A woman deposits $$$$10$ comma $000$ at the end of each year for $11$ years in an account paying $8\%$ interest compounded annually.

$($a$)$ Find the final amount she will have on deposit.

$($b$)$ Her$$ brother$-$in$-$law works in a bank that pays $7\%$ compounded annually. If she deposits money in this bank instead of the other$$ one, how much will she have in her$$ account?

$($c$)$ How much would she lose over $11$ years by using her$$ brother$-$in$-$law's bank?