Problem 5 (32 pts]: An Application of Geometric Sums: Paying off credit card debt. Directions: Credit card debt is a major problem for many people. Interest rates for credit cards are typically very high, which makes paying down large debts quite expensive. This problem explores paying off credit card debt as an application of geometric series. To solidify his status as the Calculus Sugar Daddy, Jim decides to buy a donut with diamonds for sprinkles. The bill comes to $4000, and Jim finances the purchase with a credit card whose annual interest rate is (a fairly typical) 18%. This is compounded monthly, meaning that at the start of every month, 1.5% interest is applied to the remaining balance. The repayment scheme of this purchase for the first two months is listed below. At the start of Month 1, the balance has grown to 4000 x 1.015 = 4060. The day before the end of the month, Jim pays $100 dollars. The balance is now $3960. At the start of Month 2, the previous balance of $3960 grows to 3960 x 1.015 = 4019.40 The day before the end of the month, Jim pays $100 dollars. The balance is now $3919.40. The payment scheme is repeated until the the balance is eliminated. If the balance owed during the last month is less than $100, then Jim will only pay the amount of the balance. F. [8 pts) How much money will Jim have to pay in total to pay off the diamond-encrusted donut if he follows the repayment scheme described at the beginning of the problem? Hint: Go back and read how the repayments work carefully and what the formula derived for An gives. Note that there will only be a partial payment the last month, so Jim will not make a full payment during it