WARRANT

THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED,
QUALIFIED, APPROVED OR DISAPPROVED UNDER THE SECURITIES ACT OF 1933, AS AMENDED,
OR THE SECURITIES LAWS OF ANY STATE AND MAY NOT BE SOLD OR OTHERWISE DISPOSED OF
EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER SUCH ACT AND
APPLICABLE STATE SECURITIES LAWS OR PURSUANT TO AN APPLICABLE EXEMPTION FROM THE
REGISTRATION REQUIREMENTS OF SUCH ACT OR SUCH LAWS. NEITHER THE UNITED STATES
SECURITIES AND EXCHANGE COMMISSION NOR ANY OTHER FEDERAL OR STATE REGULATORY
AUTHORITY HAS PASSED ON OR ENDORSED THE MERITS OF THESE SECURITIES.


                                                      WARRANT NO. 5


                                    WARRANT

                      TO PURCHASE SHARES OF COMMON STOCK,

                           PAR VALUE $.01 PER SHARE,

                                      OF

                      NATIONAL AUTO FINANCE COMPANY, INC.



            THIS IS TO CERTIFY THAT THE STRUCTURED FINANCE HIGH YIELD FUND, LLC
or its registered assigns (the "PURCHASER"), is the owner of Five Hundred
Ninety-Three Thousand Six Hundred Seventy-One (593,671) Warrants (the
"WARRANTS"), each of which entitles the registered holder thereof to purchase
from NATIONAL AUTO FINANCE COMPANY, INC., a Delaware corporation (the
"COMPANY"), one fully paid, duly authorized and nonassessable share of Common
Stock, par value $.01 per share, of the Company (the "COMMON STOCK"), at any
time or from time to time on or before 5:00 p.m., New York City time, on March
27, 2008 (subject to earlier expiration in certain events), at an exercise price
of $.01 per share (the "EXERCISE PRICE"), all on the terms and subject to the
conditions hereinafter set forth.



DAFS03...:\97\64897\0015\1306\WAR3138U.36B
<PAGE>
            The number of shares of Capital Stock issuable upon exercise of each
such Warrant (the "NUMBER ISSUABLE"), which is initially one (1) share of Common
Stock, is subject to adjustment from time to time pursuant to the provisions of
Section 2 of this Warrant certificate.

            Capitalized terms used herein but not otherwise defined shall have
the meanings given them in Section 11 hereof or, if not therein defined, in the
Purchase Agreement.

            1. Exercise of Warrant. Subject to the last paragraph of this
Section 1, the Warrants evidenced hereby may be exercised, in whole or in part,
by the registered holder hereof at any time or from time to time on or before
5:00 p.m., New York City time, on March 27, 2008, but in any event no later than
the date of the consummation of a Sale Transaction, upon delivery to the Company
at the principal executive office of the Company in the United States of
America, of (a) this Warrant certificate, (b) a written notice stating that such
holder elects to exercise all or any portion of the Warrants evidenced hereby in
accordance with the provisions of this Section 1 and specifying the name or
names in which such holder wishes the certificate or certificates for shares of
Common Stock to be issued in connection with such exercise and (c) payment of
the Exercise Price for the shares of Common Stock issuable upon exercise of such
Warrants, which shall be payable, subject to the immediately following
paragraph, (i) in cash, (ii) by a certified or official bank check payable to
the order of the Company or (iii) by the surrender (which surrender shall be
evidenced by cancellation of the number of Warrants represented by any Warrant
certificate presented in connection with a Cashless Exercise (as defined below))
of a Warrant or Warrants (represented by one or more relevant Warrant
certificates), and without the payment of the Exercise Price in cash, in return
for the delivery to the surrendering holder of such number of shares of Common
Stock equal to the product of (x) the number of shares of Common Stock for which
such Warrant is exercisable as of the date of exercise (if the Exercise Price
were being paid in cash) multiplied by (y) the Cashless Exercise Ratio. An
exercise of a Warrant in accordance with clause (iii) is herein called a
"CASHLESS EXERCISE." The "CASHLESS EXERCISE RATIO" shall equal a fraction, the
numerator of which is the excess of the Current Market Price per share of Common
Stock on the date of exercise over the Exercise Price per share as of the date
of exercise and the denominator of which is the Current Market Price per share
of the Common Stock on the date of exercise. Upon surrender of a Warrant
certificate representing more than one Warrant in connection with a Cashless
Exercise, the number of shares of Common Stock deliverable upon a Cashless
Exercise shall be equal to the number of Warrants that the holder specifies is
to be exercised pursuant to a Cashless Exercise multiplied by the Cashless
Exercise Ratio, (collectively, the "WARRANT EXERCISE DOCUMENTATION").



                                     2
<PAGE>
      If any holder at the time of the exercise of any Warrants is not a
"qualified institutional buyer" within the meaning of Rule 144A under the
Securities Act or an "accredited investor" within the meaning of Rule 501 under
the Securities Act such holder of the Warrants will be required to effect the
exercise of the Warrants solely pursuant to the Cashless Exercise Option.

            As promptly as practicable, and in any event within five Business
Days after receipt of the Warrant Exercise Documentation, the Company shall
deliver or cause to be delivered (a) certificates representing the number of
validly issued, fully paid and nonassessable shares of Common Stock specified in
the Warrant Exercise Documentation, (b) if applicable, cash in lieu of any
fraction of a share, as hereinafter provided, and (c) if less than the full
number of Warrants evidenced hereby are being exercised, a new Warrant
certificate or certificates, of like tenor, for the number of Warrants evidenced
by this Warrant certificate, less the number of Warrants then being exercised.
Such exercise shall be deemed to have been made at the close of business on the
date of delivery of the Warrant Exercise Documentation so that the Person
entitled to receive shares of Common Stock upon such exercise shall be treated
for all purposes as having become the record holder of such shares of Common
Stock at such time. No such surrender shall be effective to constitute the
person entitled to receive such shares as the record holder thereof while the
transfer books of the Company for the Common Stock are closed for any purpose
(but not for any period in excess of five days); but any such surrender of this
Warrant certificate for exercise during any period while such books are so
closed shall become effective for exercise immediately upon the reopening of
such books, as if the exercise had been made on the date this Warrant
certificate was surrendered and for the Number Issuable of Common Stock
specified in the Warrant Exercise Documentation and at the Exercise Price.

            The Company shall pay all expenses in connection with, and all taxes
and other governmental charges (other than income taxes of the holder) that may
be imposed in respect of, the issue or delivery of any shares of Common Stock
issuable upon the exercise of the Warrants evidenced hereby. The Company shall
not be required, however, to pay any tax or other charge imposed in connection
with any transfer involved in the issue of any certificate for shares of Common
Stock in any name other than that of the registered holder of the Warrants
evidenced hereby.

            In connection with the exercise of any Warrants evidenced hereby, no
fractions of shares of Common Stock shall be issued, but in lieu thereof the
Company shall pay a cash adjustment in respect of such fractional interest in an
amount equal to such fractional interest multiplied by the Current Market Price
per share of Common Stock on the Business Day which next precedes the day of
exercise. If more than one such Warrant shall be exercised by the holder thereof
at the same time, the number of full shares of Common Stock issuable



                                     3
<PAGE>
on such exercise shall be computed on the basis of the total number of Warrants
so exercised.

            2.  ADJUSTMENTS.

            (A) ADJUSTMENT OF NUMBER ISSUABLE. The Number Issuable shall be
subject to adjustment from time to time as follows:

                  (i) In case the Company shall at any time or from time to time
      after the Issue Date:

                        (A) pay a dividend or make a distribution on the
            outstanding shares of Common Stock in Capital Stock of the Company;

                        (B) subdivide the outstanding shares of Common Stock
            into a larger number of shares;

                        (C) combine the outstanding shares of Common Stock into
            a smaller number of shares; or

                        (D) issue any shares of its Capital Stock in a
            reclassification of the Common Stock;

      then, and in each such case, the Number Issuable in effect immediately
      prior to such event shall be adjusted (and any other appropriate actions
      shall be taken by the Company) so that the holder of any Warrant evidenced
      hereby thereafter exercised shall be entitled to receive the number of
      shares of Capital Stock of the Company which such holder would have owned
      or had been entitled to receive upon or by reason of any of the events
      described above, had such Warrant been exercised immediately prior to the
      happening of such event. An adjustment made pursuant to this clause (i)
      shall become effective retroactively (x) in the case of any such dividend
      or distribution, to a date immediately following the close of business on
      the record date for the determination of holders of shares of Common Stock
      entitled to receive such dividend or distribution, or (y) in the case of
      any such subdivision, combination or reclassification, to the close of
      business on the date upon which such corporate action becomes effective.

                  (ii) If after the Issue Date, the Company shall at any time or
      from time to time issue or sell (x) shares of Common Stock or (y)
      securities convertible into or



                                     4
<PAGE>
      exchangeable for shares of Common Stock, or any options, warrants or other
      rights to acquire shares of Common Stock (other than (a) shares of Common
      Stock issued upon exercise of the Warrants or the December Warrants and
      shares issued as a result of adjustments made under the other provisions
      of this Section 2, (b) shares of Common Stock issued pursuant to an
      underwritten Public Offering where such shares of Common Stock are listed
      on the New York Stock Exchange, Inc. or quoted or listed on any other
      national securities exchange or the National Market System of the Nasdaq
      Stock Market or (c) equity securities convertible into or exchangeable for
      shares of Common Stock, or any options, warrants or other rights to
      acquire shares of Common Stock if issued in connection with an issuance of
      debt securities as a unit (collectively, a "UNIT ISSUANCE"), but only to
      the extent (A) the Company retains a nationally recognized investment
      bank, which the Company and the holders of a majority of the outstanding
      Warrants mutually approve, to underwrite or privately place such Unit
      Issuance, or (B) if the Company and the holders of a majority of the
      outstanding Warrants do not agree on an investment bank under clause (A)
      hereof, the Company retains a nationally recognized investment bank to
      underwrite or privately place such Unit Issuance, in which case the
      holders of a majority of the outstanding Warrants may opt to retain (at
      the Company's expense) a nationally recognized investment bank that
      delivers to the holders of the outstanding Warrants, if such option is
      exercised, an opinion that the Unit Issuance is fair, from a financial
      point of view, to the stockholders of the Company) at a price per share
      that is less than the Current Market Price per share of Common Stock then
      in effect as of the record date or issue date, as the case may be,
      referred to in the following sentence (the "RELEVANT DATE") (treating the
      price per share of Common Stock, in the case of the issuance of any
      security convertible or exchangeable or exercisable into Common Stock as
      equal to (x) the sum of the price for such security convertible,
      exchangeable or exercisable into Common Stock plus any additional
      consideration payable (without regard to any anti-dilution adjustments)
      upon the conversion, exchange or exercise of such security into Common
      Stock divided by (y) the number of shares of Common Stock initially
      underlying such convertible, exchangeable or exercisable security), in
      each case, other than issuances or sales for which an adjustment is made
      pursuant to another paragraph of this Section 2, then, and in each such
      case, the Number Issuable then in effect shall be adjusted by multiplying
      the Number Issuable in effect on the day immediately prior to the Relevant
      Date by a fraction, (1) the numerator of which shall be the sum of the
      number of shares of Common Stock, on a fully diluted basis, outstanding on
      the Relevant Date, plus the number of additional shares of Common Stock
      issued or to be issued (or the maximum number into which such convertible
      or exchangeable securities initially may convert or exchange or for which
      such options, warrants or other rights initially may be exercised), and
      (2) the denominator of which shall be the



                                     5
<PAGE>
      sum of the number of shares of Common Stock, on a fully diluted basis,
      outstanding on the Relevant Date, plus the number of shares of Common
      Stock which the aggregate consideration for the total number of such
      additional shares of Common Stock so issued (or into which such
      convertible or exchangeable securities may convert or exchange or for
      which such options, warrants or other rights may be exercised plus the
      aggregate amount of any additional consideration initially payable upon
      conversion, exchange or exercise of such security) would purchase at the
      Current Market Price per share of Common Stock on the Relevant Date. Such
      adjustment shall be made whenever such shares, securities, options,
      warrants or other rights are issued, and shall become effective
      retroactively to a date immediately following the close of business (x) in
      the case of an issuance to the stockholders of the Company, as such, on
      the record date for the determination of stockholders entitled to receive
      such shares, securities, options, warrants or other rights and (y) in all
      other cases, on the date (the "ISSUE DATE") of such issuance; provided,
      that if any convertible or exchangeable securities, options, warrants, or
      other rights (or any portions thereof) which shall have given rise to an
      adjustment pursuant to this Section 2(a)(ii) shall have expired or
      terminated without the exercise thereof, then the Number Issuable
      hereunder shall be readjusted (but to no greater extent than originally
      adjusted) on the basis of eliminating from the computation any additional
      shares of Common Stock corresponding to such convertible or exchangeable
      securities, options, warrants or other rights as shall have expired or
      terminated. Solely for purposes of this clause (ii), (I) Common Stock
      shall include the Common Stock, par value $.01 per share, of the Company
      and each other class of capital stock of the Company that does not have a
      preference over any other class of capital stock of the Company as to
      dividends or upon liquidation, dissolution or winding up of the Company
      and, in each case, shall include any other class of capital stock of the
      Company into which such stock is reclassified or reconstituted and (II) if
      the provisions of any securities convertible into or exchangeable for
      shares of Common Stock or options, warrants or other rights to acquire
      shares of Common Stock are amended after the date of issuance so as to
      reduce the applicable conversion price, exchange price or exercise price
      such amendment shall be deemed to be a new issuance of such securities.

                  (iii) In case the Company shall at any time or from time to
      time after the Issue Date distribute to any holder of shares of its Common
      Stock (including any such distribution made in connection with a
      consolidation or merger in which the Company is the resulting or surviving
      corporation and the Common Stock is not changed or exchanged) cash,
      evidences of indebtedness of the Company or another issuer, securities of
      the Company or another issuer or other assets (excluding dividends or
      other distributions of shares of Common Stock or other Capital Stock for



                                     6
<PAGE>
      which adjustment is made under Section 2(a)(i) or dividends or other
      distributions received by or set aside for the benefit of the holders of
      Common Stock pursuant to Section 2(c) below) or rights or warrants to
      subscribe for or purchase securities of the Company (excluding those in
      respect of which adjustments in the Number Issuable is made pursuant to
      Section 2(a)(i) or Section 2(a)(ii)), then, and in each such case, the
      Number Issuable then in effect shall be adjusted by multiplying the Number
      Issuable in effect immediately prior to the date of such distribution by a
      fraction (x) the numerator of which shall be the Current Market Price per
      share of Common Stock on the record date referred to below and (y) the
      denominator of which shall be such Current Market Price per share of
      Common Stock less the then Fair Market Value (as determined in good faith
      by the Board of Directors of the Company, a certified resolution with
      respect to which shall be mailed to the holder of the Warrants evidenced
      hereby) of the portion of the cash, evidences of indebtedness, securities
      or other assets so distributed or of such subscription rights or warrants
      applicable to one share of Common Stock (but such denominator shall in no
      event be zero). Such adjustment shall be made whenever any such
      distribution is made and shall become effective retroactively to a date
      immediately following the close of business on the record date for the
      determination of stockholders entitled to receive such distribution.

                  (iv) In case the Company at any time or from time to time
      shall take any action which could have a dilutive effect (it being
      understood that this Section 2(a)(iv) shall not apply to percentage
      dilution) on the number of shares of Common Stock that may be issued upon
      exercise of the Warrants, other than an action described in any of Section
      2(a)(i) through 2(a)(iii), inclusive, or Section 2(b), then, the Number
      Issuable shall be adjusted in such manner and at such time as the Board of
      Directors of the Company reasonably determines to be equitable under the
      circumstances (such determination to be evidenced in a resolution, a
      certified copy of which shall be mailed to the holder of the Warrants
      evidenced hereby).

                  (v) Notwithstanding anything herein to the contrary, no
      adjustment under this Section 2(a) need be made to the Number Issuable
      unless such adjustment would require an increase or decrease of at least
      1% of the Number Issuable then in effect. Notwithstanding the foregoing,
      any lesser adjustment shall be carried forward and shall be made at the
      time of and together with the next subsequent adjustment, which, together
      with any adjustment or adjustments so carried forward, shall amount to an
      increase or decrease of at least 1% of such Number Issuable. Any
      adjustment to the Number Issuable carried forward and not theretofore made
      shall be made immediately prior to the exercise of any Warrants pursuant
      hereto.




                                     7
<PAGE>
                  (vi) The Company promptly shall deliver to each registered
      holder of Warrants at least 20 days prior to effecting any transaction
      which would result in an increase or decrease in the Number Issuable
      pursuant to this Section 2 a notice thereof, together with a certificate,
      signed by the Chief Executive Officer, the Chairman or the Vice Chairman
      and by the Chief Financial Officer, Treasurer or an Assistant Treasurer or
      the Secretary or an Assistant Secretary of the Company, setting forth in
      reasonable detail the event requiring the adjustment and the method by
      which such adjustment was, or will be, calculated and specifying the
      increased or decreased Number Issuable then in effect following such
      adjustment.

                  (vii) Notwithstanding anything contrary contained in this
      Section 2(a), the Company shall be entitled to make such upward
      adjustments in the Number Issuable, in addition to those otherwise
      required by this Section 2(a), as the Board of Directors of the Company in
      their discretion shall determine to be advisable in order that any stock
      dividend, subdivision or combination of shares, distribution of rights or
      warrants to purchase stock or securities, or distribution of securities
      convertible into or exchangeable for Common Stock, hereafter made by the
      Company to its shareholders shall not be taxable; provided, however, that
      any such adjustment shall be made, as nearly as practicable, in a manner
      which treats all holders of Warrants with similar protections on an equal
      basis.

            (B) REORGANIZATION. In case of any capital reorganization or other
change of outstanding shares of Common Stock (other than a change in par value,
or from par value to no par value, or from no par value to par value, or as a
result of a subdivision or combination) (any of the foregoing, a "TRANSACTION"),
the Company, or any successor, as the case may be, shall execute and deliver to
each holder of the Warrants evidenced hereby, at least 20 days prior to
effecting any of the foregoing Transactions, a certificate that the holder of
each such Warrant then outstanding shall have the right thereafter to exercise
such Warrant into the kind and amount of shares of stock or other securities (of
the Company or another issuer) or property or cash receivable upon such
Transaction by a holder of the number of shares of Common Stock into which such
Warrant could have been exercised immediately prior to such Transaction. Such
certificate shall provide for adjustments which shall be as nearly equivalent as
may be practicable to the adjustments provided for in this Section 2 and shall
contain other terms identical to the terms hereof. If, in the case of any such
Transaction, the stock, other securities, cash or property receivable thereupon
by a holder of Common Stock includes shares of stock or other securities of a
Person other than (i) the successor and (ii) other than the Company, which
controls or is controlled by the successor or which, in connection with such
Transaction, issues stock, securities, other property or cash to holders of
Common Stock, then such certificate also shall be executed by



                                     8
<PAGE>
such Person, and such Person shall, in such certificate, specifically assume the
obligations of such successor or purchasing Person and acknowledge its
obligations to issue such stock, securities, other property or cash to holders
of the Warrants upon exercise thereof as provided above. The provisions of this
Section 2(b) similarly shall apply to successive Transactions.

            (C) SPECIAL DISTRIBUTIONS. If the holder so elects (in lieu of an
adjustment to the Number Issuable pursuant to Section 2(a)(i) or 2(a)(iii)) by
sending a Special Notice to the Company, in the event that the Company shall
declare a dividend or make any other distribution (including, without
limitation, in cash, in capital stock (which shall include, without limitation,
any options, warrants or other rights to acquire capital stock) of the Company,
whether or not pursuant to a shareholder rights plan, "poison pill" or similar
arrangement) in other property or assets, to holders of Common Stock (a "SPECIAL
DISTRIBUTION"), then the Board of Directors shall set aside the amount of such
dividend or distribution that any holder of Warrants would have been entitled to
receive had it exercised such Warrants prior to the record date for such
dividend or distribution. Upon the exercise of a Warrant evidenced hereby, the
holder shall be entitled to receive, such dividend or distribution that such
holder would have received had such Warrant been exercised immediately prior to
the record date for such dividend or distribution. Prior to any Special
Distribution described in this section 2(c), the Company shall as provided in
Section 3 hereof notify each holder (not less than 20 days prior to the
occurrence of each Special Distribution) of its intent to make such Special
Distribution and the holder, if it elects to have such distribution set aside
the amount thereof rather than have an adjustment to the Number Issuable as
provided in Sections 2(a)(i) or 2(a)(iii), shall notify the Company by sending a
Special Notice three Business Days prior to the date of any such Special
Distribution.

            3. NOTICE OF CERTAIN EVENTS. In case at any time or from time to
time, the Company shall declare any dividend or any other distribution to the
holders of its Common Stock, or shall authorize the granting to the holders of
its Common Stock of rights or warrants to subscribe for or purchase any
additional shares of stock of any class or any other right, or shall authorize
the issuance or sale of any other shares or rights which would result in an
adjustment to the Number Issuable pursuant to Section 2(a)(i) or (ii) or would
result in a Special Distribution pursuant to Section 2(c) hereof, or there shall
be any capital reorganization or reclassification of the Common Stock of the
Company or consolidation or merger of the Company with or into another Person,
or any sale or other disposition of all or substantially all the assets of the
Company, or any Transaction, or there shall be a voluntary or involuntary
dissolution, liquidation or winding up of the Company, then, in any one or more
of such cases the Company shall mail to each holder of the Warrants evidenced
hereby at such holder's address as it appears on the transfer books of the
Company, as promptly as



                                     9
<PAGE>
practicable but in any event at least 20 days prior to the applicable date
hereinafter specified, a notice stating (a) the date on which a record is to be
taken for the purpose of such dividend, distribution, rights, warrants or
Transaction or, if a record is not to be taken, the date as of which the holders
of Common Stock of record to be entitled to such dividend, distribution, rights
or warrants, or to participate in such Transaction, are to be determined, (b)
the issue date (as defined in Section 2(a)(ii) hereof) or (c) the date on which
such reclassification, consolidation, merger, sale, conveyance, dissolution,
liquidation winding up or Transaction is expected to become effective. Such
notice also shall specify the date as of which it is expected that the holders
of Common Stock of record shall be entitled to exchange their Common Stock for
shares of stock or other securities or property or cash deliverable upon such
reorganization, reclassification, consolidation, merger, sale, conveyance,
dissolution, liquidation or winding up.

            4. CERTAIN COVENANTS. The Company covenants and agrees that all
shares of capital stock of the Company which may be issued against payment
therefor upon the exercise of the Warrants evidenced hereby will be duly
authorized, validly issued and fully paid and nonassessable. The Company shall
at all times reserve and keep available for issuance upon the exercise of the
Warrants, such number of its authorized but unissued shares of Common Stock as
will from time to time be sufficient to permit the exercise of all outstanding
Warrants, and shall take all action required to increase the authorized number
of shares of Common Stock if at any time there shall be insufficient authorized
but unissued shares of Common Stock to permit such reservation or to permit the
exercise of all outstanding Warrants. The Company shall prepare and file, and
cooperate with the holder of the Warrants so that it may prepare and file, in
each case within five Business Days of a request by such holder, notification
and report forms in compliance with the HSR Act, and shall otherwise fully
comply with the requirements of the HSR Act, to the extent required in
connection with the exercise of the Warrants. The Company shall bear all of its
own expenses and all of its own out-of-pocket expenses (including reasonable
attorneys' fees, charges and expenses) and filing fees of The Structured Finance
High Yield Fund, LLC (including any Permitted Transferee thereof)] in connection
with any such preparation and filing.

            5. REGISTERED HOLDER. The person in whose name this Warrant
certificate is registered on the books and records of the Company shall be
deemed the owner hereof and of the Warrants evidenced hereby for all purposes.
The registered holder of this Warrant certificate, in its capacity as such,
shall not be entitled to any rights whatsoever as a stockholder of the Company,
except as herein provided.




                                     10
<PAGE>
            6. TRANSFER OF WARRANTS. Any transfer of the rights represented by
this Warrant certificate shall be subject to the limitations provided herein,
and shall be effected by the surrender of this Warrant certificate, along with
the form of assignment attached hereto, properly completed and executed by the
registered holder hereof, at the principal executive office of the Company in
the United States of America, together with an appropriate opinion letter, if
deemed reasonably necessary by counsel to the Company to assure compliance with
applicable securities laws. Thereupon, the Company shall issue in the name or
names specified by the registered holder hereof and, in the event of a partial
transfer, in the name of the registered holder hereof, a new Warrant certificate
or certificates evidencing the right to purchase such number of shares of Common
Stock as shall be equal to the number of shares of Common Stock then purchasable
hereunder.

            Notwithstanding anything to the contrary contained herein, if any
holder of the Warrants desires to sell or otherwise transfer all or any portion
of his Warrants (other than to a Permitted Transferee), such holder shall first
send written notice (the "OFFERING NOTICE") to the Company which shall state (i)
the number of Warrants proposed to be sold or otherwise transferred (the
"OFFERED WARRANTS"), (ii) the proposed purchase price per Warrant which such
holder is willing to accept and (iii) the material terms and conditions of the
proposed sale or transfer. For a period of five Business Days after delivery of
the Offering Notice (the "NOTICE PERIOD"), the Company shall have the right (but
not the obligation) to purchase all but not less than all of the Offered
Warrants at a purchase price equal to the purchase price provided in the
Offering Notice and upon the terms and conditions set forth in the Offering
Notice. Upon delivery of the Offering Notice, such offer shall be irrevocable
unless and until the rights of first offer of the Company provided for herein
shall have been waived or shall have expired. Failure of the Company to respond
within Notice Period shall be deemed a rejection of such offer. If the Company
elects to accept such offer, the Offered Warrants shall be sold or transferred
to the Company in accordance with the terms and conditions provided in the
Offering Notice on the date that is three Business Days following the Company's
acceptance of such offer.

            7. DENOMINATIONS. The Company covenants that it will, at its
expense, promptly upon surrender of this Warrant certificate at the principal
executive office of the Company in the United States of America, execute and
deliver to the registered holder hereof a new Warrant certificate or
certificates in such denominations specified by such holder for an aggregate
number of Warrants equal to the number of Warrants evidenced by this Warrant
certificate provided, however, that the Company shall not be required to issue
any Warrants for fractional shares of Common Stock.




                                     11
<PAGE>
            8. REPLACEMENT OF WARRANTS. Upon receipt of evidence satisfactory to
the Company of the loss, theft, destruction or mutilation of this Warrant
certificate and, in the case of loss, theft or destruction, upon delivery of an
indemnity reasonably satisfactory to the Company (in the case of an insurance
company or other institutional investor, its own unsecured indemnity agreement
shall be deemed to be reasonably satisfactory), or, in the case of mutilation,
upon surrender and cancellation thereof, the Company will issue a new Warrant
certificate of like tenor for a number of Warrants equal to the number of
Warrants evidenced by this Warrant certificate.

            9. GOVERNING LAW. THIS WARRANT CERTIFICATE SHALL BE CONSTRUED AND
ENFORCED IN ACCORDANCE WITH, AND THE RIGHTS OF THE PARTIES SHALL BE GOVERNED BY,
THE LAWS OF THE STATE OF NEW YORK, WITHOUT REGARD TO PRINCIPLES OF CONFLICTS OF
LAW.

            10. RIGHTS INURE TO REGISTERED HOLDER. The Warrants evidenced by
this Warrant certificate will inure to the benefit of and be binding upon the
registered holder hereof and the Company and their respective successors and
permitted assigns. Nothing in this Warrant certificate shall be construed to
give to any Person other than the Company and the registered holder hereof any
legal or equitable right, remedy or claim under this Warrant certificate, and
this Warrant certificate shall be for the sole and exclusive benefit of the
Company and such registered holder.

            11.  DEFINITIONS.  For the purposes of this Warrant certificate, 
the following terms shall have the meanings indicated below:

            "BUSINESS DAY" shall mean any day other than a Saturday, Sunday or
other day on which commercial banks in the City of New York, are authorized or
required by law or executive order to close.

            "CURRENT MARKET PRICE" per share shall mean, on any date specified
herein for the determination thereof, (a) the average daily Market Price of the
Common Stock for those days during the period of 15 days, ending on such date,
on which the national securities exchange or market system on which the Common
Stock is primarily traded was open for trading, and (b) if the Common Stock is
not then listed or quoted on any exchange or market system, the Market Price on
such date.

            "EXERCISE PRICE" shall have the meaning given it in the first
paragraph of this Warrant certificate.




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<PAGE>
            "FAIR MARKET VALUE" shall mean the amount which a willing buyer,
under no compulsion to buy, would pay a willing seller, under no compulsion to
sell, in an arm's-length transaction.

            "HSR ACT" shall mean the Hart-Scott-Rodino Anti-Trust Improvements
Act of 1976, as amended and the rules and regulations of the Federal Trade
Commission promulgated thereunder.

            "ISSUE DATE" shall mean March 27, 1998.

            "MARKET PRICE" shall mean, per share of Common Stock, on any date
specified herein: (a) if the Common Stock is then listed or admitted to trading
on any national securities exchange, the closing price of the Common Stock on
such date; (b) if the Common Stock is not then listed or admitted to trading on
any national securities exchange but is designated as a national market system
security, the last sale price of the Common Stock on such date; or (c) if there
shall have been no trading of the Common Stock on such date or if the Common
Stock is not so designated, the average of the reported closing bid and asked
price of the Common Stock, on such date as shown by Nasdaq and reported by any
member firm of the NYSE selected by the Company; or (d) if neither (a), (b) nor
(c) is applicable, the Fair Market Value per share determined in good faith by
the Board of Directors of the Company which shall be deemed to be Fair Market
Value unless holders of at least 33% of Common Stock issued or issuable upon
exercise of the Warrants request that the Company obtain an opinion of a
nationally recognized investment banking firm chosen by the Company (who shall
bear the expense) and reasonably acceptable to such requesting holders of the
Warrants, in which event the Fair Market Value shall be as determined by such
investment banking firm.

            "NASDAQ" shall mean the National Market System of the Nasdaq Stock
Market.

            "NOTES" shall mean the Senior Subordinated Promissory Notes issued
by the Company pursuant to the Purchase Agreement.

            "NUMBER ISSUABLE" shall have the meaning given it in the second
paragraph of this Warrant certificate.

            "NYSE" shall mean the New York Stock Exchange, Inc.




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<PAGE>
            "PERMITTED TRANSFEREE" means any Person who is an "affiliate" as
defined in Rule 12b-2 of the General Rules and Regulations under the Securities
Exchange Act of 1934, as amended.

            "PERSON" shall mean any individual, corporation, limited liability
company, partnership, trust, incorporated or unincorporated association, joint
venture, joint stock company, government (or an agency or political subdivision
thereof) or other entity of any kind.

            "PURCHASE AGREEMENT" shall mean that certain Securities Purchase
Agreement, dated as of March 27, 1998, by and among the Company and The
Structured Finance High Yield Fund, LLC, as the same may be amended,
supplemented or modified from time to time in accordance with its terms.

            "SALE TRANSACTION" means the merger or consolidation with or into
another Person by the Company (other than a merger or consolidation in which the
Company is the surviving or resulting person) or the completion of a tender
offer and/or acquisition for any and all shares of Common Stock of the Company;
provided that, when entering into such transaction, the Company shall comply
with Section 9.14 of the Purchase Agreement.

            "SPECIAL NOTICE" shall mean the notice sent by a holder to the
Company indicating its preference to have any special distribution set aside for
its benefit upon exercise of the Warrant.

            "WARRANT EXERCISE DOCUMENTATION" shall have the meaning given it in
Section 1 hereof.

            12. NOTICES. All notices, demands and other communications provided
for or permitted hereunder shall be made in writing and shall be by registered
or certified first-class mail, return receipt requested, courier services or
personal delivery, (a) if to the holder of a Warrant, at such holder's last
known address appearing on the books of the Company; and (b) if to the Company,
at its principal executive office in the United States located at the address
designated for notices in the Purchase Agreement, or such other address as shall
have been furnished to the party given or making such notice, demand or other
communication. All such notices and communications shall be deemed to have been
duly



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<PAGE>
given: when delivered by hand, if personally delivered; when delivered to a
courier if delivered by commercial overnight courier service; and five Business
Days after being deposited in the mail, postage prepaid, if mailed.

            IN WITNESS WHEREOF, the Company has caused this Warrant certificate
to be duly executed as of the Issue Date.

                        NATIONAL AUTO FINANCE COMPANY, INC.



                        By:_______________________________________
                             Name:
                             Title:



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<PAGE>
                          FORM OF ASSIGNMENT FORM

             (To be executed upon assignment of the Warrants)

            The undersigned hereby assigns and transfers this Warrant
certificate to ____________________ whose Social Security Number or Tax ID
Number is
_________________ and whose record address is
_____________________________________, and irrevocably appoints ________________
as agent to transfer this security on the books of the Company. Such agent may
substitute another to act for such agent.

                                    Signature:



                                    ------------------------------------


                                    Signature Guarantee:



                                    ------------------------------------



Date: ___________________________




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