Withdrawals increasing at a constant rate of $3\mathrm{.}1\%$ are made semi$-$annually for seven years from an account earning $7\%$ compounded semi$-$annually.$($a$)$ What must be the balance in the account to permit the withdrawals if the first withdrawal is $$1200?($b$)$ What is the size of the last withdrawal?$($c$)$ What is the total amount withdrawn?$($d$)$ How much interest is included in the withdrawals?