<PAGE>
 
                                                                    EXHIBIT 4(e)

                            INCORPORATED UNDER THE
                          LAWS OF THE STATE OF TEXAS

                                    NUMBER

                                7% CONVERTIBLE 
                                PREFERRED STOCK

                                    SHARES

                                 CUSIP NUMBER

                      SEE REVERSE FOR CERTAIN DEFINITIONS

                         AMERICAN GENERAL CORPORATION

THIS CERTIFIES THAT

IS THE REGISTERED HOLDER OF

    FULLY PAID AND NON-ASSESSABLE SHARES WITH THE PAR VALUE OF $1.50 OF 7% 
                         CONVERTIBLE PREFERRED STOCK OF

American General Corporation the rights against the Corporation in which are
transferable on the books of the Corporation by the holder hereof in person
or by attorney upon surrender of this Certificate properly endorsed. The
designations, preferences and relative rights of each class of stock of the
Corporation, and the restrictions, limitations and qualifications thereof are
set forth in Article Four of the Articles of Incorporation. This Certificate is
not valid until countersigned by the Transfer Agent and registered by the
Registrar.

Witness, the facsimile seal of the Corporation and the facsimile signatures of 
its duly authorized officers.

DATED

/s/ Harold S. Hook
HAROLD S. HOOK, Chairman and
Chief Executive Officer

/s/ John A. Adkins
JOHN A. ADKINS,
Corporate Secretary

COUNTERSIGNED AND REGISTERED:
  FIRST CHICAGO TRUST COMPANY OF NEW YORK
                            TRANSFER AGENT
                            AND REGISTRAR,

BY

                      AUTHORIZED SIGNATURE


              [SEAL OF AMERICAN GENERAL CORPORATION APPEARS HERE]



<PAGE>
 
                         AMERICAN GENERAL CORPORATION

  A STATEMENT OF (1) THE DESIGNATIONS, PREFERENCES, LIMITATIONS, AND RELATIVE 
RIGHTS OF THE SHARES OF EACH CLASS OF STOCK OF THE CORPORATION, AND (2) THE 
VARIATIONS IN THE RELATIVE RIGHTS AND PREFERENCES OF THE SHARES OF EACH SERIES
OF PREFERRED STOCK OF THE CORPORATION, TO THE EXTENT SUCH RIGHTS AND PREFERENCES
HAVE BEEN ESTABLISHED, AND THE AUTHORITY OF THE BOARD OF DIRECTORS TO FIX AND
DETERMINE THE RELATIVE RIGHTS AND PREFERENCES OF SUBSEQUENT SERIES, IS SET FORTH
IN THE ARTICLES OF INCORPORATION OF THE CORPORATION, ON FILE IN THE OFFICE OF
THE SECRETARY OF STATE OF THE STATE OF TEXAS. THE CORPORATION WILL FURNISH A
COPY OF SUCH STATEMENT TO ANY SHAREHOLDER, WITHOUT CHARGE, UPON WRITTEN REQUEST
TO THE CORPORATION AT ITS HEADQUARTERS IN HOUSTON, TEXAS, OR TO THE TRANSFER
AGENT.

  NO SHAREHOLDER SHALL HAVE A PREEMPTIVE RIGHT TO ACQUIRE ANY SHARES OR 
SECURITIES OF ANY CLASS, WHETHER NOW OR HEREAFTER AUTHORIZED, WHICH MAY AT ANY 
TIME BE ISSUED, SOLD OR OFFERED FOR SALE BY THE CORPORATION.

  The following abbreviations, when used in the inscription on the face of 
this certificate, shall be construed as though they were written out in full 
according to applicable laws or regulations:

  TEN COM  --as tenants in common        

  TEN ENT  --as tenants by the entireties  

  JT TEN   --as joint tenants with right of
             survivorship and not as tenants
             in common

  UNIF GIFT MIN ACT--          Custodian
                     ----------         ----------
                      (Cust)               (Minor)
                     under Uniform Gifts to Minors

                     Act
                        ---------------------------
                               (State)


         Additional abbreviations may also be used though not in the above list.

  For value received,        hereby sell, assign and transfer unto

PLEASE INSERT SOCIAL SECURITY OR OTHER
   IDENTIFYING NUMBER OF ASSIGNEE
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PLEASE PRINT OR TYPEWRITE NAME AND ADDRESS INCLUDING POSTAL ZIP CODE OF 
ASSIGNEE.

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                                                                          Shares
--------------------------------------------------------------------------
of the capital stock represented by the within Certificate, and do
hereby irrevocably constitute and appoint
                                         ---------------------------------------

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Attorney to transfer the said stock on the books of the within-named
Corporation with full power of substitution in the premises.
Dated,
      -------------------------

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

NOTICE: THE SIGNATURE TO THIS ASSIGNMENT MUST CORRESPOND WITH THE NAME AS 
WRITTEN UPON THE FACE OF THE CERTIFICATE IN EVERY PARTICULAR, WITHOUT ALTERATION
OR ENLARGEMENT, OR ANY CHANGE WHATEVER.


          [BACK OF SEAL OF AMERICAN GENERAL CORPORATION APPEARS HERE]