Michael has a credit card debt of $75,000 that has a 12% APR, compounded monthly. The minimum monthly payment only requires him to pay the interest on his debt. He receives an offer for a credit card with an APR of 4% compounded monthly. If he rolls over his debt onto this card and makes the same monthly payment as before, how long will it take him to pay off his credit card debt?
A)112 months
B)113 months
C)120 months
D)122 months

Question

Quizplus · Accepted Answer

Using the formula for monthly payment to pay off a debt with interest compounded monthly, we can find that Michael's minimum monthly payment is $900.

To calculate the number of months it will take Michael to pay off his debt on the new credit card with the lower APR, we can use the formula for the amount of time it takes to pay off a debt with fixed payments:

n = -log(1 - (r * P) / A) / log(1 + r)

Where:
- n is the number of months
- r is the monthly interest rate
- P is the fixed monthly payment
- A is the initial debt

Plugging in the numbers, we get:

n = -log(1 - (0.04/12) * 900 / 75000) / log(1 + 0.04/12)
n = 122

Therefore, it will take Michael 122 months to pay off his credit card debt with the new credit card.

Michael Has a Credit Card Debt of $75,000 That Has