$1)$You are going to put $X into an account each year for $5$ years, beginning in Year $1.$ Then, from Years $9$ through $12,$ you will withdraw $$2,000$ per year. If the account has an annual interest rate of $11\%,$ what is X$?$

$2)$You deposit $$1,200$ in an account each year for $5$ years, starting at the end of Year $1.$ At the end of Year $5,$ you withdraw half of the account balance. You then deposit $$3,300$ each year for five more years $($starting at the end of Year $6).$ At the end of Year $15,$ you withdraw the entire amount. There are no additional payments in Years $11$ through $15.$ The account earns $8\%$ per year.

a$)$How much is withdrawn at the end of Year $5?$

b$)$How much is withdrawn at the end of Year $15?$