BEAR STEARNS COMPANIES INC
424B3, 1996-05-31
SECURITY BROKERS, DEALERS & FLOTATION COMPANIES
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     PRICING SUPPLEMENT NO. 1                                Rule 424(b)(3)
     DATED: May 29, 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
 $25,000,000                  [x]                  [x]

 Original Issue Date:         Fixed Rate Notes     Certificated Notes
 06/03/96                     [_]                  [_]

 Maturity Date: 06/03/97

 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): *

 [_]  Treasury Rate                    Interest Reset Period: Monthly

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

 [x]  LIBOR Telerate

 [_]  Prime Rate                       Interest Payment Period: Monthly

 [_]  CMT Rate

 Initial Interest Rate: ***

 Index Maturity:  One month

 Spread (plus or minus): +0.05%
                         
- -------------------------

*    07/03/96, 08/05/96, 09/03/96, 10/03/96, 11/04/96, 12/03/96, 01/03/97,
     02/03/97, 03/03/97, 04/03/97 and 05/05/97.

**   07/03/96, 08/05/96, 09/03/96, 10/03/96, 11/04/96, 12/03/96, 01/03/97,
     02/03/97, 03/03/97, 04/03/97, 05/05/97 and 06/03/97.

***  One month LIBOR as of 05/30/96 plus 5 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.


     NYFS04...:\25\22625\0122\1773\FFF5306P.150


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