You have a credit card that has a balance of $8,500 at an APR of 17.99%. You plan to  pay $500 each month in an effort to clear the debt quickly. How many months will it take  you to pay off the balance?

To determine how many months it will take to pay off the credit card balance of $8,500 with an APR of 17.99% while making monthly payments of $500, we need to use a formula that takes into account both the interest and the payment schedule.

The monthly interest rate is calculated as:
\[
\text{Monthly Interest Rate} = \frac{\text{APR}}{12}
\]
\[
\text{Monthly Interest Rate} = \frac{17.99\%}{12} = 0.0149925
\]

Now, we use the following formula to estimate the number of months ($n$) it will take to pay off the debt:
\[
n = \frac{-\ln(1 - \frac{P}{rB})}{\ln(1 + r)}
\]
Where:
- $r$ is the monthly interest rate (0.0149925),
- $P$ is the monthly payment ($500),
- $B$ is the current balance ($8,500).

Let me calculate this for you.It seems there's an issue with the formula because the monthly payment of $500 may be too small compared to the balance and interest rate, causing the calculation to produce a math error. This could mean that the monthly payment isn't enough to cover the interest, which would result in an ever-growing balance.

Let's first check if the payment is sufficient to cover the monthly interest on the balance. The interest for the first month would be:
\[
\text{Interest} = \text{Balance} \times \text{Monthly Interest Rate}
\]
If the monthly payment is less than or equal to the interest, the debt cannot be paid off with this amount.

Let me check that first.The first month's interest is approximately $127.43, which is less than the $500 monthly payment. This means your payment does cover the interest, so the balance will indeed decrease each month.

Let me adjust the calculation and try again. I'll calculate the number of months it will take to pay off the balance using an iterative method to ensure precision.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can calculate the number of months manually by using either an online calculator or repeating the steps monthly by considering the interest and subtracting the payment. If you need any further clarification on this process, feel free to ask.

Here are five related questions you might find useful:
1. What happens if you increase your monthly payment by $100?
2. How much total interest would you pay over the lifetime of this debt?
3. How does the APR affect the time it takes to pay off a credit card balance?
4. How would a lower APR impact your monthly payments?
5. What is the best strategy for paying off credit card debt faster?

**Tip**: Paying more than the minimum amount can significantly reduce the time it takes to pay off your debt, saving you money on interest in the long run.

You have a credit card that has a balance of $8,500 at an APR of 17.99%. You plan to pay $500 each month in an effort to clear the debt quickly. How many months will it take you to pay off the balance?

Learn how to calculate the time to pay off a $8,500 credit card balance with an APR of 17.99% and monthly payments of $500. This problem covers key concepts such as interest calculation and amortization using logarithmic functions. Suitable for Grades 10-12 and college students.

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