STATEMENT BALANCE. Your credit card statement period CLOSES on the $15$ th of every month and a new statement period OPENS on the $16$th$,$ your credit card payments have a DUE DATE on the $1$ st of every month. You have an APR of $28\mathrm{.}99\%.$

$13$a$)$ If you made a purchase for a new phone for $$900$ on October ${16}^{th},$ how many interest free days will you have left?

$13$b$)$ When will you have to pay for the purchase in full in order to avoid finance charges? $($Exact day of the exact month.$)$

$13$c$)$ If you can pay only $$80$ per month, how long would it take for you to pay it off and how much interest would you end up paying for the purchase?