BEAR STEARNS COMPANIES INC
424B3, 1998-03-18
SECURITY BROKERS, DEALERS & FLOTATION COMPANIES
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PRICING SUPPLEMENT NO. 40                                       Rule 424(b)(3)
DATED: March 13, 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
$25,000,000                     [x]                    [x]

Original Issue Date:            Fixed Rate Notes       Certificated Notes
March 18, 1998                  [_]                    [_]


Maturity Date:
March 18, 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): *

[x]         Treasury Rate                   Interest Reset Period: Weekly

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

[_]         LIBOR Telerate

[_]         Prime Rate                      Interest Payment Period: Quarterly

[_]         CMT Rate

Initial Interest Rate: ***

Index Maturity:  Three Months

Spread (plus or minus): +0.52%

<PAGE>

*        Weekly on each Tuesday, or the day following the Treasury
         auction.

**       6/18/98, 9/18/98, 12/18/98 and 3/18/99.

***      The three-month Treasury rate on March 16, 1998 plus 52
         basis points.

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


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