$5$ We deposit $1,000$ each in two banks: Bank A and Bank B$.$ Accounts in Bank A earn interest compounded continuously with force of interest: $5\%.$ Bank B offers an interest rate of $12\%$ compounded monthly. At the end of $2$ years, which account will have the greater accumulated value?

$($a$)$ Bank A

$($b$)$ Bank B

$6$ A loan of $4,500$ is being repaid by payments of $500$ at the end of each quarter for as long as necessary, plus a final smaller payment one quarter of a year after the last $500$ payment. The nominal rate of interest compounded quarterly is $12\%.$ What is the interest paid in the $6$th payment period? Please enter an amount rounded to the nearest integer.