To find the amount Lowell was charged in interest for the billing cycle, we need to follow these steps:
1. Calculate the average daily balance:
- Lowell's balance was [tex]\(\$1360\)[/tex] for the first 10 days.
- Then he made a purchase, increasing his balance to [tex]\(\$1830\)[/tex] for the next 10 days.
- Finally, he made a payment, reducing his balance to [tex]\(\$1090\)[/tex] for the last 10 days.
The average daily balance is calculated by taking the sum of the daily balances and dividing it by the number of days in the billing cycle. For each period, you multiply the balance by the number of days it was held. Then you sum these products and divide by the total number of days in the billing cycle.
[tex]\[
\text{Average Daily Balance} = \frac{(10 \cdot 1360) + (10 \cdot 1830) + (10 \cdot 1090)}{30}
\][/tex]
Let's calculate the sum of the products:
[tex]\[
10 \cdot 1360 + 10 \cdot 1830 + 10 \cdot 1090
= 13600 + 18300 + 10900 = 42800
\][/tex]
Now, divide by 30 to get the average daily balance:
[tex]\[
\text{Average Daily Balance} = \frac{42800}{30} = 1426.67
\][/tex]
2. Calculate the daily interest rate:
- The APR is [tex]\(28\%\)[/tex].
- The daily interest rate is calculated by dividing the APR by the number of days in a year ([tex]\(365\)[/tex]).
[tex]\[
\text{Daily Interest Rate} = \frac{0.28}{365}
\][/tex]
3. Calculate the interest charged for the billing cycle:
- The interest for the billing cycle can be found by multiplying the daily interest rate by the number of days in the billing cycle ([tex]\(30\)[/tex]) and then multiplying by the average daily balance.
[tex]\[
\text{Interest Charged} = \left(\frac{0.28}{365} \cdot 30\right) \cdot 1426.67
\][/tex]
The correct expression from the given options that matches this process is:
D. [tex]\(\left(\frac{0.28}{365} \cdot 30\right)\left(\frac{10 \cdot 1360 + 10 \cdot 1830 + 10 \cdot 1090}{30}\right)\)[/tex]
This expression accurately represents the steps we followed to calculate the interest charged on Lowell's credit card for the billing cycle.
