Im leaving my lease early and have given written 60 day notice. Do i receive my last months rent back?

I have given 60 day notice to terminate my 12 month lease early. My landlord has agreed to this situation. I also paid first and last months rent when i first moved in. My landlord however has informed me that this last months rent is non-refundable after i gave them 60 day notice. Why am i not receiving that 400 dollars back? Should that not be used for the second month of my 60 day notice? Am i not inclined to a month in the house in which i paid for already?