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Let's break down the problem based on the text from the image:

### Given Information:
- **Interest rate**: 18.50% per annum
- **Balance on June 12**: $398.51
- **Minimum payment made**: The minimum payment is the greater of 5% of the balance or $10.00.
- **New purchase**: $575.54 on June 14
- **Next statement date**: July 12

### Part (a) question:
What will Vlad's balance be on his next statement (dated July 12) if he makes no other purchases or payments?

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#### Step 1: Calculate the minimum payment made by June 12.

- 5% of the balance on June 12 is $ 0.05 \times 398.51 = 19.93 $.
- The minimum payment made is the greater of 5% or $10, so Vlad made a payment of **$19.93**.

#### Step 2: Calculate the new balance after the minimum payment.

- Balance after payment = $398.51 - $19.93 = **$378.58**.

#### Step 3: Add the new purchase.

- New purchase on June 14 = $575.54.
- New balance after the purchase = $378.58 + $575.54 = **$954.12**.

#### Step 4: Calculate interest accrued from June 12 to July 12.

- Interest rate = 18.50% per year, so the monthly interest rate = $ \frac{18.50\%}{12} = 1.5417\% $.
- Interest on the balance = $ 0.015417 \times 378.58 = 5.84 $ dollars (since the purchase happened later, only the initial balance will accrue interest).
- Total balance on July 12 = $954.12 + $5.84 = **$959.96**.

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### Final Answer:
Vlad's balance on his next statement dated July 12 will be **$959.96**.

Would you like more details or have any questions?

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### Related Questions:
1. How would the balance change if Vlad had made a larger payment instead of the minimum payment?
2. What would the total interest accrued be after 6 months at the current rate?
3. If Vlad continued to make only minimum payments, how long would it take to pay off the balance?
4. What is the formula to calculate the interest in different compounding intervals (e.g., daily vs. monthly)?
5. How would additional purchases made before July 12 affect the final balance?

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### Tip:
When managing credit card debt, always aim to pay more than the minimum to reduce interest charges faster.

Vlad's credit card charges 18.50% per annum interest. On his June 12 statement, he had a balance of $398.51. By the due date, he made the minimum payment (5% or $10.00, whichever is greater). On June 14, he made a purchase of $575.54. If he makes no other purchases or payments, what will his balance be on his next statement, dated July 12?

Learn how to calculate Vlad's credit card balance with an 18.50% annual interest rate after making a minimum payment and a new purchase. This solution explains the steps involved in determining the balance on his next statement, dated July 12.

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