Consider a credit card with a balance of $7500
and an APR of 12%
paid off within 5
years.
Step 1 of 2 :  What is the monthly payment amount within the time frame given? Round your answer to the nearest cent.

To calculate the monthly payment required to pay off a credit card balance within a specific time frame, we can use the formula for the monthly payment on an installment loan:

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

where:
- $ M $ is the monthly payment
- $ P $ is the loan principal (the initial balance)
- $ r $ is the monthly interest rate
- $ n $ is the total number of payments (months)

Given:
- $ P = \$7500 $
- Annual Percentage Rate (APR) = 12%, so the monthly interest rate $ r = \frac{12\%}{12} = 1\% = 0.01 $
- Time frame = 5 years, so $ n = 5 \times 12 = 60 $ months

Now, we can plug these values into the formula:

\[ M = \frac{7500 \cdot 0.01 \cdot (1 + 0.01)^{60}}{(1 + 0.01)^{60} - 1} \]

First, let's calculate the numerator:

\[ 7500 \cdot 0.01 = 75 \]

Next, calculate $(1 + 0.01)^{60}$:

\[ (1 + 0.01)^{60} = 1.01^{60} \approx 1.8167 \]

Then, the numerator becomes:

\[ 75 \cdot 1.8167 = 136.2525 \]

Now, calculate the denominator:

\[ 1.8167 - 1 = 0.8167 \]

Finally, divide the numerator by the denominator:

\[ M = \frac{136.2525}{0.8167} \approx 166.85 \]

Therefore, the monthly payment amount required to pay off the balance within 5 years is approximately $166.85.

Would you like more details or have any questions?

Here are some questions you might want to ask next:
1. How do you derive the formula for monthly payments?
2. What happens if the interest rate changes?
3. How does the payment amount change if the repayment period is shorter?
4. What is the total interest paid over the 5 years?
5. How can I use a financial calculator to verify this payment amount?

Tip: Always double-check the number of payments and interest rate conversions when calculating monthly payments.

Learn how to calculate the monthly payment required to pay off a $7500 credit card balance with a 12% APR within 5 years. This problem involves using the formula for monthly payments on installment loans, applying finance and interest calculation concepts.

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