(70 points) Consider a credit card that starts with a $2000 balance and for which, each...

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(70 points) Consider a credit card that starts with a $2000 balance and for which, each month, $500 in new charges are accrued, and interest is collected on any unpaid balance at a rate of 1.5% per month (19.56% APR). (a) Write a recurrence relation for the balance after k months, bk, when a fixed payment of p dollars is made each month. (b) Solve this recurrence relation for by as a function of p. (c) For what value of p does the monthly balance stay at $2000? (d): Find an expression for the month, k, in which the balance becomes zero as a function of p. ii) How many months does it take to pay off the balance if p = $750? What about p = $1000? How much should be paid each month to have a zero balance after exactly 6 months? After exactly 12 months? Use the bisection code from HW2 to compute the payments. (70 points) Consider a credit card that starts with a $2000 balance and for which, each month, $500 in new charges are accrued, and interest is collected on any unpaid balance at a rate of 1.5% per month (19.56% APR). (a) Write a recurrence relation for the balance after k months, bk, when a fixed payment of p dollars is made each month. (b) Solve this recurrence relation for by as a function of p. (c) For what value of p does the monthly balance stay at $2000? (d): Find an expression for the month, k, in which the balance becomes zero as a function of p. ii) How many months does it take to pay off the balance if p = $750? What about p = $1000? How much should be paid each month to have a zero balance after exactly 6 months? After exactly 12 months? Use the bisection code from HW2 to compute the payments.

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