EXHIBIT B

                                 FORM OF 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. [_]


                                     WARRANT

                       TO PURCHASE SHARES OF COMMON STOCK,

                            PAR VALUE $.01 PER SHARE,

                                       OF

                       NATIONAL AUTO FINANCE COMPANY, INC.



                  THIS IS TO CERTIFY THAT [THE 1818 MEZZANINE FUND, L.P.] [PC
INVESTMENT COMPANY] [GERLACH & CO., AS NOMINEE FOR MANUFACTURERS LIFE INSURANCE
COMPANY (U.S.A.)] or its registered assigns (the "PURCHASER"), is the owner of
______________________ ([______]) 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 December [__], 2007 (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.

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                  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.

                    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 December [__], 2007, 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 this Warrant certificate, 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 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").

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         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 on such exercise shall be computed on the basis of the total
number of Warrants so exercised.

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<PAGE>


                    ADJUSTMENTS.

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

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

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

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

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

                                            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.

                             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 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 outstanding on the Issue Date 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

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<PAGE>

         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 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

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<PAGE>

         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.

                             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 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

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<PAGE>

         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.

                             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).

                             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.

                             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

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         be, calculated and specifying the increased or decreased Number
         Issuable then in effect following such adjustment.

                             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.

                           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 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.

                           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

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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.

                    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 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

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securities or property or cash deliverable upon such reorganization,
reclassification, consolidation, merger, sale, conveyance, dissolution,
liquidation or winding up.

                    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 1818 Mezzanine
Fund, L.P.] [PC Investment Company (including any Permitted Transferee thereof)]
[Manufacturers Life Insurance Company (U.S.A.) (including any Permitted
Transferee thereof)] (but not any transferee thereof) in connection with any
such preparation and filing.

                    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.

                    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.

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                  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.

                    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.

                    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.

                    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.

                    RIGHTS INURE TO REGISTERED HOLDER.  The Warrants evidenced 
by this Warrant certificate will inure to the benefit of and be binding upon the
registered

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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.

                    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.

                  "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 December [__], 1997.

                  "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

                                       12
<PAGE>

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.

                  "PERMITTED TRANSFEREE" means (i) 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[, and (ii) with respect to The
1818 Mezzanine Fund, L.P., (x) the general partners and limited partners thereof
(each a "PARTNER"), (y) any "affiliate" (as defined in the preceding clause (i))
of a Partner if such Partner is not an individual, and (z) if a Partner is an
individual, a member of such Partner's immediate family, which shall include his
parents, spouse, siblings, children or grand-

children ("FAMILY MEMBERS"), or a trust, corporation or partnership, all of the
beneficial interests in which shall be held by such Partner or one or more
Family Members of such Partner or which would otherwise be an "affiliate" (as
defined in the preceding clause (i)) of such individual; provided, however, that
during the period any such trust, corporation, or partnership holds any right,
title or interest in any Warrants, no Person other than such Partner or one or
more Family Members of such Partner may be or become beneficiaries, stockholders
or limited or general partners thereof].1

                  "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.

--------
1 This language shall be inserted on the Warrant issued to The 1818 Mezzanine
Fund, L.P.

                                       13
<PAGE>

                  "PURCHASE AGREEMENT" shall mean that certain Securities
Purchase Agreement, dated as of December [__], 1997, by and among the Company,
The 1818 Mezzanine Fund, L.P., PC Investment Company, The Progressive Investment
Company, Inc. and Manufacturers Life Insurance Company (U.S.A.), 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.

                    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 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:

                                       14
<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: ___________________________