Michael has credit card debt of $60 000 that has an 18% 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 10% 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)72 months
B)84 months
C)98 months
D)78 months

Question

Quizplus · Accepted Answer

Using the formula for monthly compound interest, Michael's initial credit card debt will have monthly interest of:
(18%/12) = 1.5%
His monthly interest payment will be:
$60 000 x 1.5% = $900
This means that his monthly payment towards paying down the principal is:
$0 (since the minimum payment only covers interest)
If he rolls over his debt to the card with an APR of 10%, his monthly interest will be:
(10%/12) = 0.833%
Given that his monthly payment will remain the same, we can calculate how long it will take to pay off his debt using the following formula:
n = -log(1 - rP/A) / log(1+r)
Where:
r = monthly interest rate (0.00833)
A = amount of debt ($60 000)
P = monthly payment ($900)
n = number of periods (in months)
Using this formula, we get:
n = -log(1 - 0.00833(60 000)/900) / log(1+0.00833) = 97.99
Since we can't have a fraction of a month, we round up to get our final answer:
n = 98 months.

Michael Has Credit Card Debt of $60 000 That Has