Questions: For the period beginning October 10, the average daily balance on Perry's credit card was 939. If the balance at the end of the cycle was 450 and the APR on the card is 7.5%, what was the balance due on November 10? Round your answer to the nearest cent, but do not include a sign with your response.

For the period beginning October 10, the average daily balance on Perry's credit card was 939. If the balance at the end of the cycle was 450 and the APR on the card is 7.5%, what was the balance due on November 10?

Round your answer to the nearest cent, but do not include a sign with your response.

Transcript text: For the period beginning October 10, the average daily balance on Perry's credit card was $\$ 939$. If the balance at the end of the cycle was $\$ 450$ and the APR on the card is $7.5 \%$, what was the balance due on November 10? Round your answer to the nearest cent, but do not include a \$ sign with your response.

Solution

Solution Steps

Step 1: Identify the given information

Average daily balance: $939
Balance at the end of the cycle: $450
APR (Annual Percentage Rate): 7.5%

Step 2: Calculate the daily interest rate

The APR is 7.5%, so the daily interest rate is: \[ \text{Daily Interest Rate} = \frac{7.5\%}{365} = \frac{0.075}{365} \approx 0.00020548 \]

Step 3: Calculate the interest for the billing cycle

Assuming the billing cycle is 30 days, the interest for the billing cycle is: \[ \text{Interest} = \text{Average Daily Balance} \times \text{Daily Interest Rate} \times \text{Number of Days} \] \[ \text{Interest} = 939 \times 0.00020548 \times 30 \approx 5.78 \]

Step 4: Calculate the balance due on November 10

The balance due on November 10 is the balance at the end of the cycle plus the interest: \[ \text{Balance Due} = 450 + 5.78 = 455.78 \]