Consider a credit card with a balance of $6000$⁢6000 and an APR of 14.5%14.5%. If you want to make monthly payments in order to pay off the balance in 22 years, what is the total amount you will pay? Round your answer to the nearest cent, if necessary.

To determine the total amount paid on a credit card with a balance of $6,000 and an APR of 14.5%, when making monthly payments over 22 years, we can follow these steps:

### Step 1: Find the monthly interest rate
The APR (Annual Percentage Rate) is 14.5%. To convert this to a monthly interest rate, divide it by 12 (since there are 12 months in a year):

\[
\text{Monthly Interest Rate} = \frac{14.5\%}{12} = \frac{0.145}{12} = 0.0120833
\]

### Step 2: Use the formula for the monthly payment
The formula for the monthly payment on a loan with fixed monthly payments is:

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

Where:
- $ M $ is the monthly payment
- $ P $ is the principal ($6,000)
- $ r $ is the monthly interest rate (0.0120833)
- $ n $ is the total number of payments (22 years × 12 months/year = 264 payments)

### Step 3: Calculate the monthly payment
We can now substitute the known values into the formula to find the monthly payment:

\[
M = \frac{6000 \cdot 0.0120833 \cdot (1 + 0.0120833)^{264}}{(1 + 0.0120833)^{264} - 1}
\]

I'll calculate this now.The monthly payment is approximately \$75.68.

### Step 4: Calculate the total amount paid
Now, to find the total amount paid over the 22 years, multiply the monthly payment by the total number of payments:

\[
\text{Total Amount Paid} = M \times n = 75.68 \times 264
\]

I'll calculate that now.The total amount paid over 22 years will be approximately \$19,978.43.

### Summary:
- Monthly payment: \$75.68
- Total amount paid over 22 years: \$19,978.43

Would you like more details on how the calculation works or any further clarifications?

Here are 5 questions you could explore next:
1. How does reducing the repayment period affect the total amount paid?
2. What happens if you increase the monthly payments?
3. How is APR different from other interest rates like APY?
4. How does compounding interest influence the final amount paid?
5. Can refinancing the debt help reduce the total payment?

**Tip:** Making extra payments or increasing your monthly payment can help reduce the interest paid over time.

Consider a credit card with a balance of $6000 and an APR of 14.5%. If you want to make monthly payments in order to pay off the balance in 22 years, what is the total amount you will pay? Round your answer to the nearest cent, if necessary.

Learn how to calculate the total amount paid on a $6000 credit card balance with a 14.5% APR over 22 years using key finance concepts such as monthly interest rates and loan repayment formulas. This problem is suitable for students in Grades 11-12 and college-level finance courses.

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