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Let's break down the problem and solve it step by step.

### Given:
- **Balance**: $5700
- **APR (Annual Percentage Rate)**: 17% (APR is converted to a monthly rate for the calculations)
- **Payoff time**: 1 year (12 months)
- **No additional charges after January 1**

### Part (a) - Calculate your monthly payments.

We will use the formula for the monthly payment on a loan or credit card balance, which is:

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

Where:
- $ M $ is the monthly payment
- $ P $ is the initial balance ($5700)
- $ r $ is the monthly interest rate (APR divided by 12)
- $ n $ is the number of months (12)

Let's calculate:
- APR of 17% means the monthly interest rate is $ \frac{17}{12} \% = 0.01417 $ (or 1.417% per month).
- Balance ($ P $) = $5700
- Number of months ($ n $) = 12

Substituting into the formula:

\[
M = \frac{5700 \cdot 0.01417}{1 - (1 + 0.01417)^{-12}}
\]

### Part (b) - Total amount paid after 1 year.

Once we have the monthly payment from part (a), the total amount paid would simply be:

\[
\text{Total Paid} = M \times 12
\]

### Part (c) - Percentage of the payment that is interest.

The total interest paid is the difference between the total amount paid (from part b) and the original balance. The percentage of the total payment that went to interest is calculated as:

\[
\text{Interest Percentage} = \frac{\text{Total Interest Paid}}{\text{Total Paid}} \times 100
\]

---

I'll now proceed to compute the actual values.### Results:

#### (a) Monthly Payments:
- The monthly payment is approximately **$519.87**.

#### (b) Total Payment After 1 Year:
- The total amount paid over the year is approximately **$6238.41**.

#### (c) Percentage of Total Payment that is Interest:
- The percentage of your total payment that goes to interest is approximately **8.63%**.

Let me know if you need more details or clarifications! Here are some related questions you might explore:

1. What would happen to your monthly payments if the APR increased by 5%?
2. How much would the monthly payment be if the balance was $10,000 instead of $5700?
3. What would be the total interest paid if the repayment period was extended to 2 years?
4. How does the monthly payment formula change if the APR is compounded daily instead of monthly?
5. What would be the impact of making an extra payment of $100 per month?

**Tip:** Always try to pay more than the minimum monthly payment to reduce the amount of interest paid over time!

Suppose that on January 1 you have a balance of $5700 on a credit card whose APR is 17%, which you want to pay off in 1 year. Assume that you make no additional charges to the card after January 1. a. Calculate your monthly payments. b. When the card is paid off, how much will you have paid since January 1? c. What percentage of your total payment from part (b) is interest?

Learn how to calculate monthly payments on a $5700 credit card balance with an APR of 17%, paid off over 1 year. This guide covers interest calculations, total payments, and how to determine the percentage of interest paid. Ideal for high school and college students.

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