Question

HELP

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 $1,230. Her card has an APR of 13.24%, compounded monthly, and has a minimum monthly payment of 3.12% 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.)
Hint:
1st, Use the formula where P = PV *( i / [1 - (1 + i)^-n]) (watch slide 3 in instructional video to see the formula in an example) to calculate her monthly payment for the next 2 years.
2nd, find the minimum monthly credit card payment.
3rd, Find the difference between what you found in the 1st step and 2nd step, and that is how much greater her payment will be than the minimum monthly payment.
a.
$17
b.
$14
c.
$19
d.
$20



Please select the best answer from the choices provided

Answer 1

To solve this problem, we can follow these steps:

Calculate the monthly interest rate by dividing the APR by 12: 13.24% / 12 = 1.1033%.
Use the formula for the present value of an annuity to calculate the monthly payment that Rachel needs to make over a period of 24 months:
PV = 1230
i = 1.1033% / 100 = 0.011033
n = 24

P = PV * (i / (1 - (1 + i)^(-n)))
P = 1230 * (0.011033 / (1 - (1 + 0.011033)^(-24)))
P ≈ $59.96

So, Rachel needs to make monthly payments of approximately $59.96 over the next 24 months to pay off her credit card debt.

Calculate the minimum monthly payment by multiplying the total balance by 3.12%:
Minimum monthly payment = 1230 * 3.12% = $38.38

Find the difference between the monthly payment calculated in step 2 and the minimum monthly payment calculated in step 3:
Difference = $59.96 - $38.38 = $21.58

Rounded to the nearest dollar, the answer is $22. Therefore, the best answer from the choices provided is d. $20.