Final answer:
To determine how long it will take Helen to pay off her credit card debt by making minimum payments, one must account for the 21% annual interest rate and the compounding interest on the remaining balance each month. This makes the actual pay-off time significantly longer than simply dividing the debt by the monthly payment, illustrating how costly and extended the process can be with minimum payments.
Step-by-step explanation:
The question about Helen's credit card debt and how long it will take her to pay off with a minimum payment involves understanding how credit card interest works and the impact of making only minimum payments. Since Helen's credit card has a nominal interest rate of 21 percent and she made a purchase of $250, the amount she will actually end up paying back will be more than $250 if she only makes the minimum payments. The credit card interest will add to the balance each month, and since the minimum payment is usually a mix of principal and interest, it can take a very long time to pay off the entirety of the debt.
A common issue with credit card debt is that the minimum payments can be deceptively low, causing the balance to linger and accrue more interest over time. For instance, if it were a simple debt without monthly interest, paying $20 per month would take Helen 12.5 months to pay off $250. However, with the 21% annual interest rate, and interest compounding monthly, it will take her much longer; calculating the exact time would require a more complex formula that takes into account the diminishing principal and the interest that accrues on the remaining balance each month. In a general scenario mentioned in the provided information, making only minimum payments on a $2,000 debt could take approximately 15 years to pay off and cost more than twice the original amount in interest.