Suppose that on January 1 you have a balance of $4000 on a credit card whose APR is 19​%, 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?

To solve this problem, we'll break it down into steps.

### Given Data:
- **Balance (Principal):** $4000
- **APR:** 19% or 0.19
- **Loan Term:** 1 year
- **Payment Frequency:** Monthly (12 payments)

### Part (a): Calculate Monthly Payments
We'll use the amortization formula:

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

Where:
- $ P $ is the monthly payment
- $ r $ is the monthly interest rate (APR divided by 12)
- $ n $ is the total number of payments

### Part (b): Total Payments
The total payment is calculated as:

\[
\text{Total Payment} = P \times n
\]

### Part (c): Percentage of Total Payment That Is Interest
First, we calculate the total interest paid:

\[
\text{Total Interest} = \text{Total Payment} - \text{Principal}
\]

Then, the percentage of the total payment that is interest:

\[
\text{Interest Percentage} = \left(\frac{\text{Total Interest}}{\text{Total Payment}}\right) \times 100
\]

Let's calculate these values.Here are the results:

### Part (a): Monthly Payments
- **Monthly Payment:** $368.63

### Part (b): Total Payment
- **Total Payment:** $4,423.52

### Part (c): Percentage of Total Payment That Is Interest
- **Interest Percentage:** 9.57%

This means that out of the total amount you will pay over the year, about 9.57% will be interest.

Would you like more details or have any questions? Here are some related questions you might find useful:

1. How does the APR affect the total interest paid on a loan?
2. What strategies can help reduce the interest paid on a credit card balance?
3. How does paying more than the minimum payment each month affect the interest?
4. What are the consequences of only making minimum payments on a credit card?
5. How can you calculate the interest saved by paying off a credit card balance early?

**Tip:** Always aim to pay off credit card balances as quickly as possible to minimize the interest paid over time.

Learn how to calculate monthly payments, total payments, and the percentage of interest paid on a $4000 credit card balance with a 19% APR over one year. Understand the amortization formula and financial implications. Suitable for adult learners.

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