Questions: On September 7, the billing date, Verna had a balance due of 566.35 on her credit card. Assume that the interest rate is 1.1% per month. Suppose that Verna's bank uses the average daily balance method. Answer parts (a) through (d). Sept. 10 Payment 260.00 Sept. 23 Charge: Airline ticket 332.00 Sept. 24 Charge: Hotel bill 192.02 Oct. 1 Charge: Clothing 84.76 a) Determine Verna's average daily balance for the billing period from September 7 to October 7. The average daily balance for the billing period was . (Round to the nearest cent as needed.)

On September 7, the billing date, Verna had a balance due of 566.35 on her credit card. Assume that the interest rate is 1.1% per month. Suppose that Verna's bank uses the average daily balance method. Answer parts (a) through (d).

Sept. 10 Payment 260.00

Sept. 23 Charge: Airline ticket 332.00

Sept. 24 Charge: Hotel bill 192.02

Oct. 1 Charge: Clothing 84.76

a) Determine Verna's average daily balance for the billing period from September 7 to October 7.

The average daily balance for the billing period was . (Round to the nearest cent as needed.)

Transcript text: On September 7 , the billing date, Verna had a balance due of $\$ 566.35$ on her credit card. Assume that the interest rate is $1.1 \%$ per month. Suppose that Verna's bank uses the average daily balance method. Answer parts (a) through (d). \begin{tabular}{|l|l|r|} \hline Sept. 10 & Payment & $\$ 260.00$ \\ \hline Sept. 23 & Charge: Airline ticket & $\$ 332.00$ \\ \hline Sept. 24 & Charge: Hotel bill & $\$ 192.02$ \\ \hline Oct. 1 & Charge: Clothing & $\$ 84.76$ \\ \hline \end{tabular} a) Determine Verna's average daily balance for the billing period from September 7 to October 7. The average daily balance for the billing period was $\$$ $\square$ . (Round to the nearest cent as needed.)

Solution

Solution Steps

Step 1: Initial Setup

We start with Verna's initial balance on September 7, which is given as $ B_0 = 566.35 $.

Step 2: Transactions and Balance Changes

We will track the balance changes due to the transactions that occur during the billing period:

September 10: Payment of $ 260.00 $ \[ B_1 = B_0 - 260.00 = 566.35 - 260.00 = 306.35 \]
September 23: Charge for an airline ticket of $ 332.00 $ \[ B_2 = B_1 + 332.00 = 306.35 + 332.00 = 638.35 \]
September 24: Charge for a hotel bill of $ 192.02 $ \[ B_3 = B_2 + 192.02 = 638.35 + 192.02 = 830.37 \]
October 1: Charge for clothing of $ 84.76 $ \[ B_4 = B_3 + 84.76 = 830.37 + 84.76 = 915.13 \]

Step 3: Calculate Days for Each Balance

Next, we calculate the number of days each balance was in effect:

From September 7 to September 10: $ 3 $ days at $ 566.35 $
From September 10 to September 23: $ 13 $ days at $ 306.35 $
From September 23 to September 24: $ 1 $ day at $ 638.35 $
From September 24 to October 1: $ 7 $ days at $ 830.37 $
From October 1 to October 7: $ 6 $ days at $ 915.13 $

Step 4: Calculate Total Balance Days

Now we calculate the total balance days: \[ \text{Total Balance Days} = (3 \times 566.35) + (13 \times 306.35) + (1 \times 638.35) + (7 \times 830.37) + (6 \times 915.13) \] Calculating each term:

$ 3 \times 566.35 = 1699.05 $
$ 13 \times 306.35 = 3982.55 $
$ 1 \times 638.35 = 638.35 $
$ 7 \times 830.37 = 5812.59 $
$ 6 \times 915.13 = 5490.78 $

Adding these together: \[ \text{Total Balance Days} = 1699.05 + 3982.55 + 638.35 + 5812.59 + 5490.78 = 17623.32 \]

Step 5: Calculate Average Daily Balance

The total number of days in the billing period is $ 30 $ days (from September 7 to October 7). Thus, the average daily balance is calculated as: \[ \text{Average Daily Balance} = \frac{\text{Total Balance Days}}{\text{Total Days}} = \frac{17623.32}{30} = 587.44 \]