<PAGE>
PRICING SUPPLEMENT NO. 31 Rule 424(b)(3)
DATED: July 24, 1996 File No. 333-03685
(To Prospectus dated May 23, 1996
and Prospectus Supplement dated May 23, 1996)
$4,954,795,162
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
$30,000,000 [x] [x]
Original Issue Date: Fixed Rate Notes Certificated Notes
07/29/96 [_] [_]
Maturity Date: 07/29/97
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
[x] Federal Funds Rate Interest Reset Date(s): *
[_] Treasury Rate Interest Reset Period: Daily
[_] LIBOR Reuters Interest Payment Date(s): **
[_] LIBOR Telerate
[_] Prime Rate
[_] CMT Rate
Initial Interest Rate: *** Interest Payment Period: Quarterly
Index Maturity: N/A
Spread (plus or minus): +.20%
- -------------------------
* Daily on each Business Day.
** 10/29/96, 01/29/97, 04/29/97 and 07/29/97.
*** The Federal Funds Rate as of July 26, 1996 plus 20 basis points.
The distribution of Notes will conform to the requirements set forth in the
applicable sections of Schedule E to the By-laws of the National
Association of Securities Dealers, Inc.
NYFS04...:\25\22625\0122\1773\FFF6056W.40B
