Rachel has developed a plan to start paying off her credit card debt, and has stopped making purchases with her credit card. She
has a credit card balance of $1,120.87. Her card has an APR of 14.12%, compounded monthly, and has a minimum monthly payment of 3.15% of the total balance, which is calculated after the monthly interest. Rachel has decided to pay off her debt by making identical monthly payments over a period of two years. If she starts this month, how much greater will her first payment be than the minimum payment required? (Round final answer to the nearest dollar.)
Present value of annuity PV = P(1 - (1 + r/t)^-nt) / (r/t) where: p is the monthly payment, r is the APR = 14.12% = 0.1412, t is the number of payments in one year = 12, n is the number of years = 2. 1,120.87 = P(1 - (1 + 0.1412/12)^(-2 x 12)) / (0.1412 / 12) 0.1412(1120.87) = 12P(1 - (1 + 0.1412/12)^-24) P = 0.1412(1120.87) / 12(1 - (1 + 0.1412/12)^-24) = $53.88
Minimum monthly payment = 3.15% of 1120.87(1 + 0.1412/12) = 0.0315 x 1120.87(1 + 0.1412/12) = $35.72
Therefore, his first payment will be greater than the minimum payment by 53.88 - 35.72 = $18.16
