On May 1, the balance on your credit card is $579.30. On May 2, you make a purchase for $85.61. On May 9, you make a payment of $280. On May 17, you make a purchase for $31.22, and on May 29, you make a purchase for $49.25.

Assume the billing date is the 1st of the month and the monthly finance charge is 1.9%.

What is the average daily balance? $Incorrect

What is the monthly finance charge? $Incorrect

What is the balance at the start of the next month? $

Let's solve each part of this problem step-by-step, starting with the average daily balance, then moving on to the monthly finance charge, and finally determining the balance at the start of the next month.

### 1. **Average Daily Balance**

The **average daily balance** is computed by determining the balance for each day of the billing period, multiplying it by the number of days the balance is in effect, and dividing the total by the number of days in the billing cycle.

#### Key dates and events:
- **May 1 Balance**: $579.30
- **May 2 Purchase**: +$85.61
- **May 9 Payment**: -$280
- **May 17 Purchase**: +$31.22
- **May 29 Purchase**: +$49.25

Now, we'll break down the balances between the transactions:

1. **From May 1 to May 1**: Balance = $579.30 for 1 day.
2. **From May 2 to May 8**: New balance = $579.30 + $85.61 = $664.91 for 7 days.
3. **From May 9 to May 16**: New balance = $664.91 - $280 = $384.91 for 8 days.
4. **From May 17 to May 28**: New balance = $384.91 + $31.22 = $416.13 for 12 days.
5. **From May 29 to May 31**: New balance = $416.13 + $49.25 = $465.38 for 3 days.

Next, we calculate the weighted balance for each period:

\[
\text{Total Balance Days} = (579.30 \times 1) + (664.91 \times 7) + (384.91 \times 8) + (416.13 \times 12) + (465.38 \times 3)
\]

\[
\text{Total Balance Days} = 579.30 + 4,654.37 + 3,079.28 + 4,993.56 + 1,396.14 = 14,702.65
\]

The billing cycle in May has 31 days, so:

\[
\text{Average Daily Balance} = \frac{14,702.65}{31} \approx 474.28
\]

So, the **average daily balance** is **$474.28**.

---

### 2. **Monthly Finance Charge**

The finance charge is calculated based on the average daily balance and the monthly finance rate of **1.9%**.

\[
\text{Finance Charge} = 474.28 \times 0.019 = 9.01
\]

So, the **monthly finance charge** is **$9.01**.

---

### 3. **Balance at the Start of Next Month**

To find the balance at the start of the next month (June 1st), we need to add the finance charge to the final balance on May 31.

- Final balance on May 31: $465.38
- Monthly finance charge: $9.01

\[
\text{Balance on June 1} = 465.38 + 9.01 = 474.39
\]

So, the **balance at the start of next month** is **$474.39**.

---

Would you like further details or clarifications on any part of this? Here are five related questions to consider:

1. How is the average daily balance method different from other finance charge methods?
2. What would be the effect of making a larger payment earlier in the billing cycle?
3. How would the finance charge change if the monthly rate was 2% instead of 1.9%?
4. What is the significance of the billing cycle length in calculating finance charges?
5. How would a purchase at the very end of the month affect next month’s finance charge?

**Tip**: Paying off more of your balance early in the billing cycle helps reduce the average daily balance, lowering the finance charge!

On May 1, the balance on your credit card is $579.30. On May 2, you make a purchase for $85.61. On May 9, you make a payment of $280. On May 17, you make a purchase for $31.22, and on May 29, you make a purchase for $49.25. Assume the billing date is the 1st of the month and the monthly finance charge is 1.9%. 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 and monthly finance charge for a credit card balance of $579.30 with a 1.9% monthly finance charge. This step-by-step solution covers key finance concepts and helps you determine the final balance for the next billing cycle. Suitable for high school students and those learning personal finance.

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