UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 13D

Under the Securities Exchange Act of 1934

(Amendment No. 1)

Invesco Van Kampen Trust for Investment Grade New York Municipals

(Name of Issuer)

Variable Rate Muni Term Preferred Shares

(Title of Class of Securities)

46131T507

(CUSIP Number)

RBC Municipal Products, Inc.

c/o John Penn, Esq.

3 World Financial Center 200 Vesey Street

New York, New York 10281

(212) 858-7116

August 27, 2012

(Date of Event which Requires Filing of this Statement)

If the filing person has previously filed a statement on Schedule 13G to report the acquisition that is the subject of this Schedule 13D, and is filing this schedule because of §§240.13d-1(e), 240.13d-1(f) or 240.13d-1(g), check the following box:  ¨

This Amendment No. 1 (this “Amendment”) amends, as set forth below, the statement on Schedule 13D, dated May 15, 2012 and filed with the SEC on May 25, 2012 (the “Original Schedule 13D”), for Royal Bank of Canada and RBC Municipal Products, Inc. (collectively, the “Reporting Persons”) with respect to the variable rate muni term preferred shares (“VMTP”) of Invesco Van Kampen Trust for Investment Grade New York Municipals (the “Issuer”). This Amendment is being filed as a result of the merger of Invesco New York Quality Municipal Securities (“IQN”) on August 27, 2012 into the Issuer (the “Merger”) pursuant to which the Reporting Persons exchanged their 136 variable rate muni term preferred shares of IQN for an equal number of VMTP.

All capitalized terms used in this Amendment and not otherwise defined herein have the meanings ascribed to them in the Original Schedule 13D. Except as otherwise provided herein, each item of the Original Schedule 13D remains unchanged.

Item 3. Source and Amount of Funds or Other Consideration

Item 3 of the Original Schedule 13D is hereby amended and supplemented by adding the following after the second sentence of the first paragraph:

“In connection with the Merger of IQN into the Issuer, the Reporting Persons exchanged their 136 variable rate muni term preferred shares of IQN for an equal number of VMTP. MPI deposited such newly acquired 136 shares of VMTP into the TOB on August 27, 2012.”

Item 4. Purpose of Transaction

Item 4 of the Original Schedule 13D is hereby amended and supplemented by adding the following after the first paragraph:

“On August 27, 2012 MPI exchanged its 136 variable rate muni term preferred shares of IQN for an equal number of VMTP in connection with the Merger. In connection with such exchange, the Purchase Agreement was amended by Amendment to Variable Rate Muni Term Preferred Purchase Agreement, dated as of August 27, 2012 between the Issuer and RBCCM.”

Item 5. Interest in Securities of the Issuer

Item 5 of the Original Schedule 13D is hereby amended and restated in its entirety as follows:

“(a) – (b) The responses of the Reporting Persons to Rows (7) through (11) of the cover pages of this Statement are incorporated herein by reference.

(c) The responses of the Reporting Persons in Item 3 and Item 4 are incorporated herein by reference.

(d) The TOB has the right to receive dividends from, or the proceeds from the sale of, the VMTP. MPI retains the power to dispose of or direct the disposition of the VMTP while in the TOB.

(e) Not applicable.”

Item 6. Contracts, Arrangements, Understandings or Relationships With Respect to Securities of the Issuer

Item 6 of the Original Schedule 13D is hereby amended and supplemented by adding the following after the first paragraph:

“The voting and consent rights on the 136 shares of VMTP conveyed to the Voting Trust in connection with the Merger will be treated in the same manner as previously described in this Item 6.”

Item 7. Material to be Filed as Exhibits

SIGNATURE

After reasonable inquiry and to the best of my knowledge and belief, I certify that the information set forth in this statement is true, complete and correct.

Exhibit 99.1

JOINT FILING AGREEMENT

Pursuant to and in accordance with the Securities Exchange Act of 1934, as amended (the “Exchange Act”), and the rules and regulations thereunder, each party hereto hereby agrees to the joint filing, on behalf of each of them, of any filing required by such party under Section 13 or Section 16 of the Exchange Act or any rule or regulation thereunder (including any amendment, restatement, supplement, and/or exhibit thereto) with the Securities and Exchange Commission (and, if such security is registered on a national securities exchange, also with the exchange), and further agrees to the filing, furnishing, and/or incorporation by reference of this agreement as an exhibit thereto. This agreement shall remain in full force and effect until revoked by any party hereto in a signed writing provided to each other party hereto, and then only with respect to such revoking party.

IN WITNESS WHEREOF, each party hereto, being duly authorized, has caused this agreement to be executed and effective as of the date set forth below.

Exhibit 99.7

AMENDMENT TO VARIABLE RATE MUNI TERM PREFERRED SHARES

PURCHASE AGREEMENT

This amendment (this “Amendment”), dated as of August 27, 2012, to the Variable Rate Muni Term Preferred Shares Purchase Agreement, dated as of May 10, 2012, between Invesco Van Kampen Trust for Investment Grade New York Municipals, a closed-end investment company organized as a Massachusetts business trust, as issuer, and RBC Capital Markets, LLC, a Minnesota limited liability company, including its successors and assigns by operation of law (the “Purchaser”) (the “Purchase Agreement”), is entered into between Invesco Van Kampen Trust for Investment Grade New York Municipals, a closed-end investment company organized as a Delaware statutory trust, the successor to the original issuer (the “Fund”), and the Purchaser. Capitalized terms used herein without definition shall have the meanings assigned thereto in the Purchase Agreement.

WHEREAS, the parties hereto are parties to the Purchase Agreement; and

WHEREAS, the parties hereto desire to amend the terms of the Purchase Agreement as provided for herein.

ACCORDINGLY, the Purchase Agreement is hereby amended as follows:

Section 1. AMENDMENT TO THE PURCHASE AGREEMENT

(a) Schedule I of the Purchase Agreement is hereby deleted in its entirety and replaced with the Schedule I attached hereto.

(b) All references to “VMTP Shares” in the Purchase Agreement are hereby deemed to include reference to all VMTP Shares as set forth on Schedule I, as amended by this Amendment.

Section 2. MISCELLANEOUS.

(a) The parties hereto hereby agree that, except as specifically amended herein, the Purchase Agreement is and shall continue to be in full force and effect and is hereby ratified and confirmed in all respects. All references in the Purchase Agreement and other documents related thereto shall be references to the Purchase Agreement as amended by this Amendment. Except as specifically provided herein, the execution, delivery and effectiveness of this Amendment shall not operate as a waiver of any right, power or remedy of any party hereto under the Purchase Agreement, or constitute a waiver of any provision of any other agreement.

(b) This Amendment shall be construed in accordance with and governed by the domestic law of the State of New York.

THE PARTIES HERETO HEREBY SUBMIT TO THE NON-EXCLUSIVE JURISDICTION OF THE FEDERAL AND NEW YORK STATE COURTS LOCATED IN THE CITY OF NEW YORK, BOROUGH OF MANHATTAN, IN CONNECTION WITH ANY DISPUTE RELATED TO THIS AGREEMENT OR ANY MATTERS CONTEMPLATED HEREBY.

(c) This Amendment may be executed in any number of counterparts by facsimile or other written form of communication, each of which shall be deemed to be an original as against any party whose signature appears thereon, and all of which shall together constitute one and the same instrument.

(d) In case any provision of this Amendment shall be invalid, illegal, or unenforceable, the validity, legality, and enforceability of the remaining provisions shall not in any way be affected or impaired thereby so long as the intent of the parties to this Amendment shall be preserved.

(e) Each of the Fund and the Purchaser represent and warrant to each other that this Amendment has been duly and validly executed and delivered by it and constitutes its legal, valid and binding obligation, enforceable against it in accordance with its terms.

(f) This Amendment shall be binding upon and inure to the benefit of the parties hereto and their respective successors and assigns in accordance with Section 8.05 of the Purchase Agreement.

2

IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed by their respective authorized representatives as of the day and year first above written.

SCHEDULE I