Suppose a credit card was used to make a $$12,720$ purchase at $15\mathrm{.}5\%$ interest with a monthly payment of $$289.$ Complete the following.

$($a$)$ Calculate the time it will take to pay off the debt making only the given payment each month.

$($b$)$ Calculate the total interest paid.

$($c$)$ Find the amount of money saved over the lifetime of the debt if twice the amount of the given monthly payment is paid each month.

$($a$)$ If only the given payment is made each month, it will take payments to pay off the debt.

$($Round up to the nearest integer as needed.$)$