BEAR STEARNS COMPANIES INC
424B3, 1996-07-29
SECURITY BROKERS, DEALERS & FLOTATION COMPANIES
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     PRICING SUPPLEMENT NO. 33                               Rule 424(b)(3)
     DATED: July 25 1996                                 File No. 333-03685
     (To Prospectus dated May 23, 1996
     and Prospectus Supplement dated May 23, 1996)


                               $4,954,795,162
                      THE BEAR STEARNS COMPANIES INC.
                        MEDIUM-TERM NOTES, SERIES B
          WITH MINIMUM MATURITY OF NINE MONTHS FROM DATE OF ISSUE

 Principal Amount:            Floating Rate Notes  Book Entry Notes
 $5,000,000                  [x]                  [x]

 Original Issue Date:         Fixed Rate Notes     Certificated Notes
 07/30/96                     [_]                  [_]

 Maturity Date: 07/30/97

 Option to Extend Maturity:   No  [x]

                              Yes [_]   Final Maturity Date:

                                      Optional           Optional
                    Redemption        Repayment          Repayment
 Redeemable On      Price(s)          Date(s)            Price(s)
 -------------      --------          -------            --------

 N/A                N/A               N/A                N/A

Applicable Only to Fixed Rate Notes:
- -----------------------------------

Interest Rate:  

Applicable Only to Floating Rate Notes:
- --------------------------------------

 Interest Rate Basis:                  Maximum Interest Rate: N/A

 [_]  Commercial Paper Rate            Minimum Interest Rate: N/A

 [_]  Federal Funds Rate               Interest Reset Date(s): *

 [x]  Treasury Rate                    Interest Reset Period: Weekly

 [_]  LIBOR Reuters                    Interest Payment Date(s): **

 [_]  LIBOR Telerate

 [_]  Prime Rate

 [_]  CMT Rate

 Initial Interest Rate: ***            Interest Payment Period: 
                                       Quarterly

 Index Maturity: Three months

 Spread (plus or minus): +.35%

                         
- -------------------------
*    On Tuesday of each week, or the day following the Treasury auction.

**   10/30/97, 01/30/97, 04/30/97 and 07/30/97.

***  The Three Month Treasury Rate as of July 29, 1996 plus 35 basis
     points.

The distribution of Notes will conform to the requirements set forth in the
applicable sections of Schedule E to the By-laws of the National
Association of Securities Dealers, Inc.


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