Can we claim a tax credit, or deduction for the expenses incurred in providing this free housing?
No. Everything here is based on "intent". So far, I don't see any intent to make money. What you're giving here is not only free, it's classified as a gift. You "could" be required to file a gift tax return too.
Now when it comes to gifts, you can give an individual up to a maximum of $15,000 in a tax year without having to report your gift given to the IRS. Understand the reporting requirement is on the giver, not the recipient. The recipient doesn't have to report anything on any tax return to any taxing authority at any level of government. The reporting requirement is on the giver only.
Basically, for your situation if "we" is a married couple filing a joint return, each of you can give any one individual a gift up to a maximum of $15,000 from each of you individually, and there is no tax reporting requirement. So for you and your spouse that's a total of $30,000.
Gifts don't have to be in cash either, to be reportable. They just have to have monetary value. What you're giving this student has monetary value. But I seriously doubt it's more than $30,000 a year. Let's get off this gift stuff now and move on.
Basically, what you have is a 2nd home. It's not rental property because at $10/mo it's quite obvious (to a rock) that you have no intent to make money here. Therefore you have to treat it like a 2nd home. That means your only allowed deductions are for Mortgage Interest and Property Taxes. That's it. Since those are claimed on SCH A that means the SALT limits apply too. (SALT - State & Local Taxes). Basically under SALT you can deduct a maximum of $10,000 of the state and local taxes you pay - which includes any kind of tax such as property taxes. That's it.
Now if you want to declare it a rental property that you're renting for $10 a month, you can certainly do that. However, because you are renting at below FMRV (Fair Market Rental Value) that means you're losses on the property are limited to your rental income and you can "NOT" carry over your losses to the next year. You just lose them permanently and forever.
Additionally, since you are required to depreciate rental property this will hurt you big, big time when you sell the property. That's because all depreciation taken on the property is recaptured and taxed in the year you sell that property. Without the carry over losses to offset the taxability of recaptured depreciation, not only will you pay taxes on every single penny of recaptured depreciation, the recapture of that deprecation adds to your AGI and has the high potential of putting you in a higher tax bracket. I doubt thats a "gift" you're willing to give anyone.
For the student, what you provide them free of charge is considered 3rd party support for the student too. You can not take any type of any kind of deduction for that either, since the student does not, can not, and will not qualify as your dependent.
Bottom line is, you need to rent this property at FMRV or consider it a 2nd home and not even bother charging the student anything. One or the other.
