<PAGE>   1
                                                                   EXHIBIT 10.71


                             THE PIONEER GROUP, INC.

                          SUPPLEMENTAL AGREEMENT NO. 3

                                                         as of December 30, 1998

                            Re: Senior Notes due 2004

To:  The Travelers Insurance Company
     One Tower Square
     Hartford, CT 06183-2030


Ladies and Gentlemen:

         THE PIONEER GROUP, INC., a Delaware corporation (the "COMPANY"), hereby
agrees with you as follows:

         Section 1. AMENDMENTS. Pursuant to the Note Agreement dated as of
August 14, 1997 (as amended by Supplemental Agreement No. 1 and Supplement Note
Agreement No. 2, each dated as of September 30, 1998 (as so amended, the "NOTE
AGREEMENT") entered into by the Company with The Travelers Insurance Company,
the Company issued and sold $20,000,000 aggregate principal amount of its Senior
Notes due 2004 (the "NOTES"). Unless the context otherwise requires, capitalized
terms used herein without definition have the respective meanings ascribed
thereto in the Note Agreement. The Notes originally bore an interest rate of
7.95% per annum and, pursuant to Supplemental Amendment No. 1, such interest
rate was changed to a floating rate of interest as therein described. The
Company has requested you, as the holder of all the outstanding Notes, further
to amend the Note Agreement and the Notes. Subject to this Supplemental
Agreement No. 3 becoming effective as hereinafter provided, the Company and the
holder of the Notes do hereby agree that the Note Agreement and the outstanding
Notes are amended pursuant to Section 11.1 of the Note Agreement as follows:

         A.       Section 1 of the Note Agreement is amended by:

                  1.       deleting the definitions of "Adjusted Company Total
         Debt", "Applicable Margin", "Applicable Rate", "Base Rate", and
         "Combined Adjusted Mutual Fund Cash Flow" found therein.

                  2.       deleting the definitions of "Consolidated Tangible
         Net Worth" and "Default Rate" in their entirety and replacing them with
         the following new definitions:

         "'CONSOLIDATED TANGIBLE NET WORTH'"  means, at any date, the total of:

                  (a)      stockholders' equity of the Company and its
         Subsidiaries (excluding the effect of any foreign currency translation
         adjustments) determine in accordance with GAAP on a Consolidated basis,
         MINUS


<PAGE>   2

                  (b)      the amount by which such stockholders' equity has
         been increased by the write-up of any asset of the Company and its
         Subsidiaries (excluding any write-ups net of write-downs associated
         with any venture capital investments of the Company and its
         Subsidiaries), MINUS

                  (c)      assets of the Company and its Subsidiaries that are
         considered intangible assets under GAAP (including but not limited to
         customer lists, goodwill, computer software and capitalized research
         and development costs other than the capitalized development costs
         relating to the natural resource business operations of the Company or
         any of its Subsidiaries), PLUS

                  (d)      the amount by which such stockholders' equity has
         been decreased by the after-tax noncash write-down of assets employed
         in the Company's and it Subsidiaries' international operations, up to
         an aggregate of all such write-downs of $25,000,000."

                                     * * * *

                  "'DEFAULT RATE' means that rate of interest that is the
         greater of (i) 10.95% and (ii) 2% above the rate of interest publicly
         announced by Citibank, N.A. from time to time at its principal office
         in New York City as its prime rate."

                  3.       adding the following definitions:

                  "'ADDITIONAL INDEBTEDNESS' means Indebtedness for borrowed
         money incurred by the Company or any Core Mutual Fund Subsidiary on or
         after the Supplemental Agreement No. 3 Effective Date in excess of the
         amounts of Indebtedness outstanding under the Note Agreement and the
         Bank Credit Facility, respectively, as of such date."

                  "'NET CASH PROCEEDS' is defined in Section 7.11.5."

                  "'SUPPLEMENTAL AGREEMENT NO. 3 EFFECTIVE DATE' means the
         Effective Date as defined in Supplemental Agreement No. 3 to this
         Agreement."

         B.       Section 2.1 of the Note Agreement is amended by changing
"7.95%" on the second line thereof to "8.95%".

         C.       Section 4.6 of the Note Agreement is amended by:

         1.       by changing the definition of "Reinvestment Yield" by adding
the following parenthetical immediately after the term "0.50%":

                  "(or 1.0% in the case of a prepayment effected pursuant to the
         terms of Section 7.11.5)"

         2.       by changing the definition of "Remaining Scheduled Payments"
by deleting the parenthetical "(determined for such purpose at the Base Rate
only)" found on the sixth line thereof and replacing it with the phrase
"(determined for such purpose at the rate of 7.95%)". 


                                       2

<PAGE>   3
         D.       Section 7.4.3 of the Note Agreement is amended by adding the
following new clauses (i) and (j) at the end thereof:

                  "(i) As soon as prepared and in any event within five days of
         the end of each week or five Banking Days of the end of each month, as
         applicable, updated actual and forecasted weekly cash flows for the
         period commencing November 30, 1998 through December 31, 1998, and
         monthly cash flows for the period commencing January 1, 1999, in report
         form similar to that in the attached Exhibit B.

                  (j) As soon as prepared and in any event within five days of
         the end of each month beginning with July 1999 and ending with December
         1999, a report of the aggregate amount of all Investments in the
         Company's and any Subsidiary's international operations as of the end
         of such month and for the period beginning July 1, 1999 and ending at
         the end of such month."

         E.       Section 7.5.3 of the Note Agreement is amended by deleting it
in its entirety and replacing it with the following new Section 7.5.3:

         "7.5.3. CONSOLIDATED TANGIBLE NET WORTH. Consolidated Tangible Net
         Worth shall:

                  (a)      on and after December 30, 1998, and through June 30,
         1999, at all times equal or exceed $120,000,000; PROVIDED, HOWEVER,
         that on the first day of each fiscal quarter of the Company beginning
         with the fiscal quarter ending December 31, 1998, such dollar amount
         shall be increased by an amount equal to 50% of the sum of (i)
         Consolidated Net Income (only if in excess of zero) AND (ii) the
         after-tax gain on any sale or disposition of assets or capital stock of
         Pioneer Goldfields Entities for the fiscal quarter then most recently
         ended, and

                  (b)      on and after July 1, 1999, at all times equal or
         exceed $137,500,000, provided, however, that on the first day of each
         fiscal quarter of the Company beginning with the fiscal quarter ending
         September 30, 1999, such dollar amount shall be increased by an a mount
         equal to 50% of the sum of (i) Consolidated Net Income (only if in
         excess of zero) and (ii) the after-tax gain on the sale or disposition
         of assets or capital stock of Pioneer Goldfields Entities for the
         fiscal quarter then most recently ended."

         F.       Section 7.6.1 of the Note Agreement is hereby amended by
adding the following proviso at the end thereof:

                  "PROVIDED, HOWEVER, that Additional Indebtedness incurred
         under the Bank Credit Facility, when aggregated with all other
         Additional Indebtedness, shall not exceed $45,000,000 at any one time
         outstanding."

         G.       A new Section 7.6.12 is hereby added to the Note Agreement to
read as follows:

                  "7.6.12 Additional Indebtedness of the Company and the Core
         Mutual Fund Subsidiaries, PROVIDED, HOWEVER, that Additional
         Indebtedness incurred under this Section 7.6.11., when aggregated with
         all Additional Indebtedness incurred under the Bank 



                                       3

<PAGE>   4
         Credit Facility pursuant to Section 7.6.1, shall not exceed $45,000,000
         at any one time outstanding; and PROVIDED, FURTHER that immediately
         before and after giving effect to the incurrence of such Additional
         Indebtedness, no Default exits."

         H.       Section 7.9.1 of the Note Agreement is amended by deleting it
in its entirety and replacing it with the following new Section 7.9.1:

                  "7.9.1. Investments of the Company and each Subsidiary of the
         Company which is not a Core Mutual Fund Subsidiary; PROVIDED that
         immediately before and after giving effect to such Investment, no
         Default exists; PROVIDED FURTHER that on and after July 1, 1999 and
         through December 31, 1999, the Company and any Subsidiary will only
         have outstanding, acquire, commit itself to acquire or hold any new
         Investments, including Guarantees permitted by Section 7.7, in the
         Company's or any Subsidiary's international operations that in the
         aggregate, together with Guarantees permitted by Section 7.9.7, will
         not exceed $20,000,000."

         I.       Section 7.9.7 of the Note Agreement is amended by deleting it
in its entirety and replacing it with the following new Section 7.9.7:

                  "7.9.7. Guarantees permitted by Section 7.7; PROVIDED,
         HOWEVER, that on and after July 1, 1999 and though December 31, 1999,
         the Company and any Subsidiary will only have outstanding, acquire,
         commit itself to acquire or hold any new Guarantees in the Company's or
         any Subsidiary's international operations that in the aggregate,
         together with other new Investments permitted by Section 7.9.1, will
         not exceed $20,000,000."

         J.       Section 7.11.5 of the Note Agreement is amended by (a) by
deleting the words "a non-controlling equity interest" and replacing them with
"assets or an equity interest (whether controlling or non-controlling)", (b)
deleting the words "net cash proceeds" found in the fourth line thereof and
replacing them with the words "Net Cash Proceeds", (c) deleting the words "to
purchase" found on the eleventh line thereof and the remainder of said Section
and replacing it with the following:

         "to purchase or prepay (for a price at least equal to the price that
         would be paid if the Company then prepaid a like principal amount of
         the Notes pursuant to Section 4.1) pro rata among all Notes tendered,
         an aggregate principal amount of Notes at least equal to the amount
         that bears the same relation to the outstanding principal amount of the
         Notes as the amount of the permanent reduction of the Maximum Amount of
         Revolving Credit (as such term is defined in the Bank Credit Facility)
         resulting from such transaction under Section 4.2.3 of the Bank Credit
         Facility bears to such Maximum Amount of Revolving Credit before giving
         effect to such reduction, and PROVIDED, FURTHER, that any such purchase
         or prepayment of Notes shall be made prior to or concurrently with such
         prepayment of such Revolving Loan."

and (d) adding the following sentence at the end thereof:

         "For purposes of this Section 7.11.5, `Net Cash Proceeds' shall mean
         the total cash proceeds received from such public offering or equity
         sale of Pioneer Goldfields Entities, 




                                       4
<PAGE>   5

         reduced by (i) the amount required to be paid by the Company or any
         Subsidiary to repay financing obligations on any equipment being
         transferred in such sale, (ii) the amount required to be paid by the
         Company or any Subsidiary to repay the OPIC Financing, (iii) any
         federal, state, local or other tax obligations incurred by the Company
         or any Subsidiary as a result of such public offering or sale or the
         prior sale of the B Share revenues used to prepay the B Share Loan, and
         (iv) any federal, state or local tax obligations due and payable by the
         Company within 45 days of such prepayment."

         K.       Section 9.1.9 of the Note Agreement is amended by adding the
following new paragraph (c) at the end thereof:

                  "(c) The aggregate investment assets under management by the
Company and its Subsidiaries shall at any time be less than $15,000,000,000."

         L.       Exhibit 2.1 to the Note Agreement is deleted in its entirety
and replaced with Exhibit A hereto.

         M.       A new Exhibit 7.4.3(i) to the Note Agreement is added in the
form of Exhibit B hereto.

         N.       Exhibit 8.1 to the Note Agreement, entitled "The Company and
its Subsidiaries", is deleted in its entirety and replaced with Exhibit C
hereto.

         O.       Exhibit 9.1.12 to the Note Agreement, entitled "Officers of
the Company", is deleted in its entirety and replaced with Exhibit D hereto.

         Section 2. REPRESENTATIONS AND WARRANTIES OF THE COMPANY. The Company
represents and warrants to you as follows:

         A.       ORGANIZATION, AUTHORIZATION, ETC. The Company and each of its
Subsidiaries is a corporation duly organized, validly existing and in good
standing under the laws of the State of its organization, and has all requisite
power and authority to execute, deliver and perform its obligations under the
Note Agreement as amended by this Supplemental Agreement No. 3.

         The execution, delivery and performance of this Supplemental Agreement
No. 3 has been duly authorized by all necessary corporate and, if required,
stockholder action on the part of the Company and each Subsidiary Guarantor, as
applicable. This Supplemental Agreement No. 3 is a legal, valid and binding
obligation of the Company and the Subsidiary Guarantors, as applicable,
enforceable against the Company or such Subsidiary Guarantors in accordance with
its terms, except as enforceability may be limited by bankruptcy, insolvency,
reorganization, fraudulent transfer, moratorium or other similar laws relating
to or affecting creditors' rights generally and by general principles of equity
(regardless of whether such enforceability is considered in a proceeding in
equity or at law).

         B.       COMPLIANCE WITH LAWS, OTHER INSTRUMENTS, ETC. The execution,
delivery and performance by the Company or the Subsidiary Guarantors of this
Supplemental Agreement No. 3 does not and will not (A) contravene, result in any
breach of, or constitute a default under, or




                                       5

<PAGE>   6
result in the creation of any Lien in respect of any property of the Company
under any indenture, mortgage, deed of trust, loan, purchase or credit
agreement, lease, corporate charter or by-laws, or any other agreement or
instrument to which the Company or any Subsidiary is bound or by which the
Company or any Subsidiary or any of their respective properties may be bound or
affected, (B) conflict with or result in a breach of any of the terms,
conditions or provisions of any order, judgment, decree, or ruling of any court,
arbitrator or Governmental Authority applicable to the Company or any Subsidiary
or (C) violate any provision of any statute or other rule or regulation of any
Governmental Authority applicable to the Company or any Subsidiary.

         C.       GOVERNMENTAL AUTHORIZATIONS, ETC. No consent, approval or
authorization of, or registration, filing or declaration with, any Governmental
Authority is required in connection with the execution, delivery or performance
by the Company or any Subsidiary Guarantor of this Supplemental Agreement No. 3.

         D.       NO DEFAULT, ETC. No Event of Default or Default has occurred
and is continuing and neither the Company nor any Core Mutual Fund Subsidiary is
in default (whether or not waived) in the performance or observance of any of
the terms, covenants or conditions contained in any instrument evidencing any
Indebtedness and there is no pending request by the Company (except pursuant to
this Supplemental Agreement No. 3) or any Subsidiary for any amendment or waiver
in respect of any contemplated or possible default with respect to such
Indebtedness and no event has occurred and is continuing which, with notice or
lapse of time or both, would become such a default.

         E.       NO UNDISCLOSED FEES. The Company has not, directly or
indirectly, other than with respect to the payment of consideration disclosed to
the Noteholders, paid or caused to be paid any consideration (as supplemental or
additional interest, a fee or otherwise) to any party to the Bank Credit
Facility in order to induce such party to enter into an agreement substantially
similar to this Supplemental Agreement No. 3, nor has the Company agreed to made
any such payment.

         Section 3. REPRESENTATION OF THE NOTEHOLDER. You represent to the
Company that you are the beneficial owner of the Notes in an aggregate principal
amount of $20,000,000.

         Section 4. EFFECTIVENESS OF THIS SUPPLEMENTAL AGREEMENT NO. 3. The
amendments to Exhibit A to the Note Agreement and the change in the interest
rate to be borne by the Notes pursuant to this Supplemental Agreement No 3 shall
become effective on December 30, 1998. All other terms and conditions of this
Supplemental Agreement No. 3 will become effective on the date (the "EFFECTIVE
DATE") on which all of the following conditions precedent shall have been
satisfied:

         A.       PROCEEDINGS. All proceedings taken by the Company and the
Subsidiary Guarantors in connection with the transactions contemplated hereby
and all documents and papers incident thereto shall be satisfactory to you, and
you and your special counsel shall have received all such counterpart originals
or certified or other copies of such documents and papers, all in form and
substance satisfactory to you, as you or they may reasonably request in
connection therewith.

         B.       OPINION OF COUNSEL FOR THE COMPANY. On the Effective Date, you
shall have received from Hale and Dorr, special counsel to the Company, hereby
authorized and directed by the



                                       6

<PAGE>   7

Company, its opinion with respect to this Supplemental Agreement No. 3, the Note
Agreement, as amended hereby, and the transactions contemplated hereby and
thereby, which opinion shall be in form and substance satisfactory to you.

         C.       REPRESENTATIONS AND WARRANTIES. The representations and
warranties of the Company contained in Section 2 of this Supplemental Agreement
No. 3 shall be true on and as of the Effective Date as though such
representations and warranties had been made on and as of the Effective Date,
and you shall have received a certificate of a senior financial officer of the
Company, dated the Effective Date, to such effect.

         D.       PAYMENT OF FEES. The Company shall have paid the fees and
disbursements of your special counsel as contemplated by Section 6 of this
Supplemental Agreement No. 3. The Company shall have paid for the account of The
Travelers insurance Company a fee of $70,000.

         E.       PRIVATE PLACEMENT NUMBER. A new private Placement Number
issued by Standard & Poor's CUSIP Service Bureau (in cooperation with the
Securities Valuation Office of the National Association of Insurance
Commissioners) shall have been obtained for the Notes.

         Section 5. EXCHANGE OR NOTATION OF THE NOTES. Prior to the transfer
effected on or after December 30, 1998 of any Note outstanding on such date, the
holder thereof shall endorse such Note appropriately in order to indicate that
all amounts owing under such Note shall, from and after December 30, 1998, bear
interest at the rate of 8.95% per annum. Each new Note issued thereafter in
substitution or exchange for an outstanding Note shall be in the form or Exhibit
A hereto, which form of Note shall replace Exhibit 2.1 to the Note Agreement.

         Section 6. EXPENSES. Without limiting the generality of Section 5.8 of
the Note Agreement, the Company agrees, whether or not the transactions
contemplated hereby are consummated, to pay the reasonable fees and
disbursements of Willkie Farr & Gallagher, your special counsel, for their
services rendered in connection with such transactions and with respect to this
Supplemental Agreement No. 3 and any other document delivered pursuant to this
Supplemental Agreement No. 3 and to reimburse you for your out-of-pocket
expenses in connection with the foregoing.

         Section 7. RATIFICATION. Except as amended hereby, the Note Agreement
is in all respects ratified and confirmed and the provisions thereof shall
remain in full force and effect, and the Subsidiary Guarantors hereby ratify
their obligations thereunder and under the Subsidiary Guarantees to which they
are party.

         Section 8. COUNTERPARTS. This Supplemental Agreement No. 3 may be
executed in two or more counterparts, each of which shall be deemed an original,
but all of which together shall constitute one and the same instrument.

         Section 9. GOVERNING LAW. This Supplemental Agreement No. 3 shall be
governed by and construed in accordance with the laws of the State of New York.





                                       7
<PAGE>   8

         If you are in agreement with the foregoing, please sign the form of
acceptance in the space provided below, whereupon this Supplemental Agreement
No. 3 shall become a binding agreement between you and the Company, with the
approval of the Subsidiary Guarantors, subject to becoming effective as
hereinabove provided.


THE PIONEER GROUP, INC.


By: /s/ John A. Boynton
    ----------------------------------
    Title: CFO, Treasurer, Exec. VP

60 State Street
Boston, Massachusetts 02109-1820

SUBSIDIARY GUARANTORS

PIONEER INVESTMENT MANAGEMENT, INC. (formerly known as
Pioneering Management Corporation)


By: /s/ John A. Boynton
    ----------------------------------
    Title: Treasurer

60 State Street
Boston, Massachusetts 02109-1820

PIONEERING MANAGEMENT (IRELAND) LIMITED


By: /s/ Robert F. Richardson
    ----------------------------------
    Title: Managing Director

60 State Street
Boston, Massachusetts 02109-1820

PIONEERING SERVICES CORPORATION


By: /s/ John A. Boynton
    ----------------------------------
    Title: Treasurer

60 State Street
Boston, Massachusetts 02109-1820

ACCEPTED

THE TRAVELERS INSURANCE COMPANY


By: /s/ Pamela Westmoreland
    ----------------------------------
    Title: Investment Officer




                                       8
<PAGE>   9

                                                                       EXHIBIT A

                                                                     EXHIBIT 2.1

                                 [FORM OF NOTE]

                             THE PIONEER GROUP, INC.

                           8.95% Senior Note due 2004

No. R-                                                        New York, New York
$________________                                                         [Date]
PPN:  723684 a@ 5


         THE PIONEER GROUP, INC., a Delaware corporation (the "Company"), for
value received, hereby promises to pay to ____________, or registered assigns,
the principal sum of __________________ Dollars (or so much thereof as shall not
have been prepaid) on August 15, 2004, and to pay interest (computed on the
basis of a 360-day year of twelve 30-day months) on the unpaid principal balance
thereof from the date of this Note at the rate of 8.95% per annum, quarterly on
February 15, May 15, August 15 and November 15 in each year until such principal
sum shall have become due and payable (whether at maturity, at a date fixed for
prepayment or by declaration, acceleration or otherwise), and to pay on demand
interest (so computed) on any overdue principal and premium, if any, and (to the
extent permitted by applicable law) on any overdue interest, at a rate per annum
equal to the greater (determined on a daily basis) of (i) 10.95% and (ii) 2%
above the rate of interest publicly announced by Citibank, N.A. from to time to
time at its principal office in The City of New York as its prime or base rate.
Payments of principal, premium, if any, and interest shall be made in such coin
or currency of the United States of America as at the time of payment is legal
tender for the payment of public and private debts in the manner and to the
address designated by the holder hereof and, in the absence of such designation,
at said principal office of Citibank, N.A.

         This Note is one of an issue of Senior Notes of the Company issued
pursuant to the Note Agreement dated as of August 14, 1997, as amended by
Supplemental Agreement No. 1 dated as of September 30, 1998, Supplemental
Agreement No. 2 dated as of September 30, 1998 and Supplemental Agreement No. 3
dated as of December 30, 1998 (as so amended, the "Note Agreement"), entered
into by the Company and certain of its Subsidiaries, as guarantors, with an
institutional investor. The holder of this Note is entitled to the benefits of
the Note Agreement and is also entitled to the benefits of a certain
Intercreditor Agreement referred to therein.

         The Company may at its election prepay this Note, in whole or in part,
and the maturity hereof may be accelerated following an Event of Default, all as
provided in the Note Agreement, to which reference is made for the terms and
conditions of such provisions as to prepayment and acceleration, including
without limitation the payment of a make-whole premium in connection therewith.

         Upon surrender of this Note for registration of transfer or exchange,
duly endorsed or accompanied by a written instrument of transfer duly executed
by the registered holder hereof or 


                                       9
<PAGE>   10

such holder's attorney duly authorized in writing, a new Note for a like
principal amount will be issued to, and, at the option of the holder, registered
in the name of, the transferee. The Company and any agent of the Company may
deem and treat the person in whose name this Note is registered as the owner
hereof for the purpose of receiving payments of the principal of, premium, if
any, and interest hereon and for all other purposes whatsoever, whether or not
this Note is overdue, and the Company shall not be affected by any notice to the
contrary.

         As provided in the Note Agreement, this Note shall be governed by and
construed in accordance with the law of State of New York.



                                        THE PIONEER GROUP, INC.


                                        By:
                                            ----------------------------------
                                            Title:




















                          [REMAINING EXHIBITS OMITTED]




                                       10