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Melanie applied for a credit card with an annual percentage rate (APR) of 18% and purchased a stereo system for $350. Her credit card statement requires a minimum monthly payment of $10.

1. If Melanie only makes the minimum monthly payments and charges nothing else, approximately how many months will it take her to completely pay off the stereo system? Assume the credit card company compounds interest at the end of each month.

A. 32.6 months
B. 19.3 months
C. 50.0 months
D. 29.3 months
E. 20.8 months

2. Melanie decides to pay $20 per month instead. How much quicker will she pay off the stereo system?

A. 17.9 months
B. 13.9 months
C. 10.3 months
D. 11.6 months
E. 29.5 months

3. If Melanie wants to pay off the stereo system by the end of the year, what minimum monthly payment must she make?

A. $23.56
B. $23.21
C. $23.92
D. $36.10
E. $32.09

Answer :

a. If Melanie makes only the minimum monthly payments, it would take around 32.6 months to pay off the stereo system. Option A.

b. By paying twice the minimum monthly payment, she can pay it off in approximately 17.9 months. Option A.

c. To have it paid off within a year, Melanie needs to make a minimum monthly payment of approximately $32.09. Option D.

Part 1:

Melanie will take approximately 32.6 months to completely pay off the stereo system if she only makes the minimum monthly payments of $10. This calculation takes into account the compound interest charged at the end of each month. The answer is option A.

Part 2:

If Melanie decides to pay twice the minimum monthly payment, which is $20 per month, she will pay off the stereo system approximately 17.9 months quicker than if she only made the minimum payments. The answer is option A.

Part 3:

To have the stereo system paid off by the end of the year, Melanie needs to determine the minimum monthly payment required. By rearranging the formula and solving for the minimum monthly payment, Melanie must make a payment of approximately $32.09 per month. The answer is option D.

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