Fifteen years ago a couple purchased a house for $\$130{,}000.00$ by paying a 20% down payment and financing the remaining balance with a 30-year mortgage at $4.74$% compounded monthly.

(a) Find the monthly payment for this loan.

Monthly Payment: (Note: Your answer should include a dollar sign and be accurate to two decimal places)

(b) Find the balance of the loan after $17$ years and after $18$ years?

(Note: The balance amounts should include a dollar sign and be accurate to two decimal places)

(c) Find the total amount of interest paid by the couple during the 18th year.

Interest Paid During 18th year: (Note: Your answer should include a dollar sign and be accurate to two decimal places)