Consider a credit card with a balance of $⁢8000 and an APR of 16.5%. 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 balance with monthly payments over 22 years, we can use the amortization formula for monthly payments:

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

where:
- $ P = 8000 $ (initial balance),
- $ APR = 16.5\% $ (annual percentage rate),
- $ r = \frac{APR}{12} = \frac{0.165}{12} \approx 0.01375 $ (monthly interest rate),
- $ n = 22 \times 12 = 264 $ (total number of payments over 22 years).

### Step 1: Calculate Monthly Payment

1. Substitute these values into the formula to find $ M $, the monthly payment.
   
2. Once we have $ M $, multiply it by $ n = 264 $ to find the total amount paid over 22 years.

Let me calculate this for you.The total amount you will pay over 22 years is approximately **$29,851.36**.

Would you like a breakdown of each step? 

Here are 5 questions that may deepen your understanding:

1. How would the total payment change if the APR were lower, say 10%?
2. What would happen if the balance increased to $10,000?
3. How does the amortization formula adjust for different payment periods, such as weekly?
4. What impact does increasing the payment period have on the total amount paid?
5. Can we determine the portion of the payment that goes toward interest?

**Tip:** The longer the payment period with interest-bearing debt, the more interest you end up paying overall, even if monthly payments seem low.

Consider a credit card with a balance of $8000 and an APR of 16.5%. 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 credit card balance of $8000 with a 16.5% APR over a period of 22 years. This problem covers key finance mathematics concepts, including amortization and interest calculation, suitable for students in Grades 10-12.

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