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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.)

Respuesta :

nobillionaireNobley
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

Answer:

c.

$19

Step-by-step explanation:

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