Final answer:
Paying $100 monthly on an $8,000 balance with an 18% APR will not cover the 1.5% monthly interest. The payment is less than the interest accrued each month, which means the balance will never decrease. Therefore, at this rate, the credit card balance will never be paid off.
Step-by-step explanation:
To determine the time it will take to pay off the credit card balance, we need to understand that it involves an amortization situation where both principal and interest are paid together with each installment, and the interest is charged on the remaining balance each month. Using a simplified amortization formula is not practical in this case because the balance changes with each payment due to the credit card APR, so we'll have to use either a financial calculator or an iterative process like a spreadsheet.
However, without performing the detailed calculations here, we can make an educated guess. If you're paying $100 every month on an $8,000 balance with an 18% annual interest rate (which is 1.5% per month), part of each payment is going towards interest rather than paying down the principal. Given that the monthly interest alone would be $120 (1.5% of $8,000), it's clear that paying only $100 per month would not even cover the interest, let alone the principal. Therefore, the debt would continue to grow rather than shrink, indicating that at this rate, it will never be paid off.