You used your credit card to spend $6,200 to buy home theater equipment. The interest rate that your credit card company charges is 14.9 percent, compounded monthly. Calculate how long it will take you to pay off this balance on your credit card assuming that you do not charge anything else and make $120 payments every month?

Multiple Choice

7.23 years

6.40 years

7.31 years

6.93 years

5.87 years

To solve this problem, we can use the formula for calculating the time required to pay off a loan or balance with compound interest and regular payments. The formula is:

\[
n = \frac{\log \left( \frac{P}{P - A \cdot \frac{r}{12}} \right)}{\log \left( 1 + \frac{r}{12} \right)}
\]

Where:
- $ n $ is the number of months (time in months).
- $ P $ is the principal amount (the initial balance) = $6,200.
- $ r $ is the annual interest rate = 14.9% or 0.149.
- $ A $ is the monthly payment = $120.
- The interest is compounded monthly, so we divide the annual rate by 12.

Now, let’s plug the values into this equation to find how long it will take to pay off the balance.

### Step-by-step:

1. $ P = 6,200 $
2. $ A = 120 $
3. $ r = 0.149 $

We can now calculate this.It seems like there was an error in the calculation. Let me recheck the process and correct it.It seems like I can’t do more advanced data analysis right now. Please try again later.

Feel free to ask if you'd like me to explain the calculation steps manually or help with anything else!

Here are five related questions to expand on this:

1. How does compounding interest affect the total amount paid over time?
2. What is the difference between simple interest and compound interest?
3. How can you lower the time needed to pay off credit

You used your credit card to spend $6,200 to buy home theater equipment. The interest rate that your credit card company charges is 14.9 percent, compounded monthly. Calculate how long it will take you to pay off this balance on your credit card assuming that you do not charge anything else and make $120 payments every month?

Calculate how long it will take to pay off a $6,200 credit card balance with a 14.9% annual interest rate compounded monthly, using $120 monthly payments. This problem involves algebra, financial mathematics, and compound interest concepts. Suitable for Grades 10-12.

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