial loan portfolio represents
approximately 72% of gross loans. Loans in this category are typically made to
small and medium sized businesses and range between $250,000 and $10 million.
The primary source of repayment is from the borrower's operating profits and
cash flows. Based on underwriting standards, loans may be secured in whole or in
part by collateral such as liquid assets, accounts receivable, equipment,
inventory or real property. The Company's real estate loan portfolio, which
represents approximately 15% of gross loans, is secured by mortgages on real
property located principally in the City of New York and the State of Virginia.
The Company's leasing portfolio, which consists of finance leases for various
types of business equipment, represents approximately 10% of gross loans. The
collateral securing any loan may vary in value based on the success of the
business and economic conditions.

         The following table sets forth the composition of the Company's loan
portfolio:
<TABLE>
<CAPTION>
                                                                                    June 30,
                                                                      1998                           1997
                                                                      ----                           ----
                                                                              ($ in thousands)
                                                                             % of                          % of
                                                            Balances        Gross          Balances        Gross
                                                            --------        -----          --------        -----
<S>                                                        <C>            <C>             <C>             <C>
Domestic
  Commercial and industrial                                 $397,404         71.6%         $344,939         72.6%
  Equipment lease financing                                   54,110          9.8            42,932          9.1
  Real estate                                                 85,703         15.4            70,395         14.8
  Installment - individuals                                   17,060          3.1            15,822          3.3
Foreign
  Government and official institutions                           788          0.1               789          0.2
                                                            --------        -----          --------        -----
Gross loans                                                  555,065        100.0%          474,877        100.0%
                                                                            =====                          =====
  Unearned discounts                                           8,735                          7,781
                                                            --------                       --------

Loans, net of unearned discounts                            $546,330                       $467,096
                                                            ========                       ========
</TABLE>

Asset Quality
Intrinsic to the lending process is the possibility of loss. In times of
economic slowdown, the risk inherent in the Company's portfolio of loans is
increased. While management endeavors to minimize this risk, it recognizes that
loan losses will occur and that the amount of these losses will fluctuate
depending on the risk characteristics of the loan portfolio which in turn
depends on current and expected economic conditions, the financial condition of
borrowers and the credit management process.

        The allowance for credit losses is maintained through the provision for
credit losses, which is a charge to operating earnings. The adequacy of the
provision and the resulting allowance for credit losses is determined by
management's continuing review of the loan portfolio, including identification
and review of individual problem situations that may affect the borrower's
ability to repay, review of overall portfolio quality through an analysis of
current charge-offs, delinquency and nonperforming loan data, estimates of the
value of any underlying collateral, review of regulatory examinations, an
assessment of current and expected economic conditions and changes in the size

                                       15
<PAGE>   16
and character of the loan portfolio. The allowance reflects management's
evaluation of both loans presenting identified loss potential and of the risk
inherent in various components of the portfolio, including loans identified as
impaired as required by SFAS No. 114. Thus an increase in the size of the
portfolio or in any of its components could necessitate an increase in the
allowance even though there may not be a decline in credit quality or an
increase in potential problem loans. A significant change in any of the
evaluation factors described above could result in future additions to the
allowance. At June 30,1998, the ratio of the allowance to loans, net of unearned
discounts, was 1.6% and the allowance was $8,826,000. At such date, the
Company's non-accrual loans amounted to $1,031,000; $617,000 of such loans were
judged to be impaired within the scope of SFAS No. 114 and required valuation
allowances of $250,000. Based on the foregoing, as well as management's
judgement as to the current risks inherent in the loan portfolio, the Company's
allowance for credit losses was deemed adequate to absorb all reasonably
anticipated losses on specifically known and other possible credit risks
associated with the portfolio as of June 30,1998. Potential problem loans, which
are loans that are currently performing under present loan repayment terms but
where known information about possible credit problems of borrowers causes
management to have serious doubts as to the ability of the borrowers to continue
to comply with the present repayment terms, aggregated $72,000 at June 30,1998.


Deposits
The Company's principal source of funds continues to be deposits, consisting of
demand (noninterest-bearing), NOW, savings, money market and time deposits
(principally certificates of deposit).
        The following table provides certain information with respect to the
Company's deposits:


<TABLE>
<CAPTION>
                                                                              June 30,
                                                              1998                               1997
                                                              ----                               ----
                                                                         ($ in thousands)
                                                                      % of                               % of
                                                    Balances         Total             Balances         Total
                                                    --------         -----             --------         -----
<S>                                                <C>              <C>               <C>              <C>
Domestic
  Demand                                            $253,473          38.6%            $218,281          38.8%
  NOW                                                 69,085          10.5               33,412           5.9
  Savings                                             23,480           3.6               23,534           4.2
  Money Market                                       134,100          20.4              113,450          20.1
  Time deposits                                      173,065          26.5              171,755          30.5
                                                    --------         -----             --------         -----

      Total domestic deposits                        653,203          99.6              560,432          99.5
Foreign
  Time deposits                                        2,730           0.4                2,710           0.5
                                                    --------         -----             --------         -----

      Total deposits                                $655,933         100.0%            $563,142         100.0%
                                                    ========         =====             ========         =====
</TABLE>


        Fluctuations of balances in total or among categories at any date may
occur based on the Company's mix of assets and liabilities as well as on
customers' balance sheet strategies. Historically, however, average balances for
deposits have been relatively stable. Information regarding these average
balances is presented on pages 18 and 19.

                                       16
<PAGE>   17
CAPITAL

The Company and the Bank are subject to risk-based capital regulations. The
purpose of these regulations is to quantitatively measure capital against risk-
weighted assets, including off-balance sheet items. These regulations define the
elements of total capital into Tier 1 and Tier 2 components and establish
minimum ratios of 4% for Tier 1 capital and 8% for Total Capital for capital
adequacy purposes. Supplementing these regulations, is a leverage requirement.
This requirement establishes a minimum leverage ratio, (at least 3% to 5%) which
is calculated by dividing Tier 1 capital by adjusted quarterly average assets
(after deducting goodwill). Information regarding the Company's and the Bank's
risk- based capital is presented on page 22. In addition the Company and The
Bank are subject to the provisions of the Federal Deposit Insurance Corporation
Improvement Act of 1981 ("FDICIA") which imposes a number of mandatory
supervisory measures. Among other matters, FDICIA established five capital
categories ranging from "well capitalized" to "critically under capitalized".
Such classifications are used by regulatory agencies to determine a bank's
deposit insurance premium, approval of applications authorizing institutions to
increase their asset size or otherwise expand business activities or acquire
other institutions. Under the provisions of FDICIA a "well capitalized"
institution must maintain minimum leverage, Tier 1 and Total Capital ratios of
5%, 6% and 10%, respectively. At June 30,1998, the Company and the Bank exceeded
the requirements for "well capitalized" institutions.



                                       17
<PAGE>   18
                        STERLING BANCORP AND SUBSIDIARIES
                           Average Balance Sheets [1]
                           Three Months Ended June 30,

<TABLE>
<CAPTION>
                                                          1998                                         1997
                                            Average                        Average      Average                        Average
ASSETS                                      Balance        Interest         Rate        Balance        Interest         Rate
                                            --------       --------       --------      --------       --------        ------
<S>                                        <C>            <C>            <C>           <C>           <C>             <C>
Interest-bearing deposits
   with other banks                         $    830       $     31          5.17%      $  4,077       $     65          5.21%
Investment securities
   Available for sale [2]                    122,954          1,920          6.25         65,368          1,083          6.64
   Held to maturity                          221,078          3,242          6.08        237,168          4,000          6.75
Federal funds sold                            15,786            218          5.46          1,132             16          5.46
Loans, net of unearned discounts
   Domestic [3]                              494,825         12,648         11.08        429,964         11,394         11.34
   Foreign                                       788             13          6.70            789             13          6.46
                                            --------       --------                     --------        -------
         TOTAL INTEREST-EARNING
            ASSETS                           856,261         18,072          8.87        738,498         16,571          9.31
                                                           --------        -------                     --------        ------

Cash and due from banks                       43,699                                      47,005
Allowance for credit losses                   (8,754)                                     (8,108)
Goodwill                                      21,158                                      21,158
Other assets                                  22,206                                      20,880
                                            --------                                    --------

         TOTAL ASSETS                       $934,570                                    $819,433
                                            ========                                    ========

LIABILITIES AND SHAREHOLDERS'
   EQUITY
Interest-bearing deposits
   Domestic
      Savings                               $ 23,684            132          2.24       $ 24,548            133          2.17
      NOW                                     65,534            472          2.89         30,932            113          1.46
      Money Market                           140,129          1,130          3.23        125,518            983          3.14
      Time                                   185,180          2,395          5.19        171,947          2,223          5.18
   Foreign
      Time                                     2,730             37          5.43          3,722             50          5.41
                                            --------       --------                     --------       --------
      Total interest-bearing
           deposits                          417,257          4,166          4.00        356,667          3,502          3.94

Borrowings
   Federal funds purchased and
     securities sold under
      agreements to repurchase                67,597            869          5.14         92,891          1,258          5.43
   Commercial paper                           30,269            388          5.14         23,596            315          5.35
   Other short-term debt                      15,836            253          5.25          7,455            159          5.28
   Long-term debt                             41,512            526          5.08         20,027            285          5.70
                                            --------       --------                     --------       --------

         TOTAL INTEREST-BEARING
           LIABILITIES                       572,471          6,202          4.31        500,636          5,519          4.37
                                                           --------          ----                      --------          ----

Noninterest-bearing deposits                 222,841                                     195,492
Other liabilities                             43,785                                      43,395
                                            --------                                    --------
       Total liabilities                     839,097                                     739,523

Shareholders' equity                          95,473                                      79,910
                                            --------                                    --------
         TOTAL LIABILITIES AND
           SHAREHOLDERS' EQUITY             $934,570                                    $819,433
                                            ========                                    ========

Net interest income/spread                                 $ 11,870          4.56%                     $ 11,052          4.94%
                                                           ========          ====                      ========          ====

Net yield on interest-earning
   assets (margin)                                                           5.83%                                       6.18%
                                                                             ====                                        ====
</TABLE>


[1]   The average balances of assets, liabilities and shareholders' equity are
      computed on the basis of daily averages. Dollars are presented in
      thousands.
[2]   Interest on tax-exempt securities included herein is immaterial and is not
      presented on a tax equivalent basis.
[3]   Non-accrual loans are included in the average balance, which reduces the
      average yields.

                                       18
<PAGE>   19
                        STERLING BANCORP AND SUBSIDIARIES
                           Average Balance Sheets [1]
                            Six Months Ended June 30,

<TABLE>
<CAPTION>
                                                            1998                                         1997
                                            Average                        Average      Average                         Average
ASSETS                                      Balance        Interest         Rate        Balance        Interest          Rate
                                            --------       --------       --------      --------       --------         ------
<S>                                        <C>            <C>            <C>           <C>            <C>              <C>
Interest-bearing deposits
   with other banks                         $ 1,742        $    105          5.13%      $  3,546       $    123          5.39%
Investment securities
   Available for sale [2]                    122,522          3,798          6.22         71,131          2,401          6.78
   Held to maturity                          227,577          7,079          6.33        231,384          7,783          6.73
Federal funds sold                            12,994            357          5.46          3,326             90          5.37
Loans, net of unearned discounts
   Domestic [3]                              489,548         24,895         11.15        428,210         22,464         11.37
   Foreign                                       789             27          6.78            789             26          6.55
                                            --------       --------                     --------       --------
         TOTAL INTEREST-EARNING
            ASSETS                           855,172         36,261          8.96        738,386         32,887          9.31
                                                           --------        ------                      --------        ------

Cash and due from banks                       42,508                                      47,703
Allowance for credit losses                   (8,876)                                     (8,237)
Goodwill                                      21,158                                      21,158
Other assets                                  21,597                                      19,034
                                            --------                                    --------

         TOTAL ASSETS                       $931,559                                    $818,044
                                            ========                                    ========

LIABILITIES AND SHAREHOLDERS'
   EQUITY
Interest-bearing deposits
   Domestic
      Savings                               $ 23,617            262          2.24       $ 25,022            269          2.16
      NOW                                     59,581            847          2.87         31,054            198          1.29
      Money Market                           137,642          2,152          3.15        130,392          2,005          3.10
      Time                                   199,768          5,237          5.29        165,666          4,263          5.19
   Foreign
      Time                                     2,728             73          5.39          3,219             85          5.31
                                            --------       --------                     --------       --------
      Total interest-bearing
           deposits                          423,336          8,571          4.08        355,353          6,820          3.87

Borrowings
   Federal funds purchased and
     securities sold under
      agreements to repurchase                79,329          2,087          5.30         88,917          2,351          5.33
   Commercial paper                           29,213            749          5.17         25,051            645          5.20
   Other short-term debt                      15,179            497          5.22          7,626            306          4.88
   Long-term debt                             28,978            730          5.08         20,346            616          6.11
                                            --------       --------                     --------       --------

         TOTAL INTEREST-BEARING
           LIABILITIES                       576,035         12,634          4.39        497,293         10,738          4.31
                                                           --------          ----                      --------          ----

Noninterest-bearing deposits                 218,368                                     198,181
Other liabilities                             42,981                                      43,735
                                            --------                                    --------
       Total liabilities                     837,384                                     739,209

Shareholders' equity                          94,175                                      78,835
                                            --------                                    --------
         TOTAL LIABILITIES AND
           SHAREHOLDERS' EQUITY             $931,559                                    $818,044
                                            ========                                    ========

Net interest income/spread                                 $ 23,627          4.57%                     $ 22,149          5.00%
                                                           ========          ====                      ========          ====

Net yield on interest-earning
   assets (margin)                                                           5.83%                                       6.25%
                                                                             ====                                        ====
</TABLE>


[1]   The average balances of assets, liabilities and shareholders' equity are
      computed on the basis of daily averages. Dollars are presented in
      thousands.
[2]   Interest on tax-exempt securities included herein is immaterial and is not
      presented on a tax equivalent basis.
[3]   Non-accrual loans are included in the average balance, which reduces the
      average yields.

                                       19
<PAGE>   20
                        STERLING BANCORP AND SUBSIDIARIES
                              Rate/Volume Analysis
                           Three Months Ended June 30,
                                  (000 omitted)


<TABLE>
<CAPTION>
                                                             Increase/(Decrease)
                                                             Three Months Ended
                                                           June 30, 1998 and 1997
                                                   Volume           Rate           Net[1]
                                                   ------           ----           ------
<S>                                               <C>             <C>             <C>
INTEREST INCOME
Interest-bearing deposits with other banks        $   (34)        $    --         $   (34)
                                                  -------         -------         -------

Investment securities
   Available for sale [2]                             904             (67)            837
   Held to maturity                                  (308)           (450)           (758)
                                                  -------         -------         -------
      Total                                           596            (517)             79
                                                  -------         -------         -------


Federal funds sold                                    202              --             202
                                                  -------         -------         -------

Loans, net of unearned discounts [3]                1,573            (319)          1,254
                                                  -------         -------         -------
TOTAL INTEREST INCOME                             $ 2,337         $  (836)        $ 1,501
                                                  =======         =======         =======

INTEREST EXPENSE
Interest-bearing deposits
   Domestic
      Savings                                     $    (5)        $     4         $    (1)
      NOW                                             192             167             359
      Money Market                                    118              29             147
      Time                                            168               4             172
 Foreign
      Time                                            (13)             --             (13)
                                                  -------         -------         -------
   Total                                              460             204             664
                                                  -------         -------         -------

Borrowings
   Federal funds purchased and securities
    sold under agreements to repurchase              (325)            (64)           (389)
   Commercial paper                                    85             (12)             73
   Other short-term debt                               95              (1)             94
   Long-term debt                                     275             (34)            241
                                                  -------         -------         -------
      Total                                           130            (111)             19
                                                  -------         -------         -------

TOTAL INTEREST EXPENSE                            $   590         $    93         $   683
                                                  =======         =======         =======

NET INTEREST INCOME                               $ 1,747         $  (929)        $   818
                                                  =======         =======         =======
</TABLE>


[1]   The change in interest income and interest expense due to both rate and
      volume has been allocated to change due to rate and the change due to
      volume in proportion to the relationship of the absolute dollar amounts of
      the changes in each.


[2]   Includes Federal Reserve Bank and other stock investments.


[3]   Nonaccrual loans have been included in the amounts outstanding and income
      has been included to the extent accrued.

                                       20
<PAGE>   21
                        STERLING BANCORP AND SUBSIDIARIES
                              Rate/Volume Analysis
                            Six Months Ended June 30,
                                  (000 omitted)


<TABLE>
<CAPTION>
                                                             Increase/(Decrease)
                                                              Six Months Ended
                                                           June 30, 1998 and 1997
                                                   Volume           Rate           Net[1]
                                                   ------           ----           ------
<S>                                               <C>             <C>             <C>
INTEREST INCOME
Interest-bearing deposits with other banks        $   (16)        $    (2)        $   (18)
                                                  -------         -------         -------

Investment securities
   Available for sale [2]                           1,562            (165)          1,397
   Held to maturity                                  (153)           (551)           (704)
                                                  -------         -------         -------
      Total                                         1,409            (716)            693
                                                  -------         -------         -------


Federal funds sold                                    266               1             267
                                                  -------         -------         -------

Loans, net of unearned discounts [3]                2,965            (533)          2,432
                                                  -------         -------         -------
TOTAL INTEREST INCOME                             $ 4,624         $(1,250)        $ 3,374
                                                  =======         =======         =======

INTEREST EXPENSE
Interest-bearing deposits
   Domestic
      Savings                                     $   (16)        $     9         $    (7)
      NOW                                             278             371             649
      Money Market                                    114              33             147
      Time                                            891              83             974
   Foreign
      Time                                            (13)              1             (12)
                                                  -------         -------         -------
         Total                                      1,254             497           1,751
                                                  -------         -------         -------

Borrowings
   Federal funds purchased and securities
    sold under agreements to repurchase              (251)            (13)           (264)
   Commercial paper                                   108              (4)            104
   Other short-term debt                              178              13             191
   Long-term debt                                     231            (117)            114
                                                  -------         -------         -------
      Total                                           266            (121)            145
                                                  -------         -------         -------

TOTAL INTEREST EXPENSE                            $ 1,520         $   376         $ 1,896
                                                  =======         =======         =======

NET INTEREST INCOME                               $ 3,104         $(1,626)        $ 1,478
                                                  =======         =======         =======
</TABLE>


[1]   The change in interest income and interest expense due to both rate and
      volume has been allocated to change due to rate and the change due to
      volume in proportion to the relationship of the absolute dollar amounts of
      the changes in each.


[2]   Includes Federal Reserve Bank and other stock investments.


[3]   Nonaccrual loans have been included in the amounts outstanding and income
      has been included to the extent accrued.

                                       21
<PAGE>   22
                        STERLING BANCORP AND SUBSIDIARIES
                          Regulatory Capital and Ratios




RATIOS AND MINIMUMS
(Dollars in thousands)
<TABLE>
<CAPTION>
                                                                                      For Capital                 To Be Well
                                                               Actual               Adequacy Minimum              Capitalized
AS OF JUNE 30, 1998                                      Amount      Ratio          Amount      Ratio          Amount     Ratio
-------------------                                      ------      -----          ------      -----          ------     -----
<S>                                                     <C>          <C>           <C>          <C>           <C>         <C>
Total Capital (to Risk Weighted Assets):
  The Company                                           $83,884      13.82%        $48,543      8.00%         $60,679     10.00%
  The Bank                                               66,692      11.88          44,918      8.00           56,147     10.00

Tier 1 Capital (to Risk Weighted Assets):
  The Company                                            76,284      12.57          24,272      4.00           36,408      6.00
  The Bank                                               60,115      10.71          22,459      4.00           33,688      6.00

Tier 1 Leverage Capital (to Average Assets):
  The Company                                            76,284       8.35          36,536      4.00           45,671      5.00
  The Bank                                               60,115       6.87          35,010      4.00           43,763      5.00


AS OF DECEMBER 31, 1997
-----------------------
Total Capital (to Risk Weighted Assets):
  The Company                                           $79,698      11.82%        $53,935      8.00%         $67,419     10.00%
  The Bank                                               61,521       9.64          51,038      8.00           63,798     10.00

Tier 1 Capital (to Risk Weighted Assets):
  The Company                                            71,268      10.57          26,968      4.00           40,451      6.00
  The Bank                                               55,028       8.63          25,519      4.00           38,279      6.00

Tier 1 Leverage Capital (to Average Assets):
  The Company                                            71,268       8.31          34,320      4.00           42,900      5.00
  The Bank                                               55,028       6.66          33,032      4.00           41,290      5.00
</TABLE>

                                       22
<PAGE>   23
ASSET/LIABILITY MANAGEMENT

The Company's primary earnings source is net interest income; therefore, the
Company devotes significant time and has invested in resources to assist in the
management of market risk, liquidity risk, capital and asset quality. The
Company's net interest income is affected by changes in market interest rates
and by the level and composition of interest-earning assets and interest-bearing
liabilities. The Company's objectives in its asset/liability management are to
utilize its capital effectively, to provide adequate liquidity and to enhance
net interest income, without taking undue risks or subjecting the Company unduly
to interest rate fluctuations.

         The Company takes a coordinated approach to the management of market
risk, liquidity and capital. This risk management process is governed by
policies and limits established by senior management which are reviewed and
approved by the Asset/Liability Committee ("ALCO"). ALCO, which is comprised of
members of senior management and the Board, meets to review among other things,
economic conditions, interest rates, yield curve, cash flow projections,
expected customer actions, liquidity levels, capital ratios and repricing
characteristics of assets, liabilities and off-balance sheet financial
instruments.


Market Risk
Market risk is the risk of loss in a financial instrument arising from adverse
changes in market indices such as interest rates, foreign exchange rates and
equity prices. The Company's principal market risk exposure is interest rate
risk, with no material impact on earnings from changes in foreign exchange rates
or equity prices.

         Interest rate risk is the exposure to changes in market interest rates.
Interest rate sensitivity is the relationship between market interest rates and
net interest income due to the repricing characteristics of assets and
liabilities. The Company monitors the interest rate sensitivity of its on - and
off - balance sheet positions by examining its near-term sensitivity and its
longer term gap position. In its management of interest rate risk, the Company
utilizes several tools including traditional gap analysis and sophisticated
income simulation models.

         A traditional gap analysis is prepared based on the maturity and
repricing characteristics of interest-earning assets and interest-bearing
liabilities for selected time bands. The mismatch between repricings or
maturities within a time band is commonly referred to as the "gap" for that
period. A positive gap (asset sensitive) where interest-rate sensitive assets
exceed interest-rate sensitive liabilities generally will result in an
institution's net interest margin increasing in a rising rate environment and
decreasing in a falling rate environment. A negative gap (liability sensitive)
will generally have the opposite result on an institution's net interest margin.
However, the traditional gap analysis does not assess the relative sensitivity
of assets and liabilities to changes in interest rates. The Company utilizes the
gap analysis to complement its income simulations modeling, primarily focusing
on the longer term structure of the balance sheet.

         The Company's balance sheet structure is primarily short-term in nature
with a substantial portion of assets and liabilities repricing or maturing
within one year. The Company's gap analysis at June 30,1998, presented on page
26, reveals that net interest income would increase during periods of rising
interest rates and decrease during periods of falling interest rates.

         As part of its interest rate risk strategy, the Company uses
off-balance sheet financial instruments (derivatives) to hedge the interest rate
sensitivity of assets with the corresponding amortization reflected in the yield
of the related on-balance sheet assets being hedged. The Company has written
policy guidelines, which have been approved by the Board of Directors based on
recommendations of the Asset/Liability Committee, governing the use of off-
balance sheet financial instruments, including approved counterparties, risk
limits and appropriate internal control procedures. The credit risk of
derivatives arises principally from the potential for a counterparty to fail to
meet its obligation to settle a contract on a timely basis.

                                       23
<PAGE>   24
          The Company purchased interest rate floor contracts to reduce the
impact of falling rates on its floating rate commercial loans. Interest rate
floor contracts require the counterparty to pay the Company at specified future
dates the amount, if any, by which the specified interest rate (3 month LIBOR)
falls below the fixed floor rates, applied to the notional amounts. The Company
utilizes these financial instruments to adjust its interest rate risk position
without exposing itself to principal risk and funding requirements.

         At June 30,1998, the Company's off-balance sheet financial instruments
consisted of four interest rate floor contracts having a notional amount
totaling $125 million consisting of a contract with a notional amount of $50
million and a final maturity of February 27, 2000, another contract with a
notional amount of $25 million and a final maturity of October 10, 1999, another
contract with a notional amount of $25 million and a final maturity of February
9, 2001 and another contract with a notional amount of $25 million and a final
maturity of May 1, 2001. These financial instruments are being used as part of
the Company's interest rate risk management and not for trading purposes. At
June 30,1998, all counterparties have investment grade credit ratings from the
major rating agencies. Each counterparty is specifically approved for applicable
credit exposure.

         The interest rate floor contracts require the Company to pay a fee for
the right to receive a fixed interest payment. The Company paid up front
premiums of $878,750 which are amortized monthly against interest income from
the designated assets. At June 30,1998, the unamortized premiums on these
contracts totaled $412,000 and are included in other assets. At June 30,1998,
$15,000 was receivable under these contracts.

         The Company utilizes income simulation models to complement its
traditional gap analysis. While ALCO routinely monitors simulated net interest
income sensitivity over a rolling two-year horizon, it also utilizes additional
tools to monitor potential longer-term interest rate risk. The income simulation
models measure the Company's net interest income sensitivity or volatility to
interest rate changes utilizing statistical techniques that allow the Company to
consider various factors which impact net interest income. These factors include
actual maturities, estimated cash flows, repricing characteristics, deposits
growth/retention and, most importantly, the relative sensitivity of the
Company's assets and liabilities to changes in market interest rates. This
relative sensitivity is important to consider as the Company's core deposit base
is not subject to the same degree of interest rate sensitivity as its assets.
The core deposits costs are internally managed and tend to exhibit less
sensitivity to changes in interest rates than the Company's adjustable rate
assets whose yields are based on external indices and change in concert with
market interest rates.

         The Company's interest rate sensitivity is determined by identifying
the probable impact of changes in market interest rates on the yields on the
Company's assets and the rates which would be paid on its liabilities. This
modeling technique involves a degree of estimation based on certain assumptions
that management believes to be reasonable. Utilizing this process, management
can project the impact of changes in interest rates on net interest margin. The
estimated effects of the Company's interest rate floors are included in the
results of the sensitivity analysis. The Company has established certain limits
for the potential volatility of its net interest margin assuming certain levels
of changes in market interest rates with the objective of maintaining a stable
net interest margin under various probable rate scenarios. The following table
reflects the estimated exposure of the Company's net interest income for the
next twelve months, assuming a parallel and pro rata shift in interest rates.

<TABLE>
<CAPTION>
                                               Rate Change             Estimated Impact on
                                              (Basis Points)           Net Interest Income
                                              --------------           -------------------
                                                                          $           %
<S>                                         <C>                       <C>           <C>
                                                 +200                   1,097,000     2.13
                                                 -200                  (1,411,000)   (2.74)
</TABLE>

                                       24
<PAGE>   25
         The preceding sensitivity analysis does not represent a Company
forecast and should not be relied upon as being indicative of expected operating
results. These hypothetical estimates are based upon numerous assumptions
including: the nature and timing of interest rate levels including yield curve
shape, prepayments on loans and securities, deposit decay rates, pricing
decisions on loans and deposits, reinvestment/replacement of asset and liability
cash flows, and others. While assumptions are developed based upon current
economic and local market conditions, the Company cannot make any assurances as
to the predictive nature of these assumptions including how customer preferences
or competitor influences might change.

         Also, as market conditions vary from those assumed in the sensitivity
analysis, actual results will also differ due to: prepayment/refinancing levels
likely deviating from those assumed, the varying impact of interest rate change
caps or floors on adjustable rate assets, the potential effect of changing debt
service levels on customers with adjustable rate loans, depositor early
withdrawals and product preference changes, and other internal/external
variables. Furthermore, the sensitivity analysis does not reflect actions that
the Asset/Liability Committee might take in responding to or anticipating
changes in interest rates.


Liquidity Risk
Liquidity is the ability to meet cash needs arising from changes in various
categories of assets and liabilities. Liquidity is constantly monitored and
managed at both parent company and the Bank levels. Liquid assets consist of
cash and due from banks, interest-bearing deposits in banks and Federal funds
sold and securities available for sale. Primary funding sources include core
deposits, capital markets funds and other money market sources. Core deposits
include domestic noninterest-bearing and interest-bearing retail deposits, which
historically have been relatively stable. The parent company and the Bank have
significant unused borrowing capacity. Contingency plans exist and could be
implemented on a timely basis to minimize the impact of any dramatic change in
market conditions.

         While the parent company generates income from its own operations, it
also depends for its cash requirements on funds maintained or generated by its
subsidiaries, principally the Bank. Such sources have been adequate to meet the
parent company's cash equivalents throughout its history.

         Various legal restrictions limit the extent to which the Bank can
supply funds to the parent company and its nonbank subsidiaries. All national
banks are limited in the payment of dividends without the approval of the
Comptroller of the Currency to an amount not to exceed the net profits as
defined, for that year to date combined with its retained net profits for the
preceding two calendar years.

         At June 30,1998, the parent company's short-term debt, consisting
principally of commercial paper used to finance ongoing current business
activities, was approximately $36,898,000. The parent company had cash,
interest-bearing deposits with banks and other current assets aggregating
$56,199,000 and back-up credit lines with banks of $19,000,000. Since 1979, the
parent company has had no need to use available back-up lines of credit.

         While the past performance is no guarantee of the future, management
believes that the Company's funding sources (including dividends from all its
subsidiaries) and the Bank's funding sources will be adequate to meet their
liquidity and capital requirements in the future.

                                       25
<PAGE>   26
                        STERLING BANCORP AND SUBSIDIARIES
                            Interest Rate Sensitivity


To mitigate the vulnerability of earnings to changes in interest rates, the
Company manages the repricing characteristics of assets and liabilities in an
attempt to control net interest rate sensitivity. Management attempts to confine
significant rate sensitivity gaps predominantly to repricing intervals of a year
or less so that adjustments can be made quickly. Assets and liabilities with
predetermined repricing dates are placed in a time of the earliest repricing
period. Based on the analysis shown below, the Company's net interest income
would increase during periods of rising interest rates and decrease during
periods of falling interest rates. Amounts are presented in thousands.

<TABLE>
<CAPTION>
                                                                         Repricing Date
                                                                                                          Non
                                      3 months        3 months         1 year to          Over            Rate
                                      or less        to 1 year          5 years         5 years        sensitive          Total
                                      -------        ---------          -------         -------        ---------          -----
<S>                                  <C>             <C>              <C>              <C>             <C>              <C>
ASSETS
   Interest-bearing deposits
       with other banks              $     315       $      --        $      --        $      --       $      --        $     315
   Investment securities                    --          24,180           14,557          283,966           6,798          329,501
   Loans, net of unearned
    discounts                          427,959           6,332           70,188           50,586          (8,735)         546,330
   Noninterest-earning assets
    and allowance for
     credit losses                          --              --               --               --          84,784           84,784
                                     ---------       ---------        ---------        ---------       ---------        ---------

      Total Assets                     428,274          30,512           84,745          334,552          82,847          960,930
                                     ---------       ---------        ---------        ---------       ---------        ---------

LIABILITIES AND SHAREHOLDERS'
EQUITY
   Interest-bearing deposits
      Savings [1]                           --              --           23,480               --              --           23,480
      NOW [1]                               --              --           69,085               --              --           69,085
      Money market [1]                 108,940              --           25,160               --              --          134,100
      Time - domestic                   93,847          65,638           13,580               --              --          173,065
           - foreign                     1,730           1,000               --               --              --            2,730
  Federal funds purchased &
      securities sold u/a/r             53,884          14,500               --               --              --           68,384
  Commercial paper                      36,648              --               --               --              --           36,648
  Other short-term borrowings            7,701          12,850               --               --              --           20,551
   Long-term borrowings - FHLB              --          20,000           21,400               --              --           41,400
   Noninterest-bearing
    liabilities and share-
     holders' equity                        --              --               --               --         391,487          391,487
                                     ---------       ---------        ---------        ---------       ---------        ---------

       Total Liabilities and
          Shareholders' Equity         302,750         113,988          152,705               --         391,487          960,930
                                     ---------       ---------        ---------        ---------       ---------        ---------

Net Interest Rate
      Sensitivity Gap                $ 125,524       $ (83,476)       $ (67,960)       $ 334,552       $(308,640)       $      --
                                     =========       =========        =========        =========       =========        =========

Cumulative Gap at
      June 30, 1998                  $ 125,524       $  42,048        $ (25,912)       $ 308,640       $      --        $      --
                                     =========       =========        =========        =========       =========        =========

Cumulative Gap at
      June 30, 1997                  $  44,569       $  19,930        $  (7,619)       $ 277,934       $      --        $      --
                                     =========       =========        =========        =========       =========        =========

Cumulative Gap at
      December 31, 1997              $ 158,116       $  97,742        $  60,343        $ 377,414       $      --        $      --
                                     =========       =========        =========        =========       =========        =========
</TABLE>

[1]   Historically, balances in non-maturity deposit accounts have remained
      relatively stable despite changes in levels of interest rates. Balances
      are shown in repricing periods based on management's historical repricing
      practices and runoff experience.

                                       26
<PAGE>   27
                        STERLING BANCORP AND SUBSIDIARIES




                           PART II - OTHER INFORMATION



Item 4.       Submission of Matters to a Vote of Security-Holders

              (a) The Annual Meeting of Shareholders of the Company was held on
                     April 17, 1998.

              (b)    The following matters were submitted to a vote of the
                     Shareholders of the Company:

                     (1) Election of Directors *

<TABLE>
<CAPTION>
                               Nominee                        Total Votes For                Total Votes Withheld
                               -------                        ---------------                --------------------
<S>                      <C>                                  <C>                            <C>
                           Joseph M. Adamko                        6,900,074                          581,485
                           Lillian Berkman                         6,898,132                          583,427
                           Louis J. Cappelli                       6,895,790                          585,769
                           Walter Feldesman                        6,841,094                          640,465
                           Allan F. Hershfield                     6,900,661                          580,898
                           Henry J. Humphreys                      6,900,361                          581,198
                           John C. Millman                         6,900,857                          580,702
                           Maxwell M. Rabb                         6,202,845                        1,278,714
                           Eugene T. Rossides                      6,898,542                          583,017
                           William C. Warren                       6,836,949                          644,610
</TABLE>


                           * All nominees were incumbents at the time of the
                             Annual Meeting of Shareholders and all nominees
                             were re-elected.



                     (2) Amendment of Stock Incentive Plan

                           Total Votes For                       5,341,226
                           Total Votes Against                   2,084,996
                           Total Abstentions                        55,336
                           Total Broker Nonvotes                         1

                                       27
<PAGE>   28
                        STERLING BANCORP AND SUBSIDIARIES




Item 6.  Exhibits and Reports on Form 8-K

        (a) The following exhibits are filed as part of this report:

<TABLE>
<CAPTION>
            Exhibit
            -------
<S>                  <C>
             3       Amendments to By-Laws adopted May 21, 1998 
             10(i)   Amendments to Employment Agreements dated May 22, 1998

                     (a) For Louis J. Cappelli

                     (b) For John C. Millman

            10(ii)   Form of change of Control Severance Agreement entered into
                     on May 22, 1998 between the Registrant and each of six
                     executives

            11       Statement Re: Computation of Per Share Earnings

            27       Financial Data Schedule
</TABLE>


        (b)          On June 5, 1998, the Company filed a Current Report on Form
                     8-K, dated May 21, 1998, filing: (1) certain information
                     relating to the extension and updating of its shareholder
                     protection rights plan and (2) certain exhibits including
                     the new rights agreement defining the rights of holders and
                     the press release issued in connection with the foregoing.
                                   SIGNATURES


            Pursuant to the requirements of the Securities Exchange Act of 1934,
            the registrant has duly caused this report to be signed on its
            behalf by the undersigned thereunto duly authorized.

                                              STERLING BANCORP
                                              .............................
                                                  (Registrant)




 Date  8/13/98                        /s/  Louis J. Cappelli
     --------------                        ------------------------------------
                                           Louis J. Cappelli
                                           Chairman and
                                           Chief Executive Officer



 Date  8/13/98                        /s/  John W. Tietjen
     --------------                        ------------------------------------
                                           John W. Tietjen
                                           Executive Vice President, Treasurer
                                           and Chief Financial Officer

                                       28
<PAGE>   29
                        STERLING BANCORP AND SUBSIDIARIES


                                  Exhibit Index






<TABLE>
<CAPTION>
  Exhibit                                                                         Filed
   Number                Description                                             Herewith
   ------                -----------                                             --------
<S>                      <C>                                                     <C>
     3                   Amendments to By-Laws                                      X


    10(i)                Amendments to Employment Contracts                         X
                         (a) Louis J. Cappelli
                         (b) John C. Millman

      (ii)               Form of Change of Control Severance Agreement between
                         The Registrant and each of six executives                  X


    11                   Computation of Per Share Earnings                          X


    27                   Financial Data Schedule                                    X


</TABLE>

                                       29