Mary needs to borrow $$11,000.$ She can borrow the money at $6\%$ simple interest for $6$ yr or she can borrow at $5\%$ with interest compounded continuously for $6$ yr$.$

$($a$)$ How much total interest would Mary pay at $6\%$ simple interest?

$($b$)$ How much total interest would Mary pay at $5\%$ interest compounded continuously?

$($c$)$ Which option results in less total interest?

Part $1$ of $3$