I talked to someone and I SAID TO her " I owe you $1000. I am able to pay $600 this week, and I will pay THE REST/THE BALANCE AT/BY the end of this month."
You might substitute "was talking" for talked, depending on the context.
You could substitute "told" for "said to"
AT= during the last few days of the month
BY= anytime between now and the end of the month