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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.

a$.$ Calculate the amount of monthly payment.

b$.$ Calculate the unpaid balance of the loan on December $31,2022,$ just after the $312$th payment. c$.$ How much interest will be paid during January $2023?$

d$.$ How much of the principle will be paid off during the year $2022?$

e$.$ How much interest will be paid during$$the$$year$2022?$