Consider a credit card with a balance of $6000
and an APR of 16.99%
. In order to pay off the balance in 1
year, what monthly payment would you need to make? Round your answer to the nearest cent, if necessary.

To calculate the monthly payment needed to pay off a $6000 balance on a credit card with a 16.99% APR in one year, we can use the formula for the monthly payment on an amortizing loan:

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

where:
- $ M $ is the monthly payment,
- $ P $ is the principal amount (the initial balance, which is $6000),
- $ r $ is the monthly interest rate (the APR divided by 12),
- $ n $ is the number of monthly payments (12 for one year).

First, we need to calculate the monthly interest rate:

\[ r = \frac{16.99\%}{12} = \frac{0.1699}{12} = 0.0141583 \]

Next, we plug these values into the formula:

\[ M = \frac{6000 \cdot 0.0141583 \cdot (1 + 0.0141583)^{12}}{(1 + 0.0141583)^{12} - 1} \]

Now we calculate each component step-by-step.

1. Calculate $(1 + r)^{12}$:

\[ (1 + 0.0141583)^{12} \approx 1.180304 \]

2. Multiply $P \cdot r \cdot (1 + r)^{12}$:

\[ 6000 \cdot 0.0141583 \cdot 1.180304 \approx 100.1861 \]

3. Calculate the denominator $(1 + r)^{12} - 1$:

\[ 1.180304 - 1 = 0.180304 \]

4. Divide the result from step 2 by the result from step 3:

\[ M = \frac{100.1861}{0.180304} \approx 555.68 \]

So, the monthly payment needed to pay off the balance in one year is approximately $555.68.

Would you like details on any part of this process or have any questions? Here are some questions you might ask next:

1. How is the APR related to the monthly interest rate?
2. What if the payment period was two years instead of one?
3. Can you show a breakdown of the formula components?
4. How do interest rates impact the monthly payment?
5. What are some strategies to pay off credit card debt faster?

**Tip:** Always ensure you understand how the interest rate is applied (monthly vs. annually) to manage loan repayments effectively.

Learn how to calculate the monthly payment required to pay off a $6000 credit card balance with a 16.99% APR in one year. This problem involves interest calculation and amortization concepts, using the monthly payment formula for amortizing loans. Suitable for high school students and anyone interested in financial mathematics.

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