A group has purchased a new home for $$400,000.$ The group has secured a loan from a bank for the full amount at an interest rate of $6\%$ compounded annually for $30$ years. Determine the monthly payment and develop the payment plan showing the principal and interest paid in each month.

This same group sets a goal to pay $$1,000$ annually on the principal in addition to the normal monthly payment. Assess how this impacts the length of the loan and the amount of total interest paid.