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.
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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: \[ \text{Total for the last 16 days} = 1280 \times 16 = 20,480 \]
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Add the totals together to get the total balance for the entire billing cycle: \[ \text{Total balance for the cycle} = 14,700 + 20,480 = 35,180 \]
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Calculate the average daily balance for the entire billing cycle:
- The total number of days in the billing cycle is \(14 + 16 = 30\). \[ \text{Average daily balance} = \frac{35,180}{30} \approx 1,172.67 \]
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Determine the daily interest rate:
- The APR is 19%, which is expressed as a decimal for calculations: \[ \text{Daily interest rate} = \frac{19%}{365} \approx \frac{0.19}{365} \approx 0.00052055 \]
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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.
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