To solve this problem, we need to understand how to calculate the interest charged on Ted's credit card using the average daily balance method.
First, let's outline the key elements of the calculation:
1. Calculate the Average Daily Balance:
- For the first 9 days, Ted's balance was \[tex]$2030.
- For the last 21 days, his balance was \$[/tex]1450.
- The billing cycle is 30 days.
The formula for the average daily balance is:
[tex]\[
\text{Average Daily Balance} = \frac{(9 \times 2030) + (21 \times 1450)}{30}
\][/tex]
2. Calculate the Daily Interest Rate:
- The APR is 23%, so the daily interest rate is calculated by dividing the APR by the number of days in a year (365 days).
[tex]\[
\text{Daily Interest Rate} = \frac{0.23}{365}
\][/tex]
3. Calculate the Interest Charged:
- The interest charged is then:
[tex]\[
\text{Interest Charged} = \text{Daily Interest Rate} \times 30 \times \text{Average Daily Balance}
\][/tex]
Now let's break it down step-by-step with the given options:
Step 1: Calculate the Average Daily Balance:
[tex]\[
\text{Average Daily Balance} = \frac{(9 \times 2030) + (21 \times 1450)}{30}
\][/tex]
Using the numeric values:
[tex]\[
\text{Average Daily Balance} = \frac{(9 \times 2030) + (21 \times 1450)}{30} = \frac{(18270) + (30450)}{30} = \frac{48720}{30} = 1624.0
\][/tex]
Step 2: Calculate the Daily Interest Rate:
[tex]\[
\text{Daily Interest Rate} = \frac{0.23}{365} = 0.0006301369863013699
\][/tex]
Step 3: Calculate the Interest Charged:
[tex]\[
\text{Interest Charged} = 0.0006301369863013699 \times 30 \times 1624.0 \approx 30.70027397260274
\][/tex]
Given the multiple choice options, the expression that matches our setup would be:
[tex]\[
\left(\frac{0.23}{365} \cdot 30\right)\left(\frac{9 \cdot \$ 2030+21 \cdot \$ 1450}{30}\right)
\][/tex]
Thus, the correct answer is:
A.
