you recently accepted a new job after finishing your undergraduate degree. your starting salary is $$65,000$ and you expect to receive $2\mathrm{.}5\%$ raises year on year. Your employer offer $401($K$)$ and matches $50\%$ of your contributions up to $6\%$ of your salary. Assume $7\mathrm{.}00\%$ yearly retunrs and yearly retirement contributions at the beginning of each year.

$($a$)$ If you retire in $40$ years and meet the employer match how much $($$$)$ will you have in your $401$k upon retiring

$($b$)$ Your $401$k has a $6$ year graded vesting schedule. If you leave after $4$ years of working how much $($$$)$ of the total $401$k amount are you vested in$?$

$($c$)$ If you wait $10$ full years to start contributing, how much less will you have in your $401$k upon retiring? Assume no change in retirement age $?$