Alice rented her personal residence for $13$ days to summer vacationers for $$4,500.$ She has AGI of $$105,000$ before the rental income. Related expenses for the year include the following:

Real property taxes $ $4,500$

Utilities $5,000$

Insurance $900$

Mortgage interest $7,000$

Repairs $800$

Depreciation $15,000$

Calculate the effect of the rental on Alice$$s AGI. Explain your rationale, citing tax authority.