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.)

F = P (1 + r/n)^nt

Where:

F = Future value = ?
P = Principal value = 1120.87
r = annual interest = 0.1412
n = interest period = 12 months
t = duration in years

Substituting the given values:

F = 1120.87 (1 + 0.1412/12)^12(2)
F = 1484.17

To get the monthly payments needed, we are to solve for the annuity:

F = A * [((1 + r)^n - 1))/ r]
1484.17 = A * [((1 + 0.1412/12)^(12*2) - 1)/ (0.1412/12)]

A = 53.87

Minimum monthly payment = F * 0.0315 = 46.75

Difference between identical monthly payments and minimum monthly payment = 53.87 - 46.75 = 7.12 = 7

Therefore, her first payment will be $7 greater than the minimum payment required.

There are numerous information's of immense importance already given in the question. Based on those information's the answer can be easily found.
Let us assume the future value = X
Principal Amount = 1120.87 dollars
Period of interest = 12 months
Rate of annual interest = 14.12%
Let us assume the duration in years = t
Then
X = P [1 + (r/n)]^nt
   = 1120.87 [ 1 + (0.1412/12)]^(12 * 2)
   = 1484.17 dollars
Now let us concentrate on finding the monthly payments.
X = A * [((1 + r)^n - 1))/ r]
1484.17 = A [ ((1 + 0.1412/12)^(12 * 2) - 1)/(0.1412/12]
A = 53.87 dollars
Now 
The minimum monthly payment = F * 0.0315
                                                    = 46.75 dollars
So, let us calculate the difference between the minimum monthly payment and equal monthly payments = 53.87 - 46.75 dollars
                                               = 7.12 dollars
So her fist payment will be greater by $7.