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)

Answer 1

To calculate the new balance on the credit card after three months with no payments and a monthly interest rate applied, follow these steps:

1. **Convert the annual percentage rate (APR) to a monthly interest rate**:
- The APR is 22.5%. To find the monthly interest rate, divide by 12:
\[
\text{Monthly Interest Rate} = \frac{22.5\%}{12} = \frac{22.5}{100 \times 12} = 0.01875 \text{ (as a decimal)}
\]

2. **Calculate the balance after each month**:
The balance grows each month based on the interest applied to the balance from the previous month.

- **End of Month 1**:
\[
\text{New Balance} = \text{Initial Balance} \times (1 + \text{Monthly Interest Rate})
\]
\[
\text{New Balance} = 5286.00 \times (1 + 0.01875)
\]
\[
\text{New Balance} = 5286.00 \times 1.01875 = 5381.32
\]

- **End of Month 2**:
\[
\text{New Balance} = 5381.32 \times (1 + 0.01875)
\]
\[
\text{New Balance} = 5381.32 \times 1.01875 = 5480.09
\]

- **End of Month 3**:
\[
\text{New Balance} = 5480.09 \times (1 + 0.01875)
\]
\[
\text{New Balance} = 5480.09 \times 1.01875 = 5584.73
\]

3. **Final Balance After 3 Months**:
\[
\text{Balance at the End of Month 3} \approx 5584.73
\]

Thus, the balance at the end of the third month will be approximately **$5584.73**.