Certainly! Let's go through the problem step by step.
### Given:
1. Initial balance on the Visa credit card: [tex]$4500
2. Annual Percentage Rate (APR): 21%
3. Minimum payment rate: 2.5% of the current balance every month
4. Time period in question: 2 years (which is 24 months)
### Step-by-Step Solution:
1. Convert Annual Percentage Rate (APR) to Monthly Interest Rate:
- The monthly interest rate is the APR divided by 12.
- Monthly interest rate = \( \frac{21\%}{12} \) = 1.75% per month
2. Start with the initial balance: $[/tex]4500.
3. Iterate through each month, calculating the interest, adding the interest to the balance, computing the minimum payment, and then subtracting the minimum payment from the balance.
So, let's begin:
- Month 1:
- Compute interest for the month: [tex]\( \text{Interest} = \text{Balance} \times \text{Monthly Interest Rate} \)[/tex].
- Interest = [tex]$4500 \times 0.0175 = $[/tex]78.75.
- Add interest to the balance:
- New balance = [tex]$4500 + $[/tex]78.75 = [tex]$4578.75.
- Calculate minimum payment: \( \text{Minimum Payment} = \text{New Balance} \times \text{Minimum Payment Rate} \).
- Minimum Payment = $[/tex]4578.75 \times 0.025 = [tex]$114.47.
- Subtract minimum payment from the balance:
- New balance = $[/tex]4578.75 - [tex]$114.47 = $[/tex]4464.28.
- Repeat for each subsequent month for a total of 24 months.
At the end of 24 months, the balance will be:
### Final Balance:
The final balance after applying the interest calculations and minimum payments for 24 months is approximately $3716.63.
This is the rounded balance to 2 decimal places.
