$5.$ You've hit the jackpot, and your winnings will be distributed in equal quarterly installments, meaning you'll receive one payment every $3$ months. Your intention is to deposit this money into a savings account with a $15\%$ Annual Percentage Rate $($APR$),$ compounded monthly. What is the effective quarterly interest rate for the account? $($Provide your answer in percentage format, rounded to $2$ decimal places.$)$

$6.$If each payment amounts to $$2,000$ and you decide to deposit all your winnings into the account, what will be the balance after $6$ years $(24$ payments$)?$