To solve this, we can use the formula for the amortization of a loan or credit card balance, which is based on the balance, interest rate, and monthly payment. The formula for the number of months $N$ it will take to pay off the balance is:

$N = \frac{\log\left(\frac{P}{P - rB}\right)}{\log(1 + r)}$

Where:

• $P$ is the monthly payment ($400 in this case)
• $B$ is the initial balance ($5810)
• $r$ is the monthly interest rate (APR / 12)
• $N$ is the number of months to pay off the balance

Step 1: Convert the APR to a monthly rate.

The APR is 17.99%, so the monthly rate is:

$r = \frac{17.99\%}{12} = \frac{0.1799}{12} = 0.01499167$

Step 2: Substitute the values into the formula.

We have:

• $P = 400$
• $B = 5810$
• $r = 0.01499167$

$N = \frac{\log\left(\frac{400}{400 - 0.01499167 \times 5810}\right)}{\log(1 + 0.01499167)}$

Step 3: Simplify and calculate.

First, calculate the term inside the logarithm:

$0.01499167 \times 5810 = 87.138$ $400 - 87.138 = 312.862$ $\frac{400}{312.862} = 1.279$

Now, calculate the logarithms:

$\log(1.279) = 0.1063$ $\log(1 + 0.01499167) = \log(1.01499167) = 0.006507$

Now, plug these values into the formula:

$N = \frac{0.1063}{0.006507} \approx 16.34$

So, it will take you approximately 17 months (since we round up) to pay off the balance if you make monthly payments of $400.

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Would you like more details on how the formula works or any other information on this topic?

Here are 5 related questions:

1. How can I calculate the total interest paid over the life of the loan?
2. How does changing the monthly payment affect the time to pay off the balance?
3. How do credit card companies calculate interest on the outstanding balance?
4. What happens if I increase my monthly payment to $500?
5. How do I reduce my credit card debt faster through refinancing?

Tip: If you're trying to pay off debt faster, it's important to make extra payments when possible. Even small extra payments each month can significantly reduce the time it takes to clear the debt.