BEAR STEARNS COMPANIES INC
424B3, 1998-05-08
SECURITY BROKERS, DEALERS & FLOTATION COMPANIES
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PRICING SUPPLEMENT NO. 85                                        Rule 424(b)(3)
DATED: May 7, 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
$10,000,000                     [x]                    [x]

Original Issue Date:            Fixed Rate Notes       Certificated Notes
May 8, 1998                     [_]                    [_]


Maturity Date:                  CUSIP#: 073928 BV 4
May 7, 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:

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: 5.62234%

Index Maturity:  One Month

Spread (plus or minus): -0.03%

<PAGE>

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

*        The 7th of each month.

**       The 7th of each month.

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


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