Since the birth of his granddaughter, $17$ years ago, Derek has deposited $$200$ at the beginning of every month into a Registered Education Savings Plan $($RESP$).$ The interest rate on the plan was $4\mathrm{.}50\%$ compounded monthly for the first $11$ years and $5\mathrm{.}00\%$ compounded monthly for the next $6$ years.

a$.$ What was the accumulated value of the RESP at the end of $11$ years?