On February $4,$ the billing date, Carol Ann Bluesky had a balance due of $$124\mathrm{.}57$ on her credit card. Her bank charges an interest rate

of $1\mathrm{.}25\%$ per month and uses the average daily balance method. She made the transactions described in the table during the month.

a$)$ Find Carol Ann's average daily balance for the billing period from February $4$ to March $4.$ Assume it is not a leap year.

b$)$ Find the finance charge to be paid on March $4.$

c$)$ Find the balance due on March $4.$

d$)$ Compare the result obtained to those obtained using the previous balance method.

a$)$ The average daily balance for the billing period was $

$($Round to the nearest cent as needed.$)$