A loan of $5,000 is charged a 12% annual interest rate. An $80 payment is made each month. a. Write a recurrence relation for the loan balance remaining at the beginning of month n. b. Solve the recurrence relation. (See Exercise 27 of Section 2.2 for the formula for the sum of a geometric sequence.) c. How much is left of the loan balance at the beginning of the 19th month?