They want to gift it but have me pay them back over the next few years.
This isn't a gift, then, but there are various ways you could structure it. If you are paying them back, you need a formal document and should decide upon a price. You'll be able to impute mortgage interest and deduct on Schedule A or Schedule E.
If they sell it to you at a below-market price, the transaction will be part sale, part gift. You or they should speak to a CPA and explain the situation and what each of you are trying to accomplish so you'll get appropriate advice and can make the best decision.
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