Final answer:
To find out how much greater Rachel's first payment will be than the minimum payment required, we first need to calculate the minimum monthly payment, which is 3.15% of the credit card balance. Then, we can use the annuity payment formula to calculate the first payment over a period of two years. Subtract the minimum payment from the first payment to find out the difference. Round the final answer to the nearest dollar.
Step-by-step explanation:
To find out how much greater Rachel's first payment will be than the minimum payment required, we first need to calculate the minimum monthly payment. The minimum payment is 3.15% of the total balance after the monthly interest is added. So, the minimum payment is 3.15% of $1,120.87. To calculate the first payment, we need to find out how much Rachel will pay each month for two years. We can use the annuity payment formula to calculate it. The annuity payment formula is P = (r * PV) / (1 - (1 + r)^(-n)), where P is the payment, r is the monthly interest rate, PV is the present value (credit card balance), and n is the number of periods. In this case, r is (14.12% / 100) / 12, PV is $1,120.87, and n is 2 * 12 = 24. Plugging in these values, we can calculate the first payment. After calculating both the minimum payment and the first payment, subtract the minimum payment from the first payment to find out how much greater the first payment is than the minimum payment required. Round the final answer to the nearest dollar.
Let's calculate the minimum payment:
Minimum Payment = 3.15% * $1,120.87
= 0.0315 * $1,120.87
Now, let's calculate the first payment:
r = (14.12% / 100) / 12
= 0.1412 / 12
n = 2 * 12
= 24
First Payment = (r * PV) / (1 - (1 + r)^(-n))
= (0.1412 / 12) * $1,120.87 / (1 - (1 + 0.1412 / 12)^(-24))
Finally, subtract the minimum payment from the first payment to find out the difference:
Difference = First Payment - Minimum Payment