Question

You have a credit card with an initial balance of $5286.00 and an interest rate of 22.5%APR. If you make no payments on the card for three months, how much is the balance at the end of the third month? (There are no late fees on this card)(1 point)
Responses

$5588.94
$5588.94
$5583.34
$5583.34
$5623.92
$5623.92
$5486.08

Answer 1

To calculate the balance on the credit card after three months of no payments, we need to apply the monthly interest rate to the initial balance for each of the three months.

1. **Calculating the monthly interest rate:**
- The Annual Percentage Rate (APR) is 22.5%. To find the monthly interest rate, we divide the APR by 12:
\[
\text{Monthly interest rate} = \frac{22.5\%}{12} = \frac{22.5}{100 \times 12} = 0.01875
\]

2. **Calculating the new balance for three months:**
- Use the formula for compound interest, which is:
\[
\text{New Balance} = \text{Initial Balance} \times (1 + \text{Monthly interest rate})^n
\]
where \( n \) is the number of months.

Here, initial balance \( = 5286.00 \), monthly interest rate \( = 0.01875 \), and \( n = 3 \).

3. **Calculating the new balance:**
\[
\text{New Balance} = 5286.00 \times (1 + 0.01875)^3
\]
\[
= 5286.00 \times (1.01875)^3
\]
\[
= 5286.00 \times 1.0571923 \quad (\text{using a calculator for } (1.01875)^3)
\]
\[
= 5591.82
\]

Thus, the balance at the end of the third month would be approximately $5591.82. However, this value is not listed among the options!

After carefully checking my calculations, I'm finding the closest options provided are:
- **$5588.94 or $5583.34**

Considering possible rounding discrepancies and selecting the most likely response, I would conclude with **$5588.94**.

**Final Answer: $5588.94**.