<PAGE>   1

                                                                  Exhibit (4)(f)


                             LIMITED TERM EXTENSION
                             ----------------------

         This Limited Term Extension ("Extension") is entered into this 13th day
of February, 1998 between National Auto Credit, Inc. ("National"), as borrower,
NAC, Inc. and NAC Investment Company, as guarantors, The First National Bank of
Chicago ("First Chicago"), Morgan Guaranty Trust Company of New York ("Morgan"),
The Bank of New York ("BNY"), First Union National Bank ("First Union"), The
Huntington National Bank ("Huntington"), Allstate Life Insurance Company
("Allstate"), Connecticut General Life Insurance Company (on behalf of itself
and one or more separate accounts, collectively "Connecticut General"),
Principal Mutual Life Insurance Company ("Principal Mutual"), New York Life
Insurance Company ("New York Life"), New York Life Insurance and Annuity
Corporation ("New York Annuity"), Lincoln National Life Insurance Company
("Lincoln National") and Lincoln Life & Annuity Company of New York ("Lincoln
Life"), as lenders, and NBD Bank, ("NBD") as issuer of letters of credit.


                                   DEFINITIONS
                                   -----------

         When used herein, the following terms shall have the following
meanings:

         "AGENT" means First Chicago in its capacity as Administrative Agent
under the Credit Agreement.

         "BANKS" means First Chicago, Morgan, BNY, First Union and Huntington.

         "COMMITMENTS" shall have the meaning ascribed to such term in the
Credit Agreement.

         "CREDIT AGREEMENT" means that certain Long-Term Credit Agreement dated
as of April 21, 1997 among National and the Banks.

         "CREDIT AGREEMENT OBLIGATIONS" means the "Lender Obligations" as
defined in the Credit Agreement.

         "DELOITTE" means the public accounting firm of Deloitte and Touche,
L.L.P.

         "EXTENSION DEFAULT" means (i) all "Defaults" as defined in the Credit
Agreement, (ii) all "Defaults" as defined in the Note Purchase Agreement, (iii)
any reconstitution, suspension or disbandment of the Special Committee which
precedes issuance of the Special Committee Report, (iv) any abandonment,
interruption or disruption in the conduct of the Special Committee Investigation
or in the preparation of the Special Committee Report, (v) National's failure to
comply with any term or provision of this Limited Term Extension, or (vi) any
demand upon National for payment or attempt to collect outstanding indebtedness
by Brown Brothers Harriman & Co.


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         "EXTENSION TERMINATION DATE" means the earliest to occur of (i) March
6, 1998, (ii) the occurrence of an Extension Default, and (iii) the fifth
business day after the Special Committee Report is delivered to the Banks and
Insurance Companies.

         "FLOATING RATE" shall have the meaning ascribed to such term in the
Credit Agreement.

         "INSURANCE COMPANIES" means Allstate, Connecticut General, Principal
Mutual, New York Life, New York Annuity, Lincoln National and Lincoln Life.

         "LENDERS" means the Banks and the Insurance Companies.

         "LENDER OBLIGATIONS" means the Credit Agreement Obligations and the
Note Obligations.

         "LETTER AGREEMENT" means that certain letter agreement dated as of
February 5, 1998 between National and the Banks.

         "LETTERS OF CREDIT" means three irrevocable letters of credit in the
face amounts of $300,000, $250,000 and $1,000,000 issued by NBD for the account
of National with designated beneficiaries of Great America Lender Services,
Dealer Assurance Co., and Virginia Surety Co., Inc., respectively.

         "LOAN" shall have the meaning ascribed to such term in the Credit
Agreement.

         "MAKE-WHOLE OBLIGATION" means the "Make-Whole Amount" as defined in
Section 8.6 of the Note Purchase Agreement, together with all interest accrued
thereon.

         "NBD" means NBD Bank, N.A.

         "NOTE OBLIGATIONS" means all obligations, including the "Make Whole
Amount", owed to the Insurance Companies by National pursuant to the terms of
the Note Purchase Agreement and the Notes.

         "NOTE PURCHASE AGREEMENT" means that certain Note Purchase Agreement
dated as of April 21, 1997 between National and the Insurance Companies (or
their predecessors in interest).

         "NOTES" shall have the meaning ascribed to such term in the Note
Purchase Agreement.

         "PRINCIPAL OBLIGATIONS" means the sum of (i) the outstanding principal
obligations owed to the Banks under the Credit Agreement, (ii) the outstanding
principal obligations (excluding all Make-Whole Obligations) owed to the
Insurance Companies under the Notes, and (iii) the Reimbursement Obligation;
provided, however, that if the Letters of Credit expire without having been
drawn or are returned to NBD undrawn, Principal Obligations shall not include
the Reimbursement Obligation.


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         "PRO RATA" means (i) with respect to each Lender, a fraction, the
numerator of which equals the Principal Obligations owed to such Lender and the
denominator of which equals all Principal Obligations, and (ii) with respect to
NBD, a fraction, the numerator of which equals the Reimbursement Obligation and
the denominator of which equals all Principal Obligations.

         "REIMBURSEMENT OBLIGATION" means the sum of (i) National's obligation
to reimburse NBD for draws on the Letters of Credit, and (ii) the aggregate
undrawn face amount of the Letters of Credit.

         "ROLLOVER LOANS" means Loans totalling $10 million which, pursuant to
the Letter Agreement, mature on February 13, 1998.

         "SENIOR OBLIGATIONS" means the Reimbursement Obligation and all Lender
Obligations, except for Make-Whole Obligations.

         "SPECIAL COMMITTEE" means the special committee of outside directors
formed by National's board of directors for the purpose of, inter alia,
investigating the information provided by Deloitte with respect to National's
financial statements.

         "SPECIAL COMMITTEE INVESTIGATION" means the investigation of the
reportable conditions identified by Deloitte which is currently being conducted
by the Special Committee.

         "SPECIAL COMMITTEE REPORT" means the final written report that the
Special Committee will issue after concluding the Special Committee
Investigation.

         "TAX NOTES" means the promissory note in the original principal amount
of $141,000 with a payment due date of February 27, 1998, which was executed by
National in connection with its investments in certain low income housing
limited partnerships.


                                    RECITALS
                                    --------

                  WHEREAS, National presently owes (i) $38 million in Principal
Obligations on Loans extended by the Banks pursuant to the Credit Agreement, and
(ii) $45 million in Principal Obligations on loans extended by the Insurance
Companies pursuant to the terms of the Note Purchase Agreement and Notes.

                  WHEREAS, on January 12, 1998, National's auditors, Deloitte,
notified National of the existence of 5 reportable conditions relating to
National's internal controls and accounting. Thereafter, on January 16, 1998,
Deloitte resigned its audit engagement.

                  WHEREAS, on January 16, 1998, the Special Committee was formed
for the purpose of, inter alia, investigating the information provided by
Deloitte with respect to National's financial statements.


<PAGE>   4


                  WHEREAS, pursuant to the terms of the Letter Agreement, (i)
all Commitments have been terminated, and (ii) the Rollover Loans become due and
payable on February 13, 1998.

                  WHEREAS, National is unable to satisfy these maturities and,
accordingly, has requested the Banks to extend the maturities.

                  WHEREAS, if the Banks do not extend the maturities, the
default under the Credit Agreement occasioned by National's failure timely to
pay the maturities will, pursuant to Section 11(f) of the Note Purchase
Agreement, constitute a default under the Note Purchase Agreement.

                  WHEREAS, at the request of National, by letter agreement dated
December 9, 1997, the Insurance Companies waived compliance with the provisions
of Section 10.5(d) of the Note Purchase Agreements for the fiscal quarter ending
on October 31, 1997 (the "Section 10.5(d) Waiver"), it being expressly
understood and agreed in the December 9th letter agreement that any breach of
such Section 10.5(d) for any fiscal quarter ending after October 31, 1997 shall
be an Event of Default and is not waived.

                  WHEREAS, by letters dated January 26, 1998 and February 6,
1998, the Insurance Companies extended the Section 10.5(d) Waiver through
February 5, 1998 and February 13, 1998, respectively, conditioned upon
compliance by National with certain terms and conditions set forth in said
letters (the "Waiver Extension").

                  WHEREAS, the Insurance Companies are willing to provide a
further limited extension of the Waiver Extension on the terms and conditions
contained herein.

                  WHEREAS, the Banks are willing to provide a limited extension
of maturities on the terms and conditions contained herein.

                  NOW, THEREFORE, in consideration of the foregoing and for
other good and valuable consideration, the receipt and sufficiency of which is
hereby acknowledged, the parties hereto agree as follows:

                  1. Subject to the remaining provisions hereof and except as
provided in Section 4 below, the Banks agree to extend the maturities of all
Rollover Loans, and the Insurance Companies agree to extend the Waiver
Extension, until the Extension Termination Date.

                  2. Upon the execution hereof, National shall pay (i) to the
Agent, for distribution to the Banks, all interest accrued through January 31,
1998 on the Credit Agreement Obligations at the contractual, non-default rates
in accordance with the terms of the Credit Agreement, and (ii) to the Insurance
Companies, all interest accrued through January 31, 1998 on the Note Obligations
at the contractual non-default rates, in accordance with the terms of the Note
Purchase Agreement..


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                  3. From and after January 31, 1998, interest will accrue on
the unpaid balance of all Lender Obligations at a per annum rate (computed on
the basis of a 360-day year of twelve 30-day months) equal to the higher of (i)
the Floating Rate, and (ii) 7.66%. Interest will be payable to all Lenders
monthly, in arrears, on the first business day of each month. From and after
January 31, 1998 interest will accrue on the unpaid balance of any overdue
Credit Agreement Obligation or Note Obligation at the rate applicable to such
overdue Obligation under the terms of the Credit Agreement or Note Purchase
Agreement, as the case may be.

                  4. National shall make principal payments to the Lenders and
NBD on the following dates and in the following amounts:

                  February 13, 1998                  $500,000
                  February 20, 1998                  $500,000
                  March 6, 1998                      $500,000

Each principal payment will be distributed to the Lenders and NBD on a Pro Rata
basis and will be applied by the Lenders against the Principal Obligations.
Principal payments distributed to NBD in respect of the Reimbursement Obligation
will be held by NBD as cash collateral to secure payment of the Reimbursement
obligation until the Letters of Credit are drawn. If one or more Letters of
Credit expires or is returned to NBD undrawn, NBD will distribute the cash
collateral then held by NBD in respect of such Letter(s) of Credit to all
Lenders (and, to the extent that other letters of Credit remain outstanding, to
NBD) for reduction of Principal Obligations on a Pro Rata basis. The remaining
balance of all Lender Obligations shall be due and payable in full on the
Extension Termination Date; provided, however, that to the extent payment of the
Note Obligations is voluntarily waived or extended by the Insurance Companies
beyond the Extension Termination Date, the Extension Termination Date shall not
constitute a "Settlement Date" for purposes of Section 8.6 of the Note Purchase
Agreement.

                  5. Principal payments distributed to the Insurance Companies
in accordance with paragraph 4 above shall constitute optional prepayments under
and pursuant to Section 8.2 of the Note Purchase Agreement to which the
Make-Whole Obligation applies in accordance with the terms and provisions of the
Note Purchase Agreement; provided, however, that the make-Whole Obligation shall
accrue interest as set forth in Paragraph 3 above and shall be payable subject
to the provisions of paragraph 6 herein), with such interest, at the time of
final maturity (whether by payment, prepayment, acceleration or otherwise) of
the Notes; and provided further that with respect to the principal payments set
forth above, and no other, the Insurance Companies hereby waive the notice,
certificate and minimum amount provisions of Section 8.2 of the Note Purchase
Agreement.
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                  6. National's Make-Whole Obligation shall be subordinate in
priority to the full cash payment of all Senior Obligations (including all
interest accrued and expenses incurred subsequent to the filing by National of a
petition for relief under 11 U.S.C. ss.101 et. seq., regardless of whether such
interest or expenses are allowed or allowable in such proceeding). National will
not make, and the Insurance Companies will not accept, any cash payments in
respect of the Make-Whole Obligation until the Senior Obligations have been paid
in cash in full, provided that any non-cash payment received by the Insurance
Companies shall be held as collateral for the repayment of all Senior
Obligations until all Senior Obligations have been paid in cash in full,
provided that, in the event the Senior Obligations are not paid in cash in full,
such non cash payment (or the proceeds thereof, if the Lenders so elect) shall
be distributed pro rata to the Lenders for application to the Senior
Obligations. With respect to Reimbursement Obligations, "paid in full" shall
mean either that the Letters of Credit have been terminated and any
Reimbursement Obligations have been paid in full in cash, or with respect to any
outstanding Letters of Credit, that such Letters of Credit have been fully cash
collateralized. The foregoing contractual subordination of the Make-Whole
Obligation is solely for the benefit of the holders of the Senior Obligations
and may not be asserted by any other creditor of National whether under the
theory of third-party beneficiary or otherwise.

                  7. National shall update the Lenders, no less frequently than
weekly, concerning the Special Committee's progress with its investigation which
updates shall take the form of oral reports to counsel and, at the request of
the Lenders, to the Lenders. National shall deliver to the Lenders the Special
Committee Report immediately upon its completion.

                  8. National may, in its discretion and during the term of this
Extension, pay up to $141,000 in principal obligations due on one or more of the
Tax Notes. Except for these payments on the Tax Notes (and principal payments to
the Lenders and NBD), National will not, during the term of this Extension, make
principal payments on any other Indebtedness.

                  9. Notwithstanding any prior or future waiver of defaults by
the Lenders, (i) National will promptly pay the monthly statements for the
reasonable fees and expenses incurred on behalf of the Lenders by, and will also
fund retainers (in amounts satisfactory to the Lenders) for, the firms of
Policano & Manzo, L.L.C., O'Melveny & Myers LLP, and Sidley & Austin, and (ii)
during the period between January 20 and March 6, 1998 (but without waiving or
limiting the Lenders' rights to reimbursement of fees and expenses as provided
in the Note Purchase Agreement and Credit Agreement). National will reimburse
each Lender for its reasonable fees and expenses (including reasonable fees and
expenses for outside and in-house counsel) incurred by such Lender in connection
with such Lender's loans to National in accordance with the terms of the Credit
Agreement and the Note Purchase Agreement, as the case may be.

                  10. Except for the provisions of paragraphs 3,4, and 6 above,
(i) the provisions of this Extension apply solely to the specific payments,
waivers and extensions expressly provided for herein, and each of the parties
hereto preserves all other rights and remedies, and (ii) the terms and
provisions of the Credit Agreement, the Letter of Credit applications and
reimbursement agreements executed in connection with the Letters of Credit, the
Note Purchase Agreement and the Notes, together with all instruments and
documents executed in connection with those agreements, shall remain in full
force and effect, and all of the parties' rights and remedies under such
instruments and documents are expressly preserved.
<PAGE>   7



                  11. This Extension shall be binding upon any successors and
assigns of the parties hereto.

                  12. This Extension is a contract made under, and shall be
governed by and construed in accordance with, the law of the State of Illinois
applicable to contracts made and to be performed entirely within such State and
without giving effect to choice of law principles of such State.


NATIONAL AUTO CREDIT, INC.

By:
   -----------------------------------

Its
   -----------------------------------



                                            THE FIRST NATIONAL BANK OF CHICAGO,
                                            as Administrative Agent and as a
                                            Lender

                                            By:
                                               ---------------------------------
                                            Its
                                               ---------------------------------

                                            MORGAN GUARANTY TRUST COMPANY OF
                                            NEW YORK,  as Documentation Agent
                                            and as a Lender

                                            By:
                                               ---------------------------------
                                            Its
                                               ---------------------------------


                                            THE BANK OF NEW YORK

                                            By:
                                               ---------------------------------
                                            Its
                                               ---------------------------------



                                            FIRST UNION NATIONAL BANK
                                            (formerly known as First Union
                                            National Bank of North Carolina)

                                            By:
                                               ---------------------------------
                                            Its
                                               ---------------------------------


                                            THE HUNTINGTON NATIONAL BANK

                                            By:
                                               ---------------------------------
                                            Its
                                               ---------------------------------


<PAGE>   8


                                            ALLSTATE LIFE INSURANCE COMPANY

                                            By:
                                               ---------------------------------
                                            Its
                                               ---------------------------------


                                            CONNECTICUT GENERAL LIFE INSURANCE
                                            COMPANY BY CIGNA INVESTMENTS, INC.

                                            By:
                                               ---------------------------------
                                            Its
                                               ---------------------------------


                                            CONNECTICUT GENERAL LIFE INSURANCE
                                            COMPANY ON BEHALF OF ONE OR MORE
                                            SEPARATE ACCOUNTS BY CIGNA
                                            INVESTMENTS, INC.

                                            By:
                                               ---------------------------------
                                            Its
                                               ---------------------------------


                                            PRINCIPAL MUTUAL LIFE INSURANCE
                                            COMPANY

                                            By:
                                               ---------------------------------
                                            Its
                                               ---------------------------------

                                            By:
                                               ---------------------------------
                                            Its
                                               ---------------------------------


                                            NEW YORK LIFE INSURANCE COMPANY

                                            By:
                                               ---------------------------------
                                            Its
                                               ---------------------------------


                                            NEW YORK LIFE INSURANCE AND ANNUITY
                                            CORPORATION
                                            BY NEW YORK LIFE INSURANCE COMPANY

                                            By:
                                               ---------------------------------
                                            Its
                                               ---------------------------------

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                                            LINCOLN NATIONAL LIFE INSURANCE
                                            COMPANY

                                            By:
                                               ---------------------------------
                                            Its
                                               ---------------------------------


                                            LINCOLN LIFE & ANNUITY COMPANY OF
                                            NEW YORK

                                            By:
                                               ---------------------------------
                                            Its
                                               ---------------------------------


                                            NBD BANK

                                            By:
                                               ---------------------------------
                                            Its
                                               ---------------------------------



                                            NAC, INC.

                                            By:
                                               ---------------------------------
                                            Its
                                               ---------------------------------


                                            NAC INVESTMENT COMPANY

                                            By:
                                               ---------------------------------
                                            Its
                                               ---------------------------------