First, it is important to note that when you are carrying a balance from one month to the next, you lose your grace period; that is, you are paying interest on your new purchases beginning on the day of the purchase. You stated that interest charges have been accruing from the date of purchase, so I'm assuming that you were already carrying a balance/paying interest charges before this purchase happened. Keep in mind that you will continue to be operating without a grace period until the entire balance is completely paid down to $0.
Now, to your question: Credit card interest is generally compounded daily. So if you want to compute this accurately, you need to figure out how many days you are being charged interest. The formula for compound interest is:
where P is the principal ($1097.46), r is the daily interest rate as a decimal (0.0005456), and n is the number of days you are charging interest.
From November 5 to January 13 (the date of her first payment), there are 69 days. Plugging those numbers into the above formula, your roommate's accumulated interest on January 13 before she made her payment was $42.09, and her balance was up to $1139.55. She then paid you $100, making her new balance $1039.55.
The next time she makes a payment, you can calculate her balance again. For example, let's say that she pays you $100 again on February 13, 31 days from her last payment. Plugging those numbers into the formula (P=1039.55, n=31), her balance before the payment is $1057.28, and after her $100 payment it is $957.28.
If she continues making monthly $100 payments on the 13th of every month, I estimate that she will have her balance paid in full on January 13, 2018. Her last payment will only need to be about $52, and she will have paid a total of $1252 by that time, which includes about $154 in total interest.