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Let's work through this problem step-by-step.

### Problem Breakdown
1. **Initial Balance** (April 1): $337.58.
2. **Transactions**:
   - April 8: Purchase of $68.49.
   - April 16: Payment of $190.00.
   - April 25: Purchase of $86.17.
3. **Billing Cycle**: Starts on April 1, ends on April 30.
4. **Finance Charge**: 2% monthly.

The goal is to find:
1. **The average daily balance** for the month.
2. **The monthly finance charge** based on this average daily balance.
3. **The balance at the start of the next month** (May 1), including any finance charges.

### Step 1: Calculate Daily Balances for Each Period
Let's break down each period and its balance, then calculate the average daily balance.

- **April 1 to April 7**: $337.58 for 7 days.
- **April 8 to April 15**: $337.58 + $68.49 = $406.07 for 8 days.
- **April 16 to April 24**: $406.07 - $190.00 = $216.07 for 9 days.
- **April 25 to April 30**: $216.07 + $86.17 = $302.24 for 6 days.

### Step 2: Compute the Average Daily Balance
The average daily balance is calculated by taking the sum of each balance multiplied by the number of days it was held, divided by the total number of days (30).

\[
\text{Average Daily Balance} = \frac{(337.58 \times 7) + (406.07 \times 8) + (216.07 \times 9) + (302.24 \times 6)}{30}
\]

Calculating each part:
1. $337.58 \times 7 = 2363.06$
2. $406.07 \times 8 = 3248.56$
3. $216.07 \times 9 = 1944.63$
4. $302.24 \times 6 = 1813.44$

Adding these together:
\[
2363.06 + 3248.56 + 1944.63 + 1813.44 = 9369.69
\]

Now divide by 30:
\[
\text{Average Daily Balance} = \frac{9369.69}{30} = 312.32
\]

### Step 3: Calculate the Monthly Finance Charge
The finance charge is 2% of the average daily balance.

\[
\text{Finance Charge} = 312.32 \times 0.02 = 6.25
\]

### Step 4: Calculate the Balance at the Start of the Next Month
To get the balance for May 1, add the finance charge to the balance on April 30.

\[
\text{May 1 Balance} = 302.24 + 6.25 = 308.49
\]

### Answers
1. **Average Daily Balance**: $312.32
2. **Monthly Finance Charge**: $6.25
3. **Balance at the Start of Next Month**: $308.49

---

Would you like further details on any part of this calculation?

### Related Questions
1. How would the average daily balance change if a larger payment was made on April 16?
2. How does changing the billing date affect the finance charge?
3. What happens to the finance charge if the interest rate is increased to 3%?
4. How would additional purchases affect the average daily balance?
5. What if there was a payment on April 30—how would that affect the starting balance for May?

### Tip
To reduce finance charges, consider paying off part of the balance earlier in the billing cycle.

On April 1, the balance on your credit card is $337.58. On April 8, you make a purchase for $68.49. On April 16, you make a payment of $190. On April 25, you make a purchase for $86.17. Assume the billing date is the 1st of the month and the monthly finance charge is 2%. What is the average daily balance? What is the monthly finance charge? What is the balance at the start of the next month?

Learn how to calculate the average daily balance, monthly finance charge, and end-of-month balance for a credit card. In this example, a credit card starts with a balance of $337.58, with transactions throughout April. Suitable for high school students studying finance.

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