Yes, a portion of the payments are deductible. First, you have the expense of the aircraft itself. Since you obtained a loan to purchase the aircraft, the aircraft was considered paid for at that point. Thus, you are in the process of depreciating the aircraft (taking the value over time). But the depreciation is separate from the payments themselves.
However, since the aircraft is considered "paid for", what you can still deduct on the payments is the portion of interest that you are paying. Since the aircraft is considered paid for, you do not get a deduction for the portion of the payment that is for principal of the loan. This you are already claiming through depreciation.
Of course, there are other expenses: fuel, repairs, storage, taxes, insurance, licensing, and so forth that are also associated with your aircraft. But, yes, if the aircraft are 100% business use, you will be able to claim all of these deductions.
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