<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 SEPTEMBER 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 1-9997

                               KOGER EQUITY, INC.
             (Exact name of registrant as specified in its charter)

           FLORIDA                                               59-2898045
(State or other jurisdiction of                              (I.R.S. Employer
incorporation or organization)                               Identification No.)

     8880 FREEDOM CROSSING TRAIL
       JACKSONVILLE, FLORIDA                                       32256
(Address of principal executive offices)                         (Zip Code)

       Registrant's telephone number, including area code: (904) 732-1000

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.

Yes   X    No      
    ----      ----

Indicate the number of shares outstanding of each of the issuer's classes of
common stock, as of the close of the latest practicable date.

          Class                                  Outstanding at October 30, 1998
Common Stock, $.01 par value                              26,580,137 shares


<PAGE>   2




                       KOGER EQUITY, INC. AND SUBSIDIARIES

                                      INDEX
<TABLE>
<CAPTION>
                                                                                                            PAGE NO.
<S>                                                                                                         <C>
PART I.   FINANCIAL INFORMATION

            Independent Accountants' Report.............................................................        2

   Item 1.  Financial Statements:

            Condensed Consolidated Balance Sheets
               September 30, 1998 and December 31, 1997.................................................        3

            Condensed Consolidated Statements of Operations
               for the Three and Nine Month Periods Ended
               September 30, 1998 and 1997..............................................................        4

            Condensed Consolidated Statement of Changes in
               Shareholders' Equity for the Nine Month Period
               Ended September 30, 1998.................................................................        5

            Condensed Consolidated Statements of Cash Flows
               for the Nine Month Periods Ended September 30, 1998
               and 1997.................................................................................        6

            Notes to Condensed Consolidated Financial
               Statements for the Three and Nine Month Periods
               Ended September 30, 1998 and 1997........................................................        7

   Item 2.  Management's Discussion and Analysis of Financial Condition
               and Results of Operations................................................................        8

PART II. OTHER INFORMATION

   Item 1.  Legal Proceedings...........................................................................       12

   Item 5.  Other Information...........................................................................       13

   Item 6.  Exhibits and Reports on Form 8-K............................................................       16

   Signatures    .......................................................................................       17
</TABLE>


                                        1

<PAGE>   3







INDEPENDENT ACCOUNTANTS' REPORT

To the Board of Directors and Shareholders of
Koger Equity, Inc.
Jacksonville, Florida

We have reviewed the accompanying condensed consolidated balance sheet of Koger
Equity, Inc. and subsidiaries (the "Company") as of September 30, 1998, and the
related condensed consolidated statements of operations for the three and nine
month periods ended September 30, 1998 and 1997, the condensed consolidated
statement of changes in shareholders' equity for the nine month period ended
September 30, 1998 and the condensed consolidated statements of cash flows for
the nine month periods ended September 30, 1998 and 1997. These financial
statements are the responsibility of the Company's management.

We conducted our review in accordance with standards established by the American
Institute of Certified Public Accountants. A review of interim financial
information consists principally of applying analytical procedures to financial
data and of making inquiries of persons responsible for financial and accounting
matters. It is substantially less in scope than an audit conducted in accordance
with generally accepted auditing standards, the objective of which is the
expression of an opinion regarding the financial statements taken as a whole.
Accordingly, we do not express such an opinion.

Based on our review, we are not aware of any material modifications that should
be made to such condensed consolidated financial statements for them to be in
conformity with generally accepted accounting principles.

We have previously audited, in accordance with generally accepted auditing
standards, the consolidated balance sheet of the Company as of December 31,
1997, and the related consolidated statements of operations, changes in
shareholders' equity, and cash flows for the year then ended (not presented
herein); and in our report dated February 28, 1998, we expressed an unqualified
opinion on those consolidated financial statements. In our opinion, the
information set forth in the accompanying condensed consolidated balance sheet
as of December 31, 1997 is fairly stated, in all material respects, in relation
to the consolidated balance sheet from which it has been derived.





DELOITTE & TOUCHE  LLP
Jacksonville, Florida
October  29, 1998



                                       2

<PAGE>   4




                          PART I. FINANCIAL INFORMATION
ITEM 1.  FINANCIAL STATEMENTS
                       KOGER EQUITY, INC. AND SUBSIDIARIES
                      CONDENSED CONSOLIDATED BALANCE SHEETS
                (UNAUDITED - SEE INDEPENDENT ACCOUNTANTS' REPORT)
                                 (IN THOUSANDS)

<TABLE>
<CAPTION>
                                                                   SEPTEMBER 30,           DECEMBER 31,
                                                                       1998                    1997          
                                                                   ------------            ------------
<S>                                                                <C>                     <C>         
ASSETS
Real Estate Investments:
    Operating properties:
       Land                                                        $    130,058            $    111,697
       Buildings                                                        668,108                 567,332
       Furniture and equipment                                            3,316                   2,220
       Accumulated depreciation                                        (122,515)               (104,700)
                                                                   ------------            ------------
          Operating properties - net                                    678,967                 576,549
    Properties under construction:
       Land                                                              13,171                   8,978
       Buildings                                                         24,749                  18,608
    Undeveloped land held for investment                                 17,553                  13,249
    Undeveloped land held for sale                                        1,263                   1,512
Cash and temporary investments                                            3,249                  16,955
Accounts receivable, net of allowance for 
    uncollectible accounts of $288 and $250                               6,111                   5,646
Investment in Koger Realty Services, Inc.                                 1,103                     472
Cost in excess of fair value of net assets acquired,
    net of accumulated amortization of $813 and $685                      1,743                   1,870
Other assets                                                             13,256                  12,258
                                                                   ------------            ------------
       TOTAL ASSETS                                                $    761,165            $    656,097
                                                                   ============            ============

LIABILITIES AND SHAREHOLDERS' EQUITY
Liabilities:
    Mortgages and loans payable                                    $    260,481            $    181,963
    Accounts payable                                                      6,596                   8,802
    Accrued real estate taxes payable                                     7,896                   3,294
    Accrued liabilities - other                                           7,859                   6,623
    Dividends payable                                                     7,973                   6,352
    Advance rents and security deposits                                   4,715                   4,801
                                                                   ------------            ------------
       Total Liabilities                                                295,520                 211,835
                                                                   ------------            ------------

Commitments and Contingencies

Shareholders' Equity:
    Common stock                                                            286                     284
    Capital in excess of par value                                      454,909                 441,451
    Retained earnings                                                    30,752                  30,947
    Treasury stock, at cost                                             (20,302)                (28,420)
                                                                   ------------            ------------
       Total Shareholders' Equity                                       465,645                 444,262
                                                                   ------------            ------------
       TOTAL LIABILITIES AND SHAREHOLDERS' EQUITY                  $    761,165            $    656,097
                                                                   ============            ============
</TABLE>

See Notes to Condensed Consolidated Financial Statements.



                                       3
<PAGE>   5

                       KOGER EQUITY, INC. AND SUBSIDIARIES
                 CONDENSED CONSOLIDATED STATEMENTS OF OPERATIONS
                (UNAUDITED - SEE INDEPENDENT ACCOUNTANTS' REPORT)
                      (IN THOUSANDS, EXCEPT PER SHARE DATA)


<TABLE>
<CAPTION>
                                                       THREE MONTH PERIOD         NINE MONTH PERIOD
                                                       ENDED SEPTEMBER 30,       ENDED SEPTEMBER 30,
                                                      --------------------      ----------------------
                                                        1998         1997         1998           1997 
                                                      -------      -------      --------      --------
<S>                                                   <C>          <C>          <C>           <C>     
REVENUES
    Rental and other rental services                  $34,476      $28,230      $ 97,195      $ 80,250
    Management fees                                       547          639         1,738         2,209
    Interest                                               85          178           392         1,084
    Income from Koger Realty Services, Inc.               207           96         1,062           489
    Adjustment to gain on TKPL note to Southeast                                                    (9)
                                                      -------      -------      --------      --------
      Total revenues                                   35,315       29,143       100,387        84,023
                                                      -------      -------      --------      --------
EXPENSES
    Property operations                                14,370       12,037        39,197        32,824
    Depreciation and amortization                       6,766        6,124        20,416        17,238
    Mortgage and loan interest                          4,251        4,037        11,518        12,264
    General and administrative                          1,620        1,367         4,877         4,256
    Direct cost of management fees                        326          469           972         1,553
    Undeveloped land costs                                 87          107           280           341
    Loss on early retirement of debt                                   102                         144
    Recovery of loss on land held for sale                                                        (379)
                                                      -------      -------      --------      --------
      Total expenses                                   27,420       24,243        77,260        68,241
                                                      -------      -------      --------      --------

INCOME BEFORE GAIN ON SALE OR
    DISPOSITION OF ASSETS                               7,895        4,900        23,127        15,782
Gain on sale or disposition of assets                       3        2,057             6         2,057
                                                      -------      -------      --------      --------

INCOME BEFORE INCOME TAXES                              7,898        6,957        23,133        17,839
Income taxes                                              160            8           770           189
                                                      -------      -------      --------      --------
NET INCOME                                            $ 7,738      $ 6,949      $ 22,363      $ 17,650
                                                      =======      =======      ========      ========

EARNINGS PER SHARE:
    Basic                                             $  0.29      $  0.33      $   0.85      $   0.84
                                                      =======      =======      ========      ========
    Diluted                                           $  0.29      $  0.31      $   0.83      $   0.79
                                                      =======      =======      ========      ========

WEIGHTED AVERAGE SHARES:
    Basic                                              26,566       21,259        26,199        21,018
                                                      =======      =======      ========      ========
    Diluted                                            27,114       22,341        26,869        22,251
                                                      =======      =======      ========      ========
</TABLE>


See Notes to Condensed Consolidated Financial Statements.



                                       4
<PAGE>   6
 




                       KOGER EQUITY, INC. AND SUBSIDIARIES
                 CONDENSED CONSOLIDATED STATEMENT OF CHANGES IN
                              SHAREHOLDERS' EQUITY
                (UNAUDITED - SEE INDEPENDENT ACCOUNTANTS' REPORT)
                                 (IN THOUSANDS)


<TABLE>
<CAPTION>
                                     COMMON STOCK                                                                       TOTAL
                                  ---------------------       CAPITAL IN                      TREASURY STOCK            SHARE-
                                                  PAR          EXCESS OF      RETAINED      ---------------------      HOLDERS'
                                  SHARES         VALUE         PAR VALUE      EARNINGS      SHARES         COST         EQUITY 
                                 -------       --------       ----------      --------      ------      ---------      --------
<S>                              <C>           <C>            <C>             <C>           <C>         <C>            <C>     
Balance, December 31, 1997        28,389       $    284       $ 441,451       $30,947       2,982       $(28,420)      $444,262
Common stock sold                                                12,049                    (1,016)         8,378         20,427
Treasury stock purchased                                                                       18           (302)          (302)
401(k) Plan contribution                                            126                        (9)            76            202
Stock options exercised              166              2           1,283                         2            (34)         1,251
Dividends declared                                                            (22,558)                                  (22,558)
Net income                                                                     22,363                                    22,363
                                 -------       --------       ---------       -------       -----       --------       --------
Balance, September 30, 1998       28,555       $    286       $ 454,909       $30,752       1,977       $(20,302)      $465,645
                                 =======       ========       =========       =======       =====       ========       ========
</TABLE>

See Notes to Condensed Consolidated Financial Statements.



                                       5
<PAGE>   7

                       KOGER EQUITY, INC. AND SUBSIDIARIES
                 CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS
                (UNAUDITED - SEE INDEPENDENT ACCOUNTANTS' REPORT)
                                 (IN THOUSANDS)
<TABLE>
<CAPTION>
                                                                                  NINE MONTH PERIOD
                                                                                  ENDED SEPTEMBER 30,  
                                                                               ------------------------
                                                                                  1998           1997  
                                                                               ---------       --------
<S>                                                                            <C>             <C>     
OPERATING ACTIVITIES
    Net income                                                                 $  22,363       $ 17,650
Adjustments to reconcile net income to net cash
      provided by operating activities:
      Depreciation and amortization                                               20,416         17,238
      Income from Koger Realty Services, Inc.                                     (1,062)          (489)
      Recovery of loss on land held for sale                                                      (379)
      Provision for uncollectible accounts                                            94            156
      Adjustment to gain on TKPL unsecured note to Southeast                                          9
      Gain on sale or disposition of assets                                           (6)        (2,057)
      Loss on early retirement of debt                                                              144
      Amortization of mortgage discounts                                                             71
      Increase in accounts payable, accrued
        liabilities and other liabilities                                          3,895          3,828
      Decrease (increase) in receivables and other assets                        (1,764)           200
                                                                               ---------       --------
         Net cash provided by operating activities                                43,936         36,371
                                                                               ---------       --------

INVESTING ACTIVITIES
    Property acquisitions                                                        (73,845)       (45,833)
    Building construction expenditures                                           (38,404)       (11,731)
    Tenant improvements to first generation space                                 (2,829)          (135)
    Tenant improvements to existing properties                                    (7,433)        (5,622)
    Building improvements                                                         (3,015)        (2,181)
    Energy management improvements                                                  (194)          (531)
    Deferred tenant costs                                                         (1,450)        (1,220)
    Additions to furniture and equipment                                          (1,096)          (473)
    Proceeds from sale of assets                                                       6          6,345
    Dividends received from Koger Realty Services, Inc.                              431            364
                                                                               ---------       --------
         Net cash used in investing activities                                  (127,829)       (61,017)
                                                                               ---------       --------

FINANCING ACTIVITIES
    Proceeds from sale of common stock                                            20,427            257
    Proceeds from exercise of warrants and stock options                           1,104         10,141
    Proceeds from mortgage and loans                                             101,917         24,300
    Dividends paid                                                               (20,937)        (4,190)
    Principal payments on mortgages and loans                                    (31,900)       (25,428)
    Treasury stock purchase                                                         (302)        (5,750)
    Warrants redeemed                                                                              (379)
    Financing costs                                                                 (122)          (727)
                                                                               ---------       --------
         Net cash provided by (used in) financing activities                      70,187         (1,776)
                                                                               ---------       --------
Net  decrease  in cash and cash equivalents                                      (13,706)       (26,422)
Cash and cash equivalents - beginning of period                                   16,955         35,715
                                                                               ---------       --------
Cash and cash equivalents - end of period                                      $   3,249       $  9,293
                                                                               =========       ========
SUPPLEMENTAL CASH FLOW INFORMATION
    Cash paid during the period for interest, net of capitalized interest      $  10,162       $ 12,193
                                                                               =========       ========
    Cash paid during the period for income taxes                               $   1,047       $    189
                                                                               =========       ========
</TABLE>

See Notes to Condensed Consolidated Financial Statements.


                                       6
<PAGE>   8


                       KOGER EQUITY, INC. AND SUBSIDIARIES
              NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS
                      FOR THE THREE AND NINE MONTH PERIODS
                        ENDED SEPTEMBER 30, 1998 AND 1997
                (UNAUDITED - SEE INDEPENDENT ACCOUNTANTS' REPORT)

         1. BASIS OF PRESENTATION. The condensed consolidated financial
statements include the accounts of Koger Equity, Inc. and its wholly-owned
subsidiaries (the "Company"). All material intercompany transactions have been
eliminated. The financial statements have been prepared in accordance with the
rules and regulations of the Securities and Exchange Commission related to
interim financial statements.

The financial statements should be read in conjunction with the consolidated
financial statements and notes thereto for the year ended December 31, 1997,
included in the Company's Form 10-K Annual Report for the year ended December
31, 1997. The balance sheet at December 31, 1997, has been derived from the
audited financial statements at that date and is condensed.

All adjustments of a normal recurring nature, which, in the opinion of
management, are necessary to present a fair statement of the results of
operations for the interim periods, have been made. Results of operations for
the nine month period ended September 30, 1998, are not necessarily indicative
of the results to be expected for the full year.

Certain 1997 amounts have been reclassified to conform with 1998 presentations.

         2. ORGANIZATION. Koger Equity, Inc. ("KE"), a Florida corporation, was
incorporated in 1988 for the purpose of investing in the ownership of income
producing properties, primarily commercial office buildings. KE is totally
self-administered and self-managed.

In addition to managing its own properties, KE, through certain related
entities, provides property management services to third parties. In conjunction
with Koger Real Estate Services, Inc. ("KRES"), a Florida corporation and a
wholly-owned subsidiary of KE, KE manages 21 office buildings owned by Centoff
Realty Company, Inc. ("Centoff"), a subsidiary of Morgan Guaranty Trust Company
of New York.

         3. FEDERAL INCOME TAXES. The Company is operated in a manner so as to
qualify, and has elected tax treatment, as a real estate investment trust under
the Internal Revenue Code (a "REIT"). As a REIT, the Company is required to
distribute annually at least 95 percent of its REIT taxable income to its
shareholders. Since the Company had no REIT taxable income during 1997 and does
not expect to have REIT taxable income during 1998, no provision has been made
for Federal income taxes. However, the Company has recorded a provision of
$380,000 for alternative minimum tax for the nine month period ended September
30, 1998. To the extent that the Company pays dividends equal to 100 percent of
REIT taxable income, the earnings of the Company are not taxed at the corporate
level. However, the use of net operating loss carryforwards, which may reduce
REIT taxable income to zero, are limited for alternative minimum tax purposes.

         4. STATEMENTS OF CASH FLOWS. Cash in excess of daily requirements is
invested in short-term monetary securities. Such temporary cash investments have
an original maturity date of less than three months and are deemed to be cash
equivalents for purposes of the statements of cash flows. During the nine month
period ended September 30, 1998, the Company contributed 9,197 shares of common
stock to the Company's 401(k) Plan. These shares had a value of approximately
$202,000 based on the closing price of the Company's common stock on the
American Stock Exchange on December 31, 1997. During January 1998, the Company
assumed a mortgage loan with an outstanding balance of approximately $8,501,000
in conjunction with the acquisition of an office building. During the nine month
period ended September 30, 1997, the Company contributed 23,657 shares of common
stock to the Company's 401(k) Plan. These shares had a value of approximately
$444,000 based on the closing price of the Company's common stock on the
American Stock Exchange on December 31, 1996. In addition, the Company issued
15,455 shares of common stock as payment for certain 



                                       7
<PAGE>   9

1996 bonuses for senior management. These shares had a value of approximately
$278,000 based on the closing price of the Company's common stock on the
American Stock Exchange on January 6, 1997.

         5. EARNINGS PER SHARE. Basic earnings per share has been computed based
on the weighted average number of common shares outstanding during the period.
The computation of diluted earnings per share is similar to the computation of
basic earnings per share except that the denominator has been increased to
include the number of additional common shares that would have been outstanding
if the dilutive potential common shares for stock options had been issued.

         6. MORTGAGES AND LOANS PAYABLE. At September 30, 1998, the Company had
$260,481,000 of loans outstanding, which are collateralized by mortgages on
certain operating properties. Annual maturities for mortgages and loans payable
are as follows (in thousands):

<TABLE>
<CAPTION>
                           YEAR ENDING DECEMBER 31,
                           <S>                                                 <C>       
                                    1998                                       $      907
                                    1999                                           68,957
                                    2000                                            3,209
                                    2001                                            3,485
                                    2002                                           11,486
                                    Subsequent Years                              172,437
                                                                               ----------
                                          Total                                $  260,481 
                                                                               ==========
</TABLE>

         7. DIVIDENDS. The Company paid the following dividends during the nine
months ended September 30, 1998:

<TABLE>
<CAPTION>
                             PAYMENT DATE                      RECORD DATE              DIVIDEND PER SHARE
                           -----------------                -----------------           ------------------
                           <S>                              <C>                         <C>  
                           February 14, 1998                December 31, 1997                   $0.25
                           May 6, 1998                      March 31, 1998                      $0.25
                           August 6, 1998                   June 30, 1998                       $0.30
</TABLE>

During the quarter ended September 30, 1998, the Company's Board of Directors
declared a quarterly dividend of $0.30 per share payable on November 5, 1998, to
shareholders of record at the close of business on September 30, 1998. The
Company currently expects that all dividends paid during 1998 will be treated as
ordinary income to the recipient for income tax purposes.

         8. STOCK OPTIONS. During the quarter ended September 30, 1998, the
Company granted options to purchase 461,500 shares of its common stock. All
options were granted with an exercise price in excess of the market value at the
date of grant.

         9. SUBSEQUENT EVENT. On October 22, 1998, the Company completed the
acquisition of the Vanguard Office Center, a suburban office park located in
Charlotte, North Carolina, for a total purchase price of $52.3 million. This
transaction was structured as a contribution of the property to a down-REIT
partnership to be called Koger-Vanguard Partners, L.P., whose General Partner is
the Company. The purchase price was paid by the assumption of approximately
$22.2 million of debt, the issuance of 999,710 partnership operating units
(valued at approximately $22.95 million) and the balance in cash. The
partnership operating units carry with them the right to redeem the units for
common shares of the Company on a one-operating-unit-for-one-share basis or, at
the option of the Company, the units may be redeemed for cash.

ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
OF OPERATIONS

The following discussion should be read in conjunction with the condensed
consolidated financial statements and related notes appearing elsewhere in this
Form 10-Q, and the Management's Discussion and Analysis of Financial Condition
and Results of Operations included in the Company's Annual Report on Form 10-K
for the period ended December 31, 1997.

                                       8
<PAGE>   10

RESULTS OF OPERATIONS.

Rental and other rental services revenues totaled $34,476,000 for the quarter
ended September 30, 1998, compared to $28,230,000 for the quarter ended
September 30, 1997. This increase in rental revenues resulted primarily from (i)
increases in the Company's average rental rate and (ii) increases in rental
revenues from the properties acquired and construction completed during 1997 and
1998 ($5,163,000). At September 30, 1998, the Company's buildings were on
average 91 percent leased with an average rental rate of $15.63. Rental and
other rental services revenues increased to $97,195,000 during the nine month
period ended September 30, 1998, compared to $80,250,000 during the same period
last year. This increase resulted primarily from (i) increases in the Company's
average rental rate and (ii) increases in rental revenues from the properties
acquired and construction completed during 1997 and 1998 ($13,174,000).

Management fee revenues totaled $547,000 for the quarter ended September 30,
1998, compared to $639,000 for the quarter ended September 30, 1997. This
decrease was due primarily to a decrease in leasing fees earned. Management fee
revenues decreased to $1,738,000 during the nine month period ended September
30, 1998, compared to $2,209,000 during the same period last year, primarily due
to a decrease in the leasing fees earned under the management contract with
Centoff and from other sources.

Interest revenues decreased $93,000 and $692,000, respectively, for the three
and nine month periods ended September 30, 1998, compared to the same periods
last year, due to the lower average balance of cash to invest.

Property operations expense includes such charges as utilities, real estate
taxes, janitorial, maintenance, property insurance, provision for uncollectible
rents and management costs. The amounts of property operations expense and its
percentage of total rental revenues for the applicable periods are as follows:

<TABLE>
<CAPTION>
                                                                                         PERCENT OF
                                                                                        TOTAL RENTAL
                      PERIOD                                    AMOUNT                    REVENUES   
         --------------------------------                    ------------               ------------
         <S>                                                 <C>                          <C>  
         September 30, 1998 - Quarter                        $ 14,370,000                  41.7%
         September 30, 1997 - Quarter                          12,037,000                  42.6%
         September 30, 1998 - Nine Months                      39,197,000                  40.3%
         September 30, 1997 - Nine Months                      32,824,000                  40.9%
</TABLE>

Property operations expense increased primarily due to (i) increased accruals
for real estate taxes, (ii) increased utility costs, (iii) increased property
management costs and (iv) increases in operations expense for the properties
acquired and construction completed during 1997 and 1998 ($2,037,000 and
$5,460,000, respectively, for the three and nine month periods ended September
30, 1998).

Depreciation expense has been calculated on the straight line method based upon
the useful lives of the Company's depreciable assets, generally 3 to 40 years.
Depreciation expense increased $453,000 and $2,579,000 respectively, for the
three and nine month periods ended September 30, 1998, compared to the same
periods last year, due to (i) improvements made to the Company's existing
properties during 1997 and 1998 and (ii) the properties acquired and
construction completed during 1997 and 1998 ($832,000 and $2,284,000,
respectively, for the three and nine month periods ended September 30, 1998).
Amortization expense increased $189,000 and $599,000, respectively, for the
three and nine month periods ended September 30, 1998, compared to the same
periods last year, due primarily to (i) financing costs incurred during 1997 for
the secured revolving credit facility and (ii) deferred tenant costs incurred
after September 30, 1997.

Interest expense increased by $214,000 during the three month period ended
September 30, 1998, compared to the same period last year, primarily due to the
increase in the outstanding balance of mortgages and loans payable. Compared to
the same period last year, interest expense decreased by $746,000 during the
nine month period ended September 30, 1998



                                       9
<PAGE>   11

primarily due to the increase in interest capitalization due to the Company's
construction of office buildings. At September 30, 1998, the weighted average
annual interest rate on the Company's outstanding debt was approximately 8.0
percent.

General and administrative expenses for the three month periods ended September
30, 1998 and 1997, totaled $1,620,000 and $1,367,000, respectively, which is 0.8
percent and 0.8 percent (annualized) of average invested assets. General and
administrative expenses for the nine month periods ended September 30, 1998 and
1997, totaled $4,877,000 and $4,256,000, respectively, which is 0.8 percent and
0.9 percent (annualized) of average invested assets. These increases were
primarily due to (i) increases in group insurance costs, (ii) costs for
corporate office relocation and (iii) increased accruals related to a bonus
plan.

Direct costs of management contracts decreased $143,000 and $581,000,
respectively, for the three and nine month periods ended September 30, 1998,
compared to the same periods last year, due to decreased costs associated with
providing property management services for all management contracts.

Based on the proceeds received from the sale of the Miami land parcel and the
Company's analysis of the fair value of the remaining land parcels held for
sale, the Company reversed $379,000 of the provision for loss on land held for
sale, which had been previously recorded.

Net income totaled $7,738,000 for the quarter ended September 30, 1998, compared
to net income of $6,949,000 for the corresponding period of 1997. This
improvement is due primarily to the increase in rental revenues which was
partially offset by increases in (i) property operations expense and (ii)
depreciation and amortization expense and the decrease in gain on sale or
disposition of assets. Net income increased $4,713,000 during the nine month
period ended September 30, 1998, compared to the same period last year, due to
the same items detailed above.

LIQUIDITY AND CAPITAL RESOURCES.

     OPERATING ACTIVITIES - During the nine months ended September 30, 1998, the
Company generated approximately $43.9 million in net cash from operating
activities. The Company's primary internal sources of cash are (i) the
collection of rents from buildings owned by the Company and (ii) the receipt of
management fees paid to the Company in respect of properties managed on behalf
of Centoff and others. As a REIT for Federal income tax purposes, the Company is
required to pay out annually, as dividends, 95 percent of its REIT taxable
income (which, due to non-cash charges, including depreciation and net operating
loss carryforwards, may be substantially less than cash flow). In the past, the
Company has paid out dividends in amounts at least equal to its REIT taxable
income. The Company believes that its cash provided by operating activities will
be sufficient to cover debt service payments and to pay the dividends required
to maintain REIT status through 1998.

The level of cash flow generated by rents depends primarily on the occupancy
rates of the Company's buildings and changes in rental rates on new and renewed
leases and under escalation provisions in existing leases.

At September 30, 1998, leases representing approximately 7.6 percent of the
gross annualized rent from the Company's properties, without regard to the
exercise of options to renew, were due to expire during the remainder of 1998.
This represents 326 leases for space in buildings located in 20 of the 23
centers or locations in which the Company owns buildings. Certain of these
tenants may not renew their leases or may reduce their demand for space. During
the nine months ended September 30, 1998, leases were renewed on approximately
61 percent of the Company's net rentable square feet, which were scheduled to
expire during the nine month period. For those leases which renewed during the
nine months ended September 30, 1998, the average rental rate increased from
$15.03 to $15.93. Based upon the significant number of leases which will expire
during 1998 and 1999 and the competition for tenants in the markets in which the
Company operates, the Company has and expects to continue to offer incentives to
certain new and renewal tenants. These incentives may include the payment of
tenant improvements costs and in certain markets reduced rents during initial
lease periods.



                                       10
<PAGE>   12

The Company continues to benefit from improving economic conditions and reduced
vacancy levels for office buildings in many of the metropolitan areas in which
the Company owns buildings. The Company believes that the southeastern and
southwestern regions of the United States provide significant economic growth
potential due to their diverse regional economies, expanding metropolitan areas,
skilled work force and moderate labor costs. However, the Company cannot predict
whether such economic growth will continue. Cash flow from operations could be
reduced if economic growth were not to continue in the Company's markets and if
this resulted in lower occupancy rates for the Company's buildings.

Governmental tenants (including the State of Florida and the United States
Government) which account for approximately 21.2 percent of the Company's leased
space at September 30, 1998, may be subject to budget reductions in times of
recession and governmental austerity measures. Consequently, there can be no
assurance that governmental appropriations for rents may not be reduced.
Additionally, certain of the private sector tenants, which have contributed to
the Company's rent stream, may reduce their current demands, or curtail their
future need, for additional office space.

The inability of computers, software and other equipment utilizing
microprocessors to recognize and properly process data fields containing a
two-digit year is commonly referred to as the Year 2000 Compliance issue. As the
year 2000 approaches, such systems may be unable to accurately process certain
date-based information. All significant accounting applications used by the
Company are packaged software products licensed from various computer software
companies. During 1998, the Company began implementing its existing plan to
upgrade its significant accounting applications from DOS-based software to
Windows-based software. The Company has confirmed that its Windows-based
software applications are Year 2000 Compliant. The project to upgrade these
applications to Windows-based software will be completed by March 31, 1999.

The Company has also completed its initial assessment of its critical building
operating systems (HVAC, lighting, security and elevators) regarding Year 2000
Compliance. This assessment determined that the costs of dealing with timing
devices which are not Year 2000 Compliant would not be material to the Company's
financial position or results of operations. The Company is continuing to
inventory all building operating systems to confirm the Company's assessment of
these devices with the applicable manufacturers.

The total cost to the Company of these Year 2000 Compliance activities has not
been and is not anticipated to be material to its financial position or results
of operations in any given year. These costs and the date on which the Company
plans to complete its application conversions are based on management's best
estimates, which were derived utilizing numerous assumptions of future events
including the continued availability of certain resources, third party
modification plans and other factors. However, there can be no guarantee that
these estimates will be achieved and actual results could differ from these
plans.

     INVESTING ACTIVITIES - At September 30, 1998, substantially all of the
Company's invested assets were in real properties. Improvements to the Company's
existing properties have been financed through internal operations. During the
nine month period ended September 30, 1998, the Company's expenditures for
improvements to existing properties increased by $2,308,000 over the
corresponding period of the prior year primarily due to increases in
expenditures for tenant improvements to the Company's buildings.

During the quarter ended March 31, 1997, the Company sold 8.1 acres of
unimproved land located in Miami, Florida for approximately $2,908,000, net of
selling costs. On August 8, 1997, the Company sold 17.2 acres of unimproved land
located in Richmond, Virginia for approximately $3,433,000, net of selling
costs.

On January 30, 1998, the Company acquired a building, containing 127,700 net
rentable square feet, located in Richmond, Virginia for a purchase price of
$16.5 million. On February 1, 1998, the Company acquired a building, containing
19,000 net rentable square feet, located in Jacksonville, Florida for a purchase
price of $2.0 million. On March 6, 1998, the Company acquired 14.41 acres of
land located in Jacksonville, Florida for a purchase price of $2.3 million. On
April 22, 1998, the


                                       11
<PAGE>   13

Company acquired an office and retail complex consisting of (i) four office
buildings containing 279,300 net rentable square feet, (ii) a retail development
containing 112,600 net rentable square feet and (iii) approximately 22 acres of
developable land. These properties were acquired for a purchase price of
approximately $58.2 million and are located in Birmingham, Alabama. On May 18,
1998, the Company acquired 15.4 acres of land located in Jacksonville, Florida
for a purchase price of $2.68 million.

The Company has ten buildings under construction, which will contain
approximately 887,000 net rentable square feet. Expenditures for construction of
these ten buildings are expected to total approximately $75.6 million, excluding
land and tenant improvement costs.

     FINANCING ACTIVITIES - The Company has a $100 million secured revolving
credit facility ($66 million of which was outstanding on September 30, 1998)
provided by First Union National Bank of Florida, Morgan Guaranty Trust Company
of New York, AmSouth Bank, N.A. and Guaranty Federal Bank. At September 30,
1998, the Company had 74 buildings, containing 2,992,900 net rentable square
feet, which were unencumbered.

On March 27, 1998, the Company issued 1,000,000 shares of its common stock to
Wheat First Securities, Inc. at a price per share of $20.246875.

Loan maturities and normal amortization of mortgages and loans payable are
expected to total approximately $69.1 million over the next 12 months. This
assumes that the secured revolving credit facility will be repaid at its
original maturity date of April 7, 1999. However, this credit facility may be
extended annually by the lender for one year periods. Significant maturities of
the Company's remaining mortgages and loans payable do not begin to occur until
2006. The Company has filed shelf registration statements with respect to the
possible issuance of up to $300 million of its common and/or preferred stock.
The Company has issued $91.6 million of its common stock under such registration
statements.

The foregoing discussion contains forward-looking statements concerning 1998.
The actual results of operations for 1998 could differ materially from those
projected because of factors affecting the financial markets, reactions of the
Company's existing and prospective investors, the ability of the Company to
identify and execute development projects and acquisition opportunities, the
ability of the Company to renew and enter into new leases on favorable terms,
and other risks factors. See Item 7. "Management's Discussion and Analysis of
Financial Condition and Results of Operations -- Cautionary Statement Relevant
to Forward-Looking Information for Purpose of the 'Safe Harbor' Provisions of
the Private Securities Litigation Reform Act of 1995" in the Company's Annual
Report on Form 10-K for the Fiscal Year Ended December 31, 1997.

                           PART II. OTHER INFORMATION
ITEM 1.  LEGAL PROCEEDINGS

     None.






                                       12
<PAGE>   14


ITEM 5.  OTHER INFORMATION

(a)   The following table sets forth, with respect to the Company's centers or
      locations at September 30, 1998, gross square feet, net rentable square
      feet, percentage leased, and the average annual rent per net rentable
      square foot leased.

<TABLE>
<CAPTION> 
                                                                                                               AVERAGE
                                                                 NET                                            ANNUAL
                                           GROSS               RENTABLE                                        RENT PER
                                           SQUARE               SQUARE                PERCENT                   SQUARE
KOGER CENTER/LOCATION                       FEET                 FEET                LEASED (1)                FOOT (2) 
---------------------                    ----------           ----------            ----------                ---------
<S>                                      <C>                  <C>                   <C>                       <C>   
Atlanta Chamblee                          1,146,100             938,100                 95%                   $16.22
Atlanta Gwinnett (3)                        171,200             139,400                 82%                    17.61
Atlanta Perimeter                           181,100             154,100                100%                    17.50
Austin                                      458,400             370,900                100%                    19.11
Birmingham Colonnade                        326,300             279,300                 97%                    15.81
Birmingham Colonnade-Retail                 112,600             112,600                 93%                    11.43
Charlotte Carmel (4)                        339,200             283,300                 75%                    17.89
Charlotte East                              574,800             468,900                 83%                    13.79
El Paso                                     364,100             298,300                 94%                    15.50
Greensboro South                            749,200             610,700                 95%                    14.90
Greenville Park Central                     161,700             134,000                 91%                    16.97
Greenville Roper Mt. (5)                    431,000             350,900                 88%                    16.62
Jacksonville Baymeadows                     793,400             664,200                 98%                    15.15
Jacksonville Central                        828,200             666,000                 84%                    13.07
Jacksonville JTB                             29,600              23,000                100%                    16.48
Memphis Germantown                          366,400             299,100                 99%                    18.18
Orlando Central                             699,700             554,400                 91%                    15.20
Orlando University                          194,600             159,600                 98%                    18.10
Richmond Paragon                            154,300             127,700                 86%                    19.07
San Antonio Airport                         258,800             200,100                 95%                    17.28
San Antonio West                            960,700             788,900                 86%                    14.14
St. Petersburg                              625,700             509,000                 96%                    14.37
Tallahassee                                 960,300             789,600                 89%                    17.70
Tulsa                                       581,100             476,400                 85%                    11.98
                                         ----------           ---------
   TOTAL                                 11,468,500           9,398,500                 91%                   $15.63
                                         ==========           =========                ===                    ======
</TABLE>

(1)      The percent leased rates have been calculated by dividing total net
         rentable square feet leased in an office building by net rentable
         square feet in such building, which excludes public or common areas.
(2)      Rental rates are computed by dividing (a) total annualized rents for a
         center or location as of September 30, 1998 by (b) the net rentable
         square feet applicable to such total annualized rents.
(3)      Includes a building, containing 59,600 net rentable square feet, for
         which construction has been completed. This building is currently in
         the lease-up period.
(4)      Includes a building, containing 112,500 net rentable square feet, for
         which construction has been completed. This building is currently in
         the lease-up period.
(5)      Includes a building, containing 60,400 net rentable square feet, for
         which construction has been completed. This building is currently in
         the lease-up period.



                                       13
<PAGE>   15
(b)      The following schedule sets forth for all of the Company's office
         buildings (i) the number of leases which will expire during the
         remainder of calendar year 1998 and calendar years 1999 through 2006,
         (ii) the total net rentable area in square feet covered by such leases,
         (iii) the percentage of total net rentable square feet represented by
         such leases, (iv) the average annual rent per square foot for such
         leases, (v) the current annual rental represented by such leases, and
         (vi) the percentage of gross annual rental contributed by such leases.
         This information is based on the buildings owned by the Company on
         September 30, 1998 and on the terms of leases in effect as of September
         30, 1998, on the basis of then existing base rentals, and without
         regard to the exercise of options to renew. Furthermore, the
         information below does not reflect that some leases have provisions for
         early termination for various reasons, including, in the case of
         government entities, lack of budget appropriations. Leases were renewed
         on approximately 61 percent of the Company's net rentable square feet,
         which were scheduled to expire during the nine month period ended
         September 30, 1998.


<TABLE>
<CAPTION>
                                                   PERCENTAGE OF        AVERAGE                                PERCENTAGE
                                                   TOTAL SQUARE       ANNUAL RENT            TOTAL              OF TOTAL
                    NUMBER OF       NUMBER OF      FEET LEASED         PER SQUARE          ANNUALIZED         ANNUAL RENTS
                      LEASES       SQUARE FEET    REPRESENTED BY       FOOT UNDER          RENTS UNDER       REPRESENTED BY
      PERIOD         EXPIRING       EXPIRING      EXPIRING LEASES    EXPIRING LEASES     EXPIRING LEASES     EXPIRING LEASES
      ------        ---------      -----------    ---------------    ---------------     ---------------     ---------------
      <S>           <C>            <C>            <C>                <C>                 <C>                 <C>   
      1998              326           684,684           8.0%            $14.77              $ 10,109,861             7.6%
      1999              930         1,562,914          18.3%             15.10                23,600,876            17.7%
      2000              495         1,427,102          16.7%             15.95                22,767,344            17.0%
      2001              429         1,649,414          19.3%             15.88                26,196,389            19.6%
      2002              146           801,917           9.4%             15.95                12,788,278             9.6%
      2003              165         1,082,749          12.6%             16.10                17,430,220            13.0%
      2004               85           444,719           5.2%             11.78                 5,239,424             3.9%
      2005               17           108,385           1.3%             16.49                 1,787,555             1.3%
      2006               11           220,035           2.6%             18.68                 4,110,259             3.1%
      OTHER              21           569,720           6.6%             16.93                 9,644,317             7.2%
                      -----         ---------         -----             ------              ------------           ----- 

        TOTAL         2,625         8,551,639         100.0%            $15.63              $133,674,523           100.0%
                      =====         =========         =====             ======              ============           =====
</TABLE>



                                       14
<PAGE>   16

(c)      The Company believes that Funds from Operations is one measure of the
         performance of an equity real estate investment trust. Funds from
         Operations should not be considered as an alternative to net income as
         an indication of the Company's financial performance or to cash flow
         from operating activities (determined in accordance with generally
         accepted accounting principles) as a measure of the Company's
         liquidity, nor is it necessarily indicative of sufficient cash flow to
         fund all of the Company's needs. Funds from Operations is calculated as
         follows (in thousands):

<TABLE>
<CAPTION>
                                               THREE MONTH PERIOD           NINE MONTH PERIOD
                                               ENDED SEPTEMBER 30,          ENDED SEPTEMBER 30,    
                                            -----------------------       ----------------------
                                              1998           1997            1998           1997     
                                            --------       --------       --------       --------     
<S>                                         <C>            <C>            <C>            <C>     
Net Income                                  $  7,738       $  6,949       $ 22,363       $ 17,650
Depreciation - real estate                     5,983          5,571         18,243         15,703
Amortization - deferred tenant costs             389            252          1,084            739
Amortization - goodwill                           43             43            128            128
Gain on sale or disposition of assets             (3)        (2,057)            (6)        (2,057)
Adjustment to gain on TKPL note
   to Southeast                                                                                 9
Recovery of loss on land held for sale                                                       (379)
Loss on early retirement of debt                                102                           144
                                            --------       --------       --------       --------
Funds from Operations                       $ 14,150       $ 10,860       $ 41,812       $ 31,937
                                            ========       ========       ========       ========
</TABLE>

(d)      For information concerning how a shareholder may properly bring
         business before a meeting of shareholders of the Company and nominate
         persons for election as directors to the Company's Board, reference is
         made to paragraph (d) of Item 5. (Other Information) of the Company's
         quarterly report on Form 10-Q for the quarterly period ended June 30,
         1998.


                                       15
<PAGE>   17

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K

         (a) Exhibits

<TABLE>
<CAPTION>
               EXHIBIT
               NUMBER          DESCRIPTION
               -------         -----------
               <S>             <C>                                             
               11              Earnings Per Share Computations.
               15              Letter re: Unaudited interim financial information.
               27              Financial Data Schedule.
</TABLE>

         (b) Reports on Form 8-K There were no reports on Form 8-K filed
             during the quarter ended September 30, 1998.



                                       16
<PAGE>   18


                                   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.




                                               KOGER EQUITY, INC.
                                                   Registrant




                                                 (DAVID B. HILEY)      
                                          ----------------------------
                                                  DAVID B. HILEY
                                          EXECUTIVE VICE PRESIDENT AND
                                             CHIEF FINANCIAL OFFICER

Dated: November 11, 1998
                                                (JAMES L.  STEPHENS)    
                                              ------------------------
                                                 JAMES L. STEPHENS
                                                 VICE PRESIDENT AND
                                              CHIEF ACCOUNTING OFFICER




                                       17