Consider a credit card with a balance of $6500
 and an APR of 16.99%
. In order to pay off the balance in 1
 year, what monthly payment would you need to make? Round your answer to the nearest cent, if necessary.



To calculate the monthly payment needed to pay off the balance of $6,500 in one year with an APR of 16.99%, we will use the following formula for monthly payments on a loan:

\[
M = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1}
\]

Where:
- $M$ = monthly payment
- $P$ = principal (loan balance) = $6,500
- $r$ = monthly interest rate (annual rate divided by 12)
- $n$ = total number of payments (in months)

### Step 1: Convert APR to monthly interest rate
The APR is 16.99%, so the monthly interest rate $r$ is:

\[
r = \frac{16.99\%}{12} = \frac{0.1699}{12} \approx 0.0141583
\]

### Step 2: Set $n$ as the number of months
Since the balance is to be paid off in 1 year, the number of months $n$ is 12.

### Step 3: Plug values into the formula
Now, we calculate the monthly payment using these values.

\[
M = \frac{6500 \times 0.0141583 \times (1 + 0.0141583)^{12}}{(1 + 0.0141583)^{12} - 1}
\]

Let me calculate that for you.The monthly payment required to pay off the $6,500 balance in one year with an APR of 16.99% is approximately **$592.80**.

Would you like more details or have any questions?

Here are five related questions to explore further:

1. How would the payment change if the balance was $8,000 instead of $6,500?
2. What happens if the repayment period is extended to 2 years instead of 1 year?
3. How is the total interest paid over the year calculated?
4. How would a lower APR (e.g., 12%) affect the monthly payment?
5. What would the impact be if a partial payment is made in advance?

**Tip:** Paying more than the required monthly payment can reduce the total interest paid over time.

Consider a credit card with a balance of $6500 and an APR of 16.99%. In order to pay off the balance in 1 year, what monthly payment would you need to make? Round your answer to the nearest cent, if necessary.

Learn how to calculate the monthly payment needed to pay off a $6,500 credit card balance with an APR of 16.99%. This financial math problem covers key concepts such as interest rates and payment formulas. Suitable for high school students in Grades 10-12.

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