You have taken a car loan out at the bank of $12,000. The interest rate per month charged by the bank is 3%. Each month, the bank adds the monthly interest to the balance of the loan before you make a payment of $255.61 to pay off the loan. 

а. Answer the questions below. a. Write a recursive formula as a function of the previous month that calculates the balance owed after the payment is made. 

b. Use the recursive formula to develop the explicit formula for the unpaid balance (after the $255.61 payment is made), P_n, as a function of n, where n=1 is the balance after the first month and n=0 is the amount of the loan? 

c. Use either formula in part a orb to find how long it would take to pay off the loan (rounded to the nearest month).