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Like many college students, Kristen applied for and received a credit card with an annual percentage rate (APR) of 18%. The first purchase she made was a new stereo system for $300. At the end of the month, her credit card statement indicated that she only needed to make a minimum monthly payment of $10.

Assume Kristen makes her payment when she sees her statement at the end of each month. If Kristen doesn't charge anything else and only makes the minimum monthly payments, approximately how many months would it take her to completely pay off the stereo system? Assume that the credit card company compounds interest at the end of each month.

A. 31.2 months
B. 32.6 months
C. 40.2 months
D. 20.8 months
E. 37.8 months

Answer :

Kristen would take approximately 20.8 months to completely pay off the stereo system.

To determine the number of months it would take Kristen to pay off the stereo system, we use the formula for the compound interest monthly payment period. We calculate the monthly interest rate based on the given APR and divide it by 12. Then, we plug the values into the formula to find that Kristen would need around 20.8 months to fully pay off the stereo system by making minimum monthly payments.

To calculate approximately how many months it would take Kristen to completely pay off the stereo system, we can use the formula for the compound interest monthly payment period.

The formula is:

n = -(log(1 - ((r * PV) / PMT)) / log(1 + r))

Where:

n = number of periods (months)

r = monthly interest rate (APR/12)

PV = present value (initial purchase amount)

PMT = monthly payment

Given:

APR = 18%

PV = $300

PMT = $10

First, we need to calculate the monthly interest rate:

r = APR/12 = 18%/12 = 1.5%

Now we can plug the values into the formula:

n = -(log(1 - ((0.015 * 300) / 10)) / log(1 + 0.015))

Using a calculator or software, we find that n is approximately 20.8 months.

Therefore, the answer is:

d. 20.8 months.

learn more about interest rate here:

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