If you have a credit card balance of $1,500 with an annual interest rate of 18%, and you make monthly payments of 750, approximately how many months will it take to pay off the balance?

24 months

36 months

12 months

48 months

To determine how long it will take to pay off a credit card balance with regular monthly payments, we can use the formula that considers the principal balance, interest rate, and payment amount. 

Here's the given information:

- **Credit Card Balance**: $1,500
- **Annual Interest Rate**: 18% (which is 1.5% per month, since $ \frac{18\%}{12} = 1.5\% $)
- **Monthly Payment**: $750

### Step-by-step calculation:

1. **Monthly Interest Rate**: 

\[
\text{Monthly Interest Rate} = \frac{18\%}{12} = 1.5\% = 0.015
\]

2. **Setting up the equation**:

The remaining balance $ B_n $ after $ n $ months can be expressed as:

\[
B_n = B_{n-1}(1 + r) - P
\]

where:
- $ B_{n-1} $ is the previous month's balance
- $ r $ is the monthly interest rate (0.015)
- $ P $ is the monthly payment ($750)

Starting with $ B_0 = 1500 $, we apply the payments and interest.

3. **Calculating Month by Month**:

- **Month 1**: 
  \[
  B_1 = 1500 \times 1.015 - 750 = 1522.5 - 750 = 772.5
  \]

- **Month 2**: 
  \[
  B_2 = 772.5 \times 1.015 - 750 = 784.0875 - 750 = 34.0875
  \]

- **Month 3**:
  \[
  B_3 = 34.0875 \times 1.015 - 750 = 34.59881 - 750 \approx -715.40 \text{ (balance paid off)}
  \]

### Conclusion

It takes approximately **2 months** to pay off the balance. In the second month, only a small amount of the initial balance remains after the monthly payment, and it is paid off completely by the third month.

**Answer**: None of the given choices (24, 36, 12, or 48 months) are correct; it takes approximately **2 months** to pay off the credit card balance. 

Would you like more details or have any questions?

### Related Questions:

1. How does the interest rate affect the time it takes to pay off a balance?
2. What if the monthly payment was $500 instead of $750? How long would it take to pay off?
3. How can you calculate the interest paid over the duration of the loan?
4. What is the impact of making additional payments on the credit card balance?
5. How does compounding interest affect the total amount paid on a credit card balance?

**Tip:** Making higher monthly payments significantly reduces the time needed to pay off a credit card balance, especially when interest rates are high.

Learn how to calculate the time needed to pay off a credit card balance of $1,500 with an 18% annual interest rate and $750 monthly payments. Understand compound interest calculations and monthly payment strategies. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation