To finance a vacation in $3$years$,$ Elsie saves $$$$480$ at the beginning of every six months in an account paying interest at $10\%$ compounded semi dash annually.

$($a$)$ What will be the balance in her account when she takes the$$ vacation?

$($b$)$ How much of the balance will be$$ interest?

$($c$)$ If she waits an additional year to start her$$ vacation, and continues to save the same amount of$$ money, how much more money does she have to$$ spend?