2 Page 7717 3 points Suppose that someone always carries an

2. (Page 77/17) (3 points) Suppose that someone always carries an unpaid balance on a certain credit card. Each month the credit card company charges 1% interest on unpaid balance, and the person pays off 10% of that previous balance. Also during each month another s200 is charged on the credit card. (a) create a model to represent the monthly unpaid balance Un (b) What level will the unpaid balance gradually approach?

Solution

(a). If the unppaid balance at the end of the nth month is denoted by U_n, then Un = U_n-1-0.1U_n-1+0.01U_n-1

      +200 or, U_n = 0.91U_n-1+200.

(b) In view of part(a) above, U_n+1 = 0.91U_n+200 = 0.91U_n-1+200 +200 = 0.91U_n-1+ 2*200. = 0.91Un-2 +3*200 and so on. Thus, as n, the monthly unpaid balance U_n will aslso approach .