Moving Out: Rent Was Increased but I Have Already Paid "Last Month's Rent"

My question involves landlord-tenant law in the State of: California

I was wondering if you could kindly help me.

I’ve been living in the same apartment in Los Angeles for almost 25 years.

I will be giving notice on September 1st to vacate the apartment since I will be moving to the East Coast.

When I first entered the apartment about 25 years ago, I was required to pay (a) first month’s rent ($1,200) (b) last month’s rent ($1,200), and (c) a security deposit equivalent to one month’s rent ($1,200).

The rent for the apartment in 1993 when I moved into the unit was $1,200.

However, the rent for the unit is now $2,400 per month.

Since I originally paid the last month’s rent ($1,200) back in 1993, can I claim that the landlord has already been paid for the last month and that I owe no money for the last month?

Or would I have to pay the difference in rent from the current rent amount ($2,400) and the amount I originally paid in 1993 ($1,200)?

In other words, would I have to pay $1,200?

Any assistance you could provide would be deeply appreciated.

Thank you very much for your kind attention, time and help!

Moving Out: Rent Was Increased but I Have Already Paid "Last Month's Rent"