Consider a credit card with a balance of $7000
 and an APR of 12.5%
. If you want to make monthly payments in order to pay off the balance in 1
 year, what is the total amount you will pay? Round your answer to the nearest cent, if necessary.



To calculate the total amount you will pay on a credit card with a balance of $7,000 and an APR of 12.5% over 1 year, we first need to compute the monthly payment required and the total payment over the 12 months.

### Step 1: Convert APR to Monthly Interest Rate
The annual percentage rate (APR) is 12.5%. To find the monthly interest rate, divide the APR by 12:

\[
\text{Monthly Interest Rate} = \frac{12.5\%}{12} = 1.04167\% = 0.0104167 \, \text{(decimal form)}
\]

### Step 2: Use the Amortization Formula
The amortization formula to calculate the monthly payment is:

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

Where:
- $ M $ is the monthly payment
- $ P $ is the loan balance ($7,000)
- $ r $ is the monthly interest rate (0.0104167)
- $ n $ is the number of months (12)

Substitute the values into the formula:

\[
M = \frac{7000 \cdot 0.0104167}{1 - (1 + 0.0104167)^{-12}}
\]

### Step 3: Calculate Monthly Payment

First, calculate the denominator:

\[
1 - (1 + 0.0104167)^{-12} = 1 - (1.0104167)^{-12} = 1 - 0.8839608 = 0.1160392
\]

Now calculate the monthly payment $ M $:

\[
M = \frac{7000 \cdot 0.0104167}{0.1160392} = \frac{72.9169}{0.1160392} = 628.21
\]

### Step 4: Total Amount Paid

The total amount paid is the monthly payment multiplied by 12:

\[
\text{Total Payment} = 628.21 \times 12 = 7538.52
\]

### Conclusion:

The total amount you will pay over 1 year is **$7,538.52**.

Would you like further clarification or details on any step?

---

Here are 5 related questions to expand your understanding:

1. What happens to the total payment if the APR increases to 15%?
2. How would the total payment change if you paid off the balance in 2 years instead of 1 year?
3. What is the impact of a higher balance (e.g., $10,000) on the monthly payment?
4. How is the interest calculated if you only make minimum payments each month?
5. What would be the total interest paid over the course of the year?

**Tip:** Always try to pay more than the minimum payment on your credit card to reduce the total interest paid over time!

Consider a credit card with a balance of $7000 and an APR of 12.5%. If you want to make monthly payments in order to pay off the balance in 1 year, what is the total amount you will pay? Round your answer to the nearest cent, if necessary.

Learn how to calculate the total payment for a $7,000 credit card balance with a 12.5% APR. This example demonstrates amortization techniques and monthly interest rate conversion, ideal for high school students studying financial math. The total amount paid over 1 year is $7,538.52.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation