You have $3,500 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 find the monthly payment needed to pay off the $3,500 credit card balance with a 22% annual interest rate over 4 years, we can use the formula for calculating the monthly payment on a loan or debt:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the principal, or the initial amount ($3,500).
- $ r $ is the monthly interest rate (annual rate divided by 12).
- $ n $ is the total number of payments (years times 12).

### Step 1: Define the known values
- $ P = 3500 $
- Annual interest rate = 22%, so the monthly interest rate is $ r = \frac{22}{100} \div 12 = 0.01833 $ (rounded to 5 decimal places).
- $ n = 4 \times 12 = 48 $ months.

### Step 2: Substitute these values into the formula and solve for $ M $.

I'll calculate this now.The monthly payment needed to pay off the $3,500 credit card balance with a 22% annual interest rate over 4 years is approximately **$110.27**.

Would you like more details or have any further questions?

Here are five related questions you might find helpful:
1. What is the total amount paid over the 4 years?
2. How much interest will be paid over the life of the loan?
3. What would happen if the interest rate were lower, say 18%?
4. How can early payments reduce the total interest paid?
5. How would the monthly payment change if you paid it off in 3 years instead?

**Tip:** Paying more than the minimum monthly payment can significantly reduce the amount of interest paid over time.

You have $3,500 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)?

Discover how to calculate the monthly payment needed to pay off a $3,500 credit card balance with a 22% annual interest rate over 4 years. This problem involves the loan payment formula and key concepts in finance, suitable for high school students in Grades 10-12.

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