BEAR STEARNS COMPANIES INC
424B3, 1998-03-19
SECURITY BROKERS, DEALERS & FLOTATION COMPANIES
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PRICING SUPPLEMENT NO. 42                                       Rule 424(b)(3)
DATED: March 18, 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
$15,000,000                    [x]                        [x]

Original Issue Date:           Fixed Rate Notes           Certificated Notes
March 23, 1998                 [_]                        [_]


Maturity Date:                                            CUSIP#: 073928 AA 1
March 23, 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: ***

Index Maturity:  One Month

Spread (plus or minus): -0.03%

<PAGE>

*        The 23rd of each month.

**       The 23rd of each month.

***      The one-month LIBOR rate on March 19, 1998 minus 3 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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