On October $22,$ you plan to purchase a $$3,000$ computer by using one of your two credit cards. The Silver Card charges $18\%$ interest and calculates interest based on the balance on the first day of the previous month. The Gold Card charges $18\%$ interest and calculates interest based on the average daily balance. Both cards have a $$0$ balance as of October $1.$ The closing date is the end of the month for each card.

Your plan is to make a $$1,000$ payment in November, make a $$1,000$ 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.

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

b$.$ Which card is the better deal and by how much?