BEAR STEARNS COMPANIES INC
424B3, 1997-09-22
SECURITY BROKERS, DEALERS & FLOTATION COMPANIES
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PRICING SUPPLEMENT NO. 34                                Rule 424 (b)(3)    
DATED: September 19, 1997                              File No. 333-31277
(To Prospectus dated August 13, 1997
and Prospectus Supplement dated August 13, 1997)  

                                 $5,180,520,162
                         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
$80,000,000                   [x]                      [x]

Original Issue Date:          Fixed Rate Notes         Certificated Notes
September 24, 1997            [_]                      [_]

Maturity Date:
September 24, 1998

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): -0.03%
- -------------------------

*        10/24/97, 11/24/97, 12/24/97, 1/26/98, 2/24/98, 3/24/98,
         4/24/98, 5/26/98, 6/24/98, 7/24/98 and 8/24/98.

**       10/24/97, 11/24/97, 12/24/97, 1/26/98, 2/24/98, 3/24/98, 4/24/98,
         5/26/98, 6/24/98, 7/24/98, 8/24/98 and 9/24/98.

***      The one month LIBOR rate as of September 22, 1997 minus 3
basis points.

The distribution of Notes will conform to the requirements set forth in Rule
2720 of the NASD Conduct Rules.

NYFS04...:\25\22625\0122\1324\SUP9227L.430


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