Ronnie has a credit card that uses the previous balance method. The opening balance of one of his 30-day billing cycles was \[tex]$4790 for the first 4 days of the billing cycle. He then paid off his entire balance and didn't make any new purchases. If his credit card's APR is 15%, which expression could be used to calculate the amount Ronnie was charged in interest for the billing cycle?

A. \(\left(\frac{0.15}{365} \cdot 30\right)\left(\frac{4 \cdot \$[/tex]0 + 26 \cdot \[tex]$4790}{30}\right)\)

B. \(\left(\frac{0.15}{365} \cdot 30\right)(\$[/tex]0)\)

C. [tex]\(\left(\frac{0.15}{365} \cdot 30\right)\left(\frac{4 \cdot \$4790 + 26 \cdot \$0}{30}\right)\)[/tex]

D. [tex]\(\left(\frac{0.15}{365} \cdot 30\right)(\$4790)\)[/tex]



Answer :

Let's break down the problem step by step to find the correct expression used to calculate the interest charged for Ronnie's billing cycle.

### Step 1: Understanding the Days with Balance and Without Balance

- Opening Balance: $4790
- Days with this Balance: 4 days
- Total Days in Billing Cycle: 30 days
- Days Without Balance: 30 days - 4 days = 26 days

### Step 2: Calculate the Average Daily Balance
We need to compute the average daily balance over the 30-day billing cycle.

The formula for the average daily balance when there are days with a balance and days without a balance is:

[tex]\[ \text{Average Daily Balance} = \frac{(\text{Days with Balance} \times \text{Balance}) + (\text{Days without Balance} \times 0)}{\text{Total Days in Billing Cycle}} \][/tex]

Using Ronnie's data:
[tex]\[ \text{Average Daily Balance} = \frac{(4 \text{ days} \times 4790 \text{ dollars}) + (26 \text{ days} \times 0 \text{ dollars})}{30 \text{ days}} = \frac{4 \times 4790}{30} \][/tex]

Performing the calculation:

[tex]\[ \text{Average Daily Balance} = \frac{19160}{30} = 638.6666666666666 \text{ dollars} \][/tex]

### Step 3: Calculate the Interest Charged
Interest is charged based on the average daily balance and the annual percentage rate (APR).

The formula for interest charged over the billing cycle is:

[tex]\[ \text{Interest Charged} = \left(\frac{\text{APR}}{\text{Days in a Year}} \times \text{Total Days in Billing Cycle}\right) \times \text{Average Daily Balance} \][/tex]

Given:
- APR: 0.15 (15%)
- Days in a Year: 365
- Total Days in Billing Cycle: 30

Using the data:
[tex]\[ \text{Interest Charged} = \left(\frac{0.15}{365} \times 30\right) \times 638.6666666666666 \][/tex]

Performing the calculation:

[tex]\[ \text{Interest Charged} = \left(\frac{0.15}{365} \times 30\right) \times 638.6666666666666 = 7.873972602739725 \text{ dollars} \][/tex]

### Step 4: Identify the Correct Expression
Now, from the given options, we need to select the correct expression that corresponds to our calculation.

The correct expression that matches our step-by-step breakdown is:
[tex]\[ \left(\frac{0.15}{365} \cdot 30\right) \left(\frac{4 \times 4790 + 26 \times 0}{30}\right) \][/tex]

### Conclusion
The correct expression for calculating the interest charged is:

[tex]\[ \boxed{\left(\frac{0.15}{365} \cdot 30\right)\left(\frac{4 \cdot 4790+26 \cdot 0}{30}\right)} \][/tex]

Which corresponds to option C.