Apollo Investment Management, L.P. 9 West 57th St. 43rd Floor New York, NY 10019 May 15, 2006

Exhibit 10.29

Apollo Investment Management, L.P.

9 West 57th St. 43rd Floor

New York, NY 10019

May 15, 2006

Personal and Confidential

James C. Zelter

[Address on File with Company]

Dear James:

We are pleased to offer you the opportunity to join Apollo Investment Management, L.P. (“Apollo”) as lead partner with senior management responsibility for capital markets investment advisory activities for the management companies of Apollo Distressed Investment Fund, L.P. (“DIF”), Apollo Investment Corporation (“AIC”), Apollo Strategic Value Fund, L.P. (“SVF”), the proposed European mezzanine investment fund (“EMP”), the first fund we form to invest primarily in public securities of companies in China, Hong Kong, and/or Japan (“ACM”), the first fund we form to invest primarily in public securities of infrastructure companies (“INF”), and the first fund we form to invest primarily in public securities of real estate-related companies (“REF”). You shall also have senior management responsibility for other future funds as determined by you and the general partner. As lead partner, the investment professionals of such funds will report to you.

We are excited to have you join our team. Apollo will use its reasonable best efforts to cause you to become a member of the Board of Directors of AIC. You will also serve as chief executive officer of EMF and as a member of its board.

Key terms of your offer are as follows:

The above points represent your proportionate share of the management fee income net of allocated expenses (including bonuses of investment professionals who do not share in net management fee income) and net incentive compensation available for distribution to Apollo partners (which is the income that is available to Apollo partners from such funds excluding their returns on capital invested in such funds) based on amounts earned by the applicable investment manager under the management agreement or the general partner under the partnership agreement for such fund.

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You will also receive 20 out of 2,000 points in Apollo Advisors VI, L.P. (“Advisors VI”), which serves as the general partner to, and earns the carried interest in Apollo Investment Fund VI, L.P. (“Fund VI”). A copy of the partnership agreement of Advisors VI has been provided to you.

In addition, you will receive $10,000,000 in the form of a profits interest in Fund VI (which interest represents a profits interest derived from the Apollo management waiver program and is generally payable out of the first realized investment gains of Fund VI), to be funded as capital is drawn in Fund VI. Although no assurance can be given as to the value of such profits interest, if Fund VI performs in a manner consistent with prior Apollo funds, such interest would be worth in excess of $15,000,000 over time.

All distributions will be payable in the same manner as such distributions are generally made to partners of Apollo, and you shall be subject to the same vesting provisions and other terms (e.g., regarding confidentiality, nonsolicitation and noncompetition) as are generally applicable to other partners of Apollo. Your interests in the entities described above shall he granted as of your start date, pursuant to definitive documentation in the form generally applicable to other partners of the respective entities.

Your start date will be a date to be mutually agreed by the parties, but not later than 60 days after the date hereof. You represent to Apollo that other than the 60-day notice/garden leave provisions with Citigroup, there are no obligations or restrictions that would keep you from joining Apollo and performing the services contemplated thereby or would restrict Apollo from publicly disclosing, after the date hereof, that you are a partner at the firm. However, solely for purposes of your compensation, you will be treated as if your start date had been January 1, 2006. In addition, to the extent that all cash payments to you from all Apollo-related entities relating to the year ending December 31, 2006 (including any such payments customarily made on or before April 15, 2007) are less than $10,000,000 in the aggregate, you will receive an additional amount as necessary for you to receive total cash payments for such year of $10,000,000.

A portion of your cash compensation will be deferred pursuant to a deferred compensation plan to be established by Apollo for deferral of compensation in funds for which you have senior management responsibility. Any amounts deferred under the plan will be subject to three year vesting in equal annual installments, which vesting shall be contingent on your continued service through each vesting date. The amounts deferred shall be as follows:

Notwithstanding the foregoing, no such amount shall be deferred to the extent such deferral would cause your total cash payments received for 2006 to be less than $10,000,000.

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The effectiveness of these terms is subject to your execution and return of this letter on or before May 16, 2006 and is subject to customary background and reference checks. This letter supersedes any other arrangements or understandings with respect to the subject matter hereof.