On December $31,1996,$ a house was purchased with the buyer taking out a $30-$year, $$112475$ mortgage at $9\%$ interest compound monthly. The mortgage payment is made at the end of each month.

$1-$Calculate the amount of monthly payment.

$2-$Calculate the unpaid balance of the loan on December $31,2022,$ just after the $312$th payment.

$3-$How much interest will be paid during January $2023?$

$4-$How much of the principle will be paid off during the year $2022?$

$5-$How much interest will be paid during the year $2022?$