You have maxed out your credit card and owe $$5,100.$ Its interest rate is $21\%.$ Each month, you make the minimum required payment of $$31.($Round your answers to the nearest cent.$)$

$($a$)$ During the September $20$ through October $19$ billing period, you pay the minimum required payment on October $1.$ Find the average daily balance, the finance charge, and the new balance.

average daily balance $

finance charge $

new balance $

$($b$)$ During the October $20$ through November $19$ billing period, you pay the minimum required payment on November $11.$ Find the average daily balance, the finance charge, and the new balance.

average daily balance $

finance charge $

new balance $

$($c$)$ During the November $20$ through December $19$ billing period, you pay the minimum required payment on November $30.$ Find the average daily balance, the finance charge, and the new balance.

average daily balance $

finance charge $

new balance $