On October $24,$ you plan to purchase a $$1,800$ computer by using one of your two credit cards. The Silver Card charges $18\%$ interest and calculates interest based on the balance on the first day of the previous month. The Gold Card charges $18\%$ interest and calculates interest based on the average daily balance. Both cards have a $$0$ balance as of October $1.$ The closing date is the end of the month for each card.

Your plan is to make a $$600$ payment in November, make a $$600$ payment in December, and pay off the remaining balance in January. All your payments will be received and posted on the $10$th of each month. No other charges will be made on the account. $($Round your answers to the nearest cent.$)$

$($a$)$

Based on this information, calculate the interest $($in $$)$ charged by each card for this purchase.

Silver Card $ :$?$

Gold Card $:$?$

$($b$)$

Which card is the better deal and by how much $($in $$)?$