Suppose that on January 1 you have a balance of ​$2900 on a credit card whose APR is 16​%, which you want to pay off in 1 year. Assume that you make no additional charges to the card after January 1.
a. Calculate your monthly payments.
b. When the card is paid​ off, how much will you have paid since January​ 1?
c. What percentage of your total payment from part​ (b) is​ interest?
Question content area bottom
Part 1
a. The monthly payment is ​$

enter your response here.
​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

To solve this, we can break the problem down as follows:

### a. **Calculate your monthly payments.**

We use the formula for the monthly payment of a loan with interest:

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

Where:
- $ P $ = principal balance (in this case, $2900),
- $ r $ = monthly interest rate (which is the annual rate divided by 12),
- $ n $ = number of months (12 months for 1 year).

1. The APR is 16%, so the monthly interest rate $ r $ is:

\[
r = \frac{16\%}{12} = \frac{0.16}{12} = 0.013333\ldots
\]

2. Plug these values into the formula:

\[
M = \frac{2900 \cdot 0.013333}{1 - (1 + 0.013333)^{-12}}
\]

Let me calculate this.

The monthly payment is approximately **$263.12**.

### b. **Total payment over the year:**

To calculate the total payment over the year, we multiply the monthly payment by 12:

\[
\text{Total payment} = M \times 12 = 263.12 \times 12
\]

Let me calculate that for you.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can calculate the total payment by multiplying the monthly payment of $263.12 by 12, which gives:

\[
263.12 \times 12 = 3157.44
\]

So, the total payment over the year is **$3,157.44**.

### c. **Percentage of the total payment that is interest:**

The interest paid is the total payment minus the original balance. So,

\[
\text{Interest} = 3157.44 - 2900 = 257.44
\]

Now, to find what percentage of the total payment is interest:

\[
\text{Interest percentage} = \frac{257.44}{3157.44} \times 100
\]

This will give you the percentage of the payment that is interest.

---

Would you like to go over the detailed steps of any part of this?

Here are some related questions:
1. What happens if you adjust the APR to 18%?
2. How does the monthly payment change with a 2-year payment plan?
3. How much interest would you save by making double monthly payments?
4. How would a 6-month repayment period affect the total interest?
5. What if the balance was $5000 instead of $2900?

**Tip:** If you're looking to reduce interest, paying more than the minimum payment can save you significant amounts over time!

Suppose that on January 1 you have a balance of ​$2900 on a credit card whose APR is 16​%, 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 for a $2900 credit card balance with a 16% APR over one year. Detailed step-by-step solution, including how to calculate total payment and interest percentage. Perfect for high school students studying finance and loan repayment.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation