Question

Jerry has a credit card that uses the average daily balance method. For the first 14 days of one of his billing cycles, his balance was $1050, and for the last 16 days of the billing cycle, his balance was $1280. If his credit card’s APR is 19%, which of these expressions could be used to calculate the amount Jerry was charged in interest for the billing cycle?

Answer 1

To calculate the interest charge using the average daily balance method, we first need to determine the average daily balance for the entire billing cycle.

1. **Calculate total balances for each period:**
- For the first 14 days, Jerry's balance was $1050:
\[
\text{Total for the first 14 days} = 1050 \times 14 = 14,700
\]
- For the last 16 days, Jerry's balance was $1280:
\[
\text{Total for the last 16 days} = 1280 \times 16 = 20,480
\]

2. **Add the totals together to get the total balance for the entire billing cycle:**
\[
\text{Total balance for the cycle} = 14,700 + 20,480 = 35,180
\]

3. **Calculate the average daily balance for the entire billing cycle:**
- The total number of days in the billing cycle is \(14 + 16 = 30\).
\[
\text{Average daily balance} = \frac{35,180}{30} \approx 1,172.67
\]

4. **Determine the daily interest rate:**
- The APR is 19%, which is expressed as a decimal for calculations:
\[
\text{Daily interest rate} = \frac{19\%}{365} \approx \frac{0.19}{365} \approx 0.00052055
\]

5. **Calculate the interest charged for the billing cycle:**
- Multiply the average daily balance by the daily interest rate and then by the number of days in the billing cycle:
\[
\text{Interest for the billing cycle} = \text{Average daily balance} \times \text{Daily interest rate} \times \text{Number of days}
\]
Plugging in the numbers:
\[
\text{Interest} = 1,172.67 \times 0.00052055 \times 30
\]

Thus, any expression that models \( \frac{35,180}{30} \times \frac{0.19}{365} \times 30 \) can be used to calculate the amount Jerry was charged in interest for the billing cycle.

Another way to express the interest can be simplified as:
\[
\text{Interest} = \frac{35,180 \times 0.19}{365}
\]

These would be valid representations of the interest charged for Jerry's billing cycle.