Annuity is a sequence of equal periodic payments .One type of annuity is a large amount of money deposited into a bank account and then a fixed amount is withdrawn each month

Suppose you deposit $1000 into the account paying 3.6% compounded monthly ,and then withdraw $600 at the end of each month . the monthly interest rate will be .036/12 or .003, and the balance in the account at the end of each month will be computed as:

[balance at the end of the month] = (1.003) * [balance at end of previous month] - 600 

After how many months will the account contain less than $600, and what will be the amount at that time?