Tenant to pay off in a furnishing apartment so rent can reduce

[Peace Lily]

Dear BP members,

The tenant rented my room with furnishing $850 (I bought the brand new basic furniture for her before she moved in). If the room was not furnishing, it would have been $800.  Originally her contract is only for 4 months.  One month after she moved in, she would like to extend the lease for another 5 months and she would like the rent to be at $800.  She asked me to give her the total price of the furniture  I bought so she will pay me off in one check payment. From then on, the rent will drop to $800.

Question: Does that mean the furniture will become hers OR she is just paying off the rent that would have been the furnishing cost, meaning that I still have the possess of the furniture?  What is the standard?

Thank you very much,

Ling