U.S. SECURITIES AND EXCHANGE COMMISSION
                        Washington, D.C.  20549

                        FORM 24F-2
                        Annual Notice of Securities Sold
                        Pursuant to Rule 24f-2

1.    Name and address of issuer:

        First Trust Portfolios L.P.
        120 E. Liberty Drive
        Wheaton, Illinois 60187

2.    The name of each series or class of securities for which this Form
      is filed:  FT Series 2782

3.    Investment Company Act File Number: 811-05903

      Securities Act File Number: 333-171528

4.    (a) Last day of fiscal year for which this Form is filed:
        April 27, 2011

      (b) :     :  Check box if this Form is being filed late(i.e., more that 90
                 calendar days after the end of the issuer's fiscal year.

      (c) :     :  Check box if this is the last time the issuer will be filing
                     this Form.

5.     Calculation of registration fee:

 (i) Aggregate sale price of securities sold
      during the fiscal year pursuant to section 24(f): $ 17,015,032.56

(ii) Aggregate price of securities redeemed or
        repurchased during the fiscal year:             $ (145,768.64)

(iii)Aggregate price of securities redeemed or
      repurchased during any prior fiscal year ending
        no earlier than October 11, 1995 that were not
        previously used to reduce registration fees
      payable to the Commission:                         $ -0-

 (iv)   Total available redemption credits(add items
         5(ii) and 5(iii):                               $ (145,768.64)

 (v)    Net sales - if Item 5(i) is greater than Item
         5(iv)[subtract Item 5(iv) from Item 5(i)]:      $ 16,869,263.92

(vi)  Redemption credits available for use in future years
      --if Item 5(i) is less than Item 5(iv) [subtract item
        5(iv) from Item 5(i)]:                           $ -0-

(vii)   Multiplier for determining registration fee:        x .0001161

(viii)  Registration fee due [multiply Item 5(v) by
         Item 5(vii)](enter "0" if no fee is due):       =$ 1,958.52

6.  Prepaid Shares

    If the response to Item 5(i) was determined by deducting an
    amount of securities that were registered under the Securities
    Act of 1933 pursuant to rule 24e-2 as in effect before[effective
    date of rescission of rule 24e-2], then report the amount of
    securities (number of shares or other units) deducted here: ___________.

    If there is a number of shares or other units that were registered
    pursuant to rule 24e-2 remaining unsold at the end of the fiscal
    year for which this form is filed that are available for use by
    the issuer in future fiscal years, then state that number
    here:  ________________.

7.  Interest due - if this Form is being filed more than 90 days after
   the end of the issuer's fiscal year:                         +$ -0-

8.  Total of the amount of the registration fee due plus any interest
   due [line 5(viii) plus line 7]:                         =$1,958.52

9.  Date the registration fee and any interest payment was sent to the
   Commission's lockbox depository:  May 26, 2011

       Method of Delivery:
                                        [ X ]  Wire Transfer
                                        [   ]  Mail or other means

                        SIGNATURES

This report has been signed below by the following persons on
behalf of the issuer and in the capacities and on the dates
indicated.

By:  Jason T. Henry
     Senior Vice President

May 27, 2011