A credit card bill for $$500$ was issued on November $14$th$.$ During the next billing cycle, a

purchase of $$50$ was made on November $19$th$,$ a payment of $$100$ was made on November

$25$th$,$ and another payment of $$150$ was made on November $30$th$.$

a$)$ Calculate the average daily balance for the bill issued on December $14$th$.$

b$)$ Using your answer from part a$,$ calculate the finance charge on the bill issued on

December $14$th$.$ Assume that the annual interest rate is $8\%.$