Alright you can have immortality BUT!
You have to live in this house forever, and the only time you can leave or be seen is from Oct 1st 12:00am to Oct 31st 11:59pm NOT EXCEPTIONS. The consequences for breaking these rule is death and the end of your immortality.
You will never age outside of that window of time Oct 1st to Oct 31st. Outside of that time you are invisible, the house belongs to a trust you will own so it's yours forever.
Would you take the arrangement?