You have $4,500 on a credit card that charges a 22% interest rate. If you want to pay off the credit card in 4 years, how much will you need to pay each month (assuming you don't charge anything new to the card)?

To calculate the monthly payment needed to pay off a credit card balance of $4,500 over 4 years with an annual interest rate of 22%, we use the formula for the monthly payment on an amortizing loan:

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

Where:
- $M$ is the monthly payment
- $P$ is the principal amount (the balance on the card), which is $4,500
- $r$ is the monthly interest rate (annual interest rate divided by 12)
- $n$ is the total number of payments (loan term in months)

### Step 1: Convert the annual interest rate to a monthly rate
The annual interest rate is 22%, so the monthly interest rate is:

\[
r = \frac{22\%}{12} = \frac{0.22}{12} = 0.01833
\]

### Step 2: Determine the total number of payments
Since the card will be paid off in 4 years, the number of months is:

\[
n = 4 \times 12 = 48 \text{ months}
\]

### Step 3: Calculate the monthly payment
Substitute the values into the formula:

\[
M = \frac{4500 \cdot 0.01833(1 + 0.01833)^{48}}{(1 + 0.01833)^{48} - 1}
\]

Now, calculating this step-by-step:

1. $ 1 + 0.01833 = 1.01833 $
2. $ 1.01833^{48} \approx 2.396 $
3. Multiply by the interest rate and principal: $ 4500 \times 0.01833 \times 2.396 \approx 197.47 $
4. Denominator: $ 2.396 - 1 = 1.396 $
5. Divide the result: $ \frac{197.47}{1.396} \approx 141.44 $

So, the monthly payment is approximately **$141.44**.

Let me know if you need more details or clarifications!

### Related Questions:
1. How much total interest will you pay over the 4 years?
2. What would the monthly payment be if the interest rate were reduced to 18%?
3. How does increasing the repayment term to 5 years affect the monthly payment?
4. What happens if you make an extra payment of $100 in the first month?
5. How much faster could you pay off the debt if you increase your monthly payment by 20%?

### Tip:
Always pay more than the minimum monthly payment on credit card debt if possible. This reduces the total interest paid and shortens the repayment period.

Calculate the monthly payment needed to pay off a $4,500 credit card balance with a 22% interest rate over 4 years. Learn how to apply the amortization formula, convert annual interest to monthly interest, and determine total payments over 48 months. Suitable for high school students in Grades 11-12.

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