On May $1,$ the balance on your credit card is $$655\mathrm{.}12.$ On May $3,$ you make a purchase for $$122\mathrm{.}55.$ On May $13,$ you make a payment of $$335.$ On May $15,$ you make a purchase for $$42\mathrm{.}47,$ and on May $25,$ you make a purchase for $$68\mathrm{.}77.$

Assume the billing date is the $1$st of the month and the monthly finance charge is $2\mathrm{.}1\%.$

What is the average daily balance? $

What is the monthly finance charge? $

What is the balance at the start of the next month? $