The question in the image is asking how long it will take to pay off a credit card balance. Here are the details provided:

• Balance: $6,500
• Annual Percentage Rate (APR): 16.99%
• Monthly payment: $400

The problem asks for the number of months it will take to pay off the debt if you consistently pay $400 each month.

We can approach this problem using a formula that accounts for the balance, APR, monthly payments, and how interest accrues each month. The formula to calculate the number of months $n$ to pay off a debt under a fixed monthly payment and an interest rate is:

$n = \frac{\log\left(\frac{P}{P - r \cdot B}\right)}{\log(1 + r)}$

Where:

• $B$ is the balance (6500),
• $P$ is the monthly payment (400),
• $r$ is the monthly interest rate, calculated as $\frac{\text{APR}}{12 \cdot 100} = \frac{16.99}{12 \cdot 100}$,
• $n$ is the number of months.

I'll now calculate the value of $n$.It will take approximately 19 months to pay off the balance of $6,500 with monthly payments of $400 at an APR of 16.99%.

Would you like more details on the steps or any further questions?

Here are 5 related questions you may find interesting:

1. What happens if you increase your monthly payment?
2. How does changing the APR affect the number of months required?
3. What is the total interest paid over the 19 months?
4. How would a lump sum payment impact the payoff time?
5. What if the minimum payment is less than $400—how long would it take then?

Tip: Paying more than the minimum monthly payment helps reduce the interest paid over time.