Certainly! Let's walk through calculating the amount Terry was charged in interest for the billing cycle step by step.
1. Identify relevant details:
- Days first period: 18 days
- Balance first period: \[tex]$350
- Days second period: 12 days
- Balance second period: \$[/tex]520
- Annual Percentage Rate (APR): 14% or 0.14
- Days in a year: 365 days
- The billing cycle is for 30 days.
2. Calculate Average Daily Balance (ADB):
[tex]\[
\text{ADB} = \frac{\text{(Number of days with balance 1} \times \text{balance 1}) + (\text{Number of days with balance 2} \times \text{balance 2})}{\text{Total number of days}}
\][/tex]
Plugging in the numbers:
[tex]\[
\text{ADB} = \frac{(18 \times 350) + (12 \times 520)}{30}
\][/tex]
First, compute the individual products:
[tex]\[
18 \times 350 = 6300
\][/tex]
[tex]\[
12 \times 520 = 6240
\][/tex]
Now sum these results:
[tex]\[
6300 + 6240 = 12540
\][/tex]
Divide by the total number of days in the billing cycle:
[tex]\[
\text{ADB} = \frac{12540}{30} = 418
\][/tex]
3. Calculate Daily Periodic Rate:
[tex]\[
\text{Daily Periodic Rate} = \frac{\text{APR}}{\text{Days in a year}}
\][/tex]
Given APR is 0.14:
[tex]\[
\text{Daily Periodic Rate} = \frac{0.14}{365}
\][/tex]
4. Calculate Interest for the Billing Cycle:
Use the Daily Periodic Rate and multiply by the number of days in the billing cycle (30 days):
[tex]\[
\text{Interest} = \left(\frac{0.14}{365} \times 30\right) \times \text{ADB}
\][/tex]
The Average Daily Balance (ADB) was calculated to be 418.
5. Substitute in one expression:
Expression A is:
[tex]\[
\left(\frac{0.14}{365} \cdot 30\right)\left(\frac{18 \times 350 + 12 \times 520}{30}\right)
\][/tex]
This matches our calculations exactly, as we already determined the correct method for calculating Terry's interest.
### Conclusion:
The appropriate expression to calculate the amount Terry was charged in interest is:
[tex]\[ \boxed{\text{A}} \][/tex]
