PRICING SUPPLEMENT NO. 31 Rule 424(b)(3) DATED: August 20, 2002 File No. 333-76894 (To Prospectus dated January 25, 2002, and Prospectus Supplement dated January 25, 2002) $10,006,693,162 THE BEAR STEARNS COMPANIES INC. MEDIUM-TERM NOTES, SERIES B Principal Amount: $300,000,000 Floating Rate Notes [x] Book Entry Notes [x] Original Issue Date: 8/23/2002 Fixed Rate Notes [ ] Certificated Notes [ ] Maturity Date: 8/25/2003 CUSIP#: 073928XM0 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 Dates: Applicable Only to Floating Rate Notes: Interest Rate Basis: Maximum Interest Rate: N/A [ ] Commercial Paper Rate Minimum Interest Rate: N/A [ ] Federal Funds Effective Rate [ ] Federal Funds Open Rate Interest Reset Date(s): Daily [ ] Treasury Rate Interest Reset Period: Daily [ ] LIBOR Reuters Interest Payment Date(s): * [ ] LIBOR Telerate [x] Prime Rate + [ ] CMT Rate Initial Interest Rate: 1.86% Interest Payment Period: Quarterly Index Maturity: N/A Spread (plus or minus): -2.89% + Prime Rate as reported on Telerate Page 5 under the heading "Bank Rates/Prime." * 11/25/02, 2/25/03, 5/25/03 and 8/25/03 The distribution of Notes will conform to the requirements set forth in Rule 2720 of the NASD Conduct Rules.