Yes, because your sister is paying less than fair market rent, it is considered "personal days". You so not have to report the income, and you can deduct the interest etc on your Schedule A. Per IRS:
If you use a dwelling unit as a home and you rent it less than 15 days during the year, its primary function isn’t considered to be rental and it shouldn’t be reported on Schedule E (Form 1040). You aren’t required to report the rental income and rental expenses from this activity. Any expenses related to the home, such as mortgage interest, property taxes, and any qualified casualty loss, will be reported as normally allowed on Schedule A (Form 1040).
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