<PAGE>

                                                                EXHIBIT 10.72(f)

                              AMENDMENT NUMBER SIX
                                     to the
                      Amended and Restated Letter Agreement
                           dated as of October 1, 2004
                                  by and among
                        NEW CENTURY MORTGAGE CORPORATION
                             NC CAPITAL CORPORATION
                         NEW CENTURY CREDIT CORPORATION
                                       and
                      CITIGROUP GLOBAL MARKETS REALTY CORP.


                This AMENDMENT NUMBER SIX (this "Amendment Number Six") is made
this 14th day of June, 2005, among NEW CENTURY MORTGAGE CORPORATION, having an
address at 18400 Von Karman, Suite 1000, Irvine, California 92612 ("NC
Mortgage"), NC CAPITAL CORPORATION, having an address at 18400 Von Karman, Suite
1000, Irvine, California 92612 ("NC Capital"), NEW CENTURY CREDIT CORPORATION,
having an address at 18400 Von Karman, Suite 1000, Irvine, California 92612 ("NC
Credit") and CITIGROUP GLOBAL MARKETS REALTY CORP., having an address at 390
Greenwich Street, New York, New York 10013 ("Citigroup") to the Amended and
Restated Letter Agreement, dated as of October 1, 2004, among NC Mortgage, NC
Capital, NC Credit and Citigroup, as amended (the "Letter Agreement").

                                    RECITALS

                WHEREAS, NC Mortgage, NC Capital and NC Credit have requested
that Citigroup agree to add Forty Year Mortgage Loans to the facility as more
expressly set forth below and Citigroup has agreed to such request.

                WHEREAS, NC Mortgage, NC Capital and NC Credit have requested
that Citigroup agree to extend the termination date as more expressly set forth
below and Citigroup has agreed to such request.

                WHEREAS, as of the date of this Amendment Number Six, each of NC
Mortgage, NC Capital and NC Credit represents to Citigroup that it is in
compliance with all of the representations and warranties and all of the
affirmative and negative covenants set forth in the Letter Agreement and the
Amended and Restated Purchase and Sale Agreement, dated as of October 1, 2004,
among NC Capital, NC Credit and Citigroup (the "Purchase and Sale Agreement")
and is not in default under the Letter Agreement or the Purchase and Sale
Agreement.

                NOW THEREFORE, for good and valuable consideration, the receipt
and sufficiency of which are hereby acknowledged, and of the mutual covenants
herein contained, the parties hereto hereby agree as follows:


<PAGE>

                SECTION 1. Effective as of June 14, 2005, the first paragraph of
Section 1(a) of the Letter Agreement is hereby amended by deleting the words
"June 30, 2005" on the second and third lines thereof and replacing each with
"September 30, 2005".



                SECTION 2. Effective as of June 14, 2005, the following is
hereby inserted after the ninth paragraph of Section 2(a) of the Letter
Agreement:

                The aggregate principal balance of Mortgage Loans with a forty
                (40) year amortization period but which become due and payable
                in full at the end of the thirtieth year (each a "Forty Year
                Mortgage Loan") shall not exceed 20% of the aggregate principal
                balance of all of the Mortgage Loans on the Financing Line at
                any one time.

                SECTION 3. Effective as of June 14, 2005, the first paragraph of
Section 4(c) of the Letter Agreement is hereby amended by deleting the words
"June 30, 2005" on the second and third lines thereof and replacing each with
"September 30, 2005".

                SECTION 4. Fees and Expenses. NC Capital agrees to pay to
Citigroup all fees and out of pocket expenses incurred by Citigroup in
connection with this Amendment Number Six (including all reasonable fees and out
of pocket costs and expenses of Citigroup's legal counsel incurred in connection
with this Amendment Number Six), in accordance with Section 5(i) of the Letter
Agreement.

                SECTION 5. Defined Terms. Any terms capitalized but not
otherwise defined herein shall have the respective meanings set forth in the
Letter Agreement.

                SECTION 6. Representations. In order to induce Citigroup to
execute and deliver this Amendment Number Six, NC Capital, NC Mortgage and NC
Credit hereby represent to Citigroup that as of the date hereof, after giving
effect to this Amendment Number Six, each of NC Capital, NC Mortgage and NC
Credit is in full compliance with all of the terms and conditions of the Letter
Agreement and the Purchase and Sale Agreement and no Termination Event or
material adverse change has occurred under the Letter Agreement and no Seller
default or Seller Event of Default has occurred under the Purchase and Sale
Agreement.

                SECTION 7. Limited Effect. This Amendment Number Six shall
become effective upon the execution hereof by the parties hereto. Except as
expressly amended and modified by this Amendment Number Six, the Letter
Agreement shall continue in full force and effect in accordance with its terms.
Reference to this Amendment Number Six need not be made in the Letter Agreement
or any other instrument or document executed in connection therewith, or in any
certificate, letter or communication issued or made pursuant to, or with respect
to, the Letter Agreement, any reference in any of such items to the Letter
Agreement being sufficient to refer to the Letter Agreement as amended hereby.

                SECTION 8. GOVERNING LAW. THIS AMENDMENT NUMBER SIX SHALL BE
CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW



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<PAGE>

YORK AND THE OBLIGATIONS, RIGHTS, AND REMEDIES OF THE PARTIES HEREUNDER SHALL BE
DETERMINED IN ACCORDANCE WITH SUCH LAWS WITHOUT REGARD TO CONFLICT OF LAWS
DOCTRINE APPLIED IN SUCH STATE (OTHER THAN SECTION 5-1401 OF THE NEW YORK
GENERAL OBLIGATIONS LAW).

                SECTION 9. Counterparts. This Amendment Number Six may be
executed by each of the parties hereto on any number of separate counterparts,
each of which shall be an original and all of which taken together shall
constitute one and the same instrument.

                            [SIGNATURE PAGE FOLLOWS]



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<PAGE>

                IN WITNESS WHEREOF, NC Capital, NC Mortgage, NC Credit and
Citigroup have caused this Amendment Number Six to be executed and delivered by
their duly authorized officers as of the day and year first above written.

                                        CITIGROUP GLOBAL MARKETS REALTY CORP.


                                        By:    /s/ James Xanthos
                                               ---------------------------------
                                        Name:  James Xanthos
                                               ---------------------------------
                                        Title: Authorized Signer
                                               ---------------------------------


                                        NC CAPITAL CORPORATION


                                        By:    /s/ Kevin Cloyd
                                               ---------------------------------
                                        Name:  Kevin Cloyd
                                               ---------------------------------
                                        Title: President
                                               ---------------------------------


                                        NEW CENTURY MORTGAGE CORPORATION


                                        By:    /s/ Kevin Cloyd
                                               ---------------------------------
                                        Name:  Kevin Cloyd
                                               ---------------------------------
                                        Title: Executive Vice President
                                               ---------------------------------


                                        NEW CENTURY CREDIT CORPORATION


                                        By:    /s/ Kevin Cloyd
                                               ---------------------------------
                                        Name:  Kevin Cloyd
                                               ---------------------------------
                                        Title: Executive Vice President
                                               ---------------------------------


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