Jack owes $1,100 on his credit card. The bank charges a monthly interest rate of 1.575%. If Jack wants to pay off his credit card using equal monthly payments over the next 6 months, what would the monthly payment be, to the nearest dollar?

We can calculate Jack's monthly payment using the formula for the monthly payment on a loan with a constant interest rate:

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

Where:
- $M$ is the monthly payment
- $P$ is the principal (the amount owed, $1,100)
- $r$ is the monthly interest rate as a decimal (1.575% = 0.01575)
- $n$ is the number of months (6 months)

Let me calculate that for you.# Given values
P = 1100  # Principal amount
r = 0.01575  # Monthly interest rate as a decimal
n = 6  # Number of months

# Monthly payment formula
M = (P * r * (1 + r)**n) / ((1 + r)**n - 1)
M_rounded = round(M)  # Rounding to the nearest dollar
M_roundedThe monthly payment Jack needs to make to pay off his credit card over 6 months is approximately **$194**.

Would you like more details or have any questions? Here are some related questions to explore:

1. What happens if the interest rate changes during the repayment period?
2. How does the length of the repayment period affect the monthly payments?
3. What would Jack's total interest cost be over the 6 months?
4. How can Jack reduce the overall interest paid on the credit card?
5. How would paying extra each month affect the loan?

**Tip:** Paying more than the required monthly amount can significantly reduce the total interest paid.

Discover how to calculate the monthly payment for a $1,100 credit card debt with a 1.575% monthly interest rate over 6 months. This problem illustrates key financial concepts like compound interest and loan amortization, making it ideal for students in Grades 10-12.

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