BEAR STEARNS COMPANIES INC
424B3, 1998-05-05
SECURITY BROKERS, DEALERS & FLOTATION COMPANIES
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PRICING SUPPLEMENT NO. 81                                        Rule 424(b)(3)
DATED: May 4, 1998                                           File No. 333-43565
(To Prospectus dated January 21, 1998
and Prospectus Supplement dated January 21, 1998)


                                 $7,096,595,162
                         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
$13,000,000                    [x]                          [x]

Original Issue Date:           Fixed Rate Notes             Certificated Notes
May 5, 1998                    []                           [_]


Maturity Date:                 CUSIP#: 073928 BR 3
May 5, 1999

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:

Interest Payment Date:

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

Interest Rate Basis:                         Maximum Interest Rate: N/A

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

[x]         Federal Funds Rate               Interest Reset Date(s): Daily

[_]         Treasury Rate                    Interest Reset Period: Daily

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

[_]         LIBOR Telerate

[_]         Prime Rate                       Interest Payment Period: Quarterly

[_]         CMT Rate


Initial Interest Rate: **

Index Maturity:  N/A

Spread (plus or minus): +0.12%

<PAGE>

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

*        On the 5th of each August, November, February and at
         maturity.

**       5.5800%

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


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