BEAR STEARNS COMPANIES INC
424B3, 1996-10-25
SECURITY BROKERS, DEALERS & FLOTATION COMPANIES
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PRICING SUPPLEMENT NO. 84                                    Rule 424(b)(3)
DATED: October 24, 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
 11/01/96                     [_]                  [_]

 Maturity Date: 11/01/2000

 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: 9.50%

 [_]  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): +0.30%
                         
- -------------------------

  *  On the 1st day of each month commencing on 12/02/96 and through and
     including 10/02/2000.

 **  On the 1st day of each month commencing on 12/02/96 and through and
     including 11/01/2000.

***  The one month LIBOR rate as of October 30, 1996 plus 30 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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