You have a credit card that has a balance of $8980$⁢8980 at an APR of 19.99%19.99%. You plan to pay $500$⁢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, we can use the formula for paying off a loan or credit card with a fixed monthly payment. The formula is:

\[
n = \frac{\log\left(\frac{P}{P - rB}\right)}{\log(1 + r)}
\]

Where:
- $ P $ is the monthly payment amount,
- $ r $ is the monthly interest rate (which is the APR divided by 12),
- $ B $ is the initial balance (credit card debt),
- $ n $ is the number of months to pay off the balance.

### Given values:
- $ B = 8980 $
- APR = 19.99%, so the monthly interest rate $ r = \frac{19.99\%}{12} = \frac{0.1999}{12} $
- $ P = 500 $

Now we can substitute these values into the formula and solve for $ n $. Let's compute it.

I'll calculate this now.It will take approximately 22 months to pay off the credit card balance of $8,980 with a monthly payment of $500, assuming an APR of 19.99%.

Would you like more details on the calculations or have any questions?

Here are five related questions:
1. How does increasing the monthly payment affect the time to pay off the debt?
2. What would the total interest paid over these 22 months be?
3. How does the APR influence the number of months needed to pay off the balance?
4. What happens if you miss a payment for one month?
5. How can paying more than the minimum amount save on interest?

**Tip**: Paying a little extra each month can significantly reduce the total interest paid over time.

You have a credit card that has a balance of $8980 at an APR of 19.99%. 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 credit card balance of $8980 with a monthly payment of $500 at an APR of 19.99%. This problem involves algebraic concepts such as logarithms and finance mathematics. Suitable for high school students in Grades 10-12.

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