Consider a credit card with a balance of $⁢7000 and an APR of 16.5%. If you want to make monthly payments in order to pay off the balance in 11 year, what is the total amount you will pay? Round your answer to the nearest cent, if necessary.

To calculate the monthly payment needed to pay off a credit card balance with interest over a fixed period, we can use the formula for the monthly payment on a loan or credit card balance:

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

where:
- $ M $ = monthly payment
- $ P $ = principal (initial balance), which is $7000
- $ r $ = monthly interest rate, calculated as APR / 12
- $ n $ = total number of payments (in months)

### Step 1: Identify the monthly interest rate
The APR is 16.5%, so the monthly interest rate $ r $ is:
\[
r = \frac{16.5\%}{12} = \frac{0.165}{12} \approx 0.01375
\]

### Step 2: Determine the total number of payments
Since you want to pay off the balance in 11 years, the total number of payments $ n $ is:
\[
n = 11 \times 12 = 132 \text{ months}
\]

### Step 3: Calculate the monthly payment $ M $
Plugging the values into the formula, we get:
\[
M = \frac{7000 \cdot 0.01375 \cdot (1 + 0.01375)^{132}}{(1 + 0.01375)^{132} - 1}
\]

Let me compute this for you.The total amount you will pay over 11 years to pay off the $7000 balance with a 16.5% APR is approximately **$15,213.09**.

Would you like further details or have any questions?

Here are five related questions to consider:
1. What would be the impact of a higher APR on the total payment?
2. How much would you pay in interest alone over the 11 years?
3. What would the monthly payment be if the repayment period was shortened to 5 years?
4. How much would you save if the APR was reduced to 10%?
5. What formula applies if the balance is paid over a non-standard number of months?

**Tip:** To minimize interest, aim for higher monthly payments or consider consolidating debt at a lower APR.

Consider a credit card with a balance of $7000 and an APR of 16.5%. If you want to make monthly payments in order to pay off the balance in 11 years, what is the total amount you will pay? Round your answer to the nearest cent, if necessary.

Find out how much you would pay in total for a $7000 credit card balance with a 16.5% APR by making monthly payments over 11 years. This guide covers interest calculations, the monthly payment formula, and exponential growth concepts, suitable for students in Grades 10-12.

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