Muriel has a line of credit with a limit of $$10000.$ She owed $$8195$ on July $1.$ Principal withdrawals for the period July $1$ to November $30$ were $$3000$ on August $20$ and $$600$ on October $25.$ The line of credit agreement requires regular payments of $$300$ on the $15$th day of each month. Muriel has made all required payments. Interest $($including overdraft interest$)$ is charged to the account on the last day of each month. The interest rate was $8\%$ on July $1,$ but was changed to $7\mathrm{.}5\%$ effective September $15.$ Overdraft interest is $16\%$ for any balance in excess of $$10000.$

a$.$ Calculate the interest charges on July $31,$ August $31,$ September $30,$ October $31,$ and November $30.$

b$.$ Calculate the account balance on November $30.$