Let's break down the steps to calculate each part of the problem:

1. Average Daily Balance:

To find the average daily balance, we need to determine the balance on each day in the billing cycle and then find the weighted average based on the number of days each balance was held.

The billing cycle runs from April 1 to April 30 (30 days).

• April 1–7 (7 days): The balance is $407.08.
• April 8–15 (8 days): After a purchase of $51.90, the new balance is $407.08 + 51.90 = 458.98$.
• April 16–22 (7 days): After a payment of $185, the new balance is $458.98 - 185 = 273.98$.
• April 23–30 (8 days): After a purchase of $84.55, the new balance is $273.98 + 84.55 = 358.53$.

Now, we'll calculate the average daily balance using these time intervals:

$\text{Average Daily Balance} = \frac{(407.08 \times 7) + (458.98 \times 8) + (273.98 \times 7) + (358.53 \times 8)}{30}$

Let's calculate this.

2. Monthly Finance Charge:

The monthly finance charge is 1.9% of the average daily balance.

$\text{Finance Charge} = \text{Average Daily Balance} \times 1.9\%$

3. Balance at the Start of the Next Month:

The balance at the start of the next month is the final balance on April 30 plus the finance charge.

$\text{Next Month Balance} = \text{Final Balance on April 30} + \text{Finance Charge}$

I'll calculate these step-by-step.### Results:

1. Average Daily Balance: $376.92
2. Monthly Finance Charge: $7.16
3. Balance at the Start of the Next Month: $365.69

Would you like further details on any of these calculations or have any questions?

Here are some related questions to explore:

1. How would the balance change if an