A recently married couple ran up a $9,069 credit card balance for wedding expenses.  Their credit card charges interest with a 13.99% annual percentage rate.  What monthly payment is required if the couple wants to pay off this debt with 5 monthly payments over the next 5 months? Use two decimal place accuracy (Hint: Y=5/12 )

To calculate the monthly payment required to pay off a credit card balance of $9,069 over 5 months at an interest rate of 13.99% APR, we can follow these steps:

### Step 1: Identify the given values
- **Principal (P)** = $9,069 (the balance to pay off)
- **Annual Percentage Rate (APR)** = 13.99%
- **Number of monthly payments (N)** = 5
- **Fraction of year (Y)** = $ \frac{5}{12} $ (as the hint says, representing 5 months in terms of a year)

### Step 2: Calculate the monthly interest rate
The monthly interest rate is the annual interest rate divided by 12:
\[
\text{Monthly interest rate} = \frac{13.99\%}{12} = \frac{0.1399}{12} = 0.011658 \text{ (or 1.1658% per month)}
\]

### Step 3: Set up the formula for monthly payments
The formula for monthly payments with interest is:
\[
M = \frac{P \cdot r}{1 - (1 + r)^{-N}}
\]
where:
- $ M $ = monthly payment
- $ P $ = principal amount (balance)
- $ r $ = monthly interest rate (as a decimal)
- $ N $ = number of months

### Step 4: Plug in the values
\[
M = \frac{9069 \cdot 0.011658}{1 - (1 + 0.011658)^{-5}}
\]

Now let's calculate that:

The required monthly payment is approximately **$1,877.73** to pay off the $9,069 balance in 5 months at a 13.99% annual percentage rate.

Would you like more details or have any questions?

Here are 5 related questions you might consider:
1. How much total interest will the couple pay over the 5 months?
2. What would the payment be if they decided to pay over 10 months instead?
3. How is the interest portion of the first payment calculated?
4. What if they made an extra payment in one month—how would that affect the remaining balance?
5. How would the monthly payment change if the APR was 10% instead of 13.99%?

**Tip:** The shorter the repayment period, the less interest you'll pay overall, even if monthly payments are higher!

A recently married couple ran up a $9,069 credit card balance for wedding expenses. Their credit card charges interest with a 13.99% annual percentage rate. What monthly payment is required if the couple wants to pay off this debt with 5 monthly payments over the next 5 months? Use two decimal place accuracy (Hint: Y=5/12).

Discover how to calculate the monthly payment for a $9,069 credit card balance with a 13.99% annual percentage rate, using 5 monthly payments over 5 months. This problem uses algebraic formulas for interest calculation and financial mathematics, making it ideal for high school or college-level students.

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