Luke deposited $$4000$ into a savings account that earns $3\mathrm{.}00\%$ annually but is compounded $12$ times per year. He plans to leave the funds in the accounts for $3\mathrm{.}50$ years.

However, at the end of $1\mathrm{.}50$ years, Luke has to withdraw $$900.$ What amount will be in the account at the end of the original $3\mathrm{.}50$ years