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5 August, 08:17

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.)

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  1. 5 August, 08:23
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    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
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