Suppose you have a balance of $3,450 on your credit card, which charges an APR of 22%, compounded monthly. If you want to pay off the balance in 6 months, how much should you pay each month? Assume that you charge no additional expenses to the card.

$632.45

$612.45

$712.45

$522.45

None of the above.

To determine the monthly payment necessary to pay off the balance in 6 months, we can use the formula for calculating the monthly payment on a loan or credit card balance with compound interest:

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

Where:
- $M$ is the monthly payment,
- $P$ is the initial balance (in this case, $3,450),
- $r$ is the monthly interest rate (which is the APR divided by 12),
- $n$ is the number of months over which the loan will be repaid.

### Step 1: Calculate the monthly interest rate
The annual percentage rate (APR) is 22%, so the monthly interest rate is:

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

### Step 2: Use the formula
Now, plugging the values into the formula:
- $P = 3450$,
- $r \approx 0.01833$,
- $n = 6$.

\[
M = \frac{3450 \cdot 0.01833 \cdot (1+0.01833)^6}{(1+0.01833)^6 - 1}
\]

Let's calculate the value of $M$.The monthly payment required to pay off the balance in 6 months is approximately **$612.45**.

Therefore, the correct answer is **$612.45**.

Would you like more details, or do you have any questions?

Here are 5 related questions to consider:
1. How would the monthly payment change if the balance were higher, say $4,500?
2. What would the payment be if the APR were lower, like 15%?
3. How does the number of months affect the monthly payment?
4. What if the payment term was extended to 12 months instead of 6 months?
5. How can you reduce the overall interest paid on a credit card balance?

**Tip:** Paying off credit card balances quickly helps minimize the amount of interest you pay over time!

Suppose you have a balance of $3,450 on your credit card, which charges an APR of 22%, compounded monthly. If you want to pay off the balance in 6 months, how much should you pay each month? Assume that you charge no additional expenses to the card.
$632.45
$612.45
$712.45
$522.45
None of the above.

Calculate how much you need to pay monthly to pay off a $3,450 credit card balance with 22% APR in 6 months. This solution uses compound interest formulas to determine the payment amount, suitable for high school students learning financial math.

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