To borrow $100$ million VND within $70$ days, a business contacts $2$ banks. Bank $1$ proposed an interest rate of $9\%,$ but required that the interest be paid at the time of loan disbursement. Bank $2$ accepts interest paid after $70$ days but requires an interest rate of $9\mathrm{.}05\%.$ a$)$ Which bank will be selected? b$)$ Bank $1,$ because it does not want to lose customers, will have to adjust its interest rate based on bank $2\text{'}$s interest rate, while still requiring customers to pay interest in advance. What interest rate will bank $1$ notify customers?