On September $5$th$,$ the billing date, Kim had a balance due of $$625\mathrm{.}30$ on her credit card.$$ The transactions during the following month were: Sept $8$ Payment$$ $$250$ Sept $21$ Charge:$$ Airline Ticket$$ $$320$ Sept $27$ Charge:$$ Hotel Bill$$ $$190$ Oct $2$ Charge:$$ Clothing $$ $$85$ The Average Daily Balance on the Credit Card was stated as $$530\mathrm{.}15$ The APR on the credit card is $18\mathrm{.}4\%$ a$.$ How much interest is due on October $5$th$?($Use $30$ days in the billing cycle since Sept $5-$Oct $5$ is $30$ days.$)$ b$.$ What is the new balance on the account on October $5$th$?$