The balance on Ramon Felipe's credit card on January $12,$ his billing date, was $$283\mathrm{.}91.$ For the period ending February $12,$ Ramon had the following transactions to the right.

a$)$ Find the average daily balance for the billing period.

b$)$ Find the finance charge to be paid on February $12.$ Assume an interest rate of $1\mathrm{.}2\%$ per month.

c$)$ Find the balance due on February $12.$

January $14$ Charge: $$46\mathrm{.}68$

January $29$ Payment: $$130\mathrm{.}00$

February $5$ Charge: $$44\mathrm{.}84$

February $7$ Charge: $$167\mathrm{.}59$