A worker deposits $$850$ at the end of each month for $3$ years in an investment account with a guaranteed interest rate of $4\mathrm{.}84\%$ compounded monthly.

$($a$)$ Find the value in the account at the end of the $3$ years.

$($b$)$ A rival financial planner offers the worker an investment strategy of depositing $$750$ a month for $3$ years with a guaranteed interest rate of $6\mathrm{.}77\%$ compounded monthly. What is the value of this investment strategy at the end of $3$ years?

$($c$)$ How much more money is gained by investing in the better strategy described in part $($a$)$ or in part $($b$)?$