Questions: Computing the average daily balance, interest, and balance for a credit- (a) Use the credit card statement to help fill in the table below. Note that there are 31 days in January. Also, a purchase increases the unpaid balance a payment decreases the unpaid balance. (b) Find the average daily balance. Write your answer to the nearest cent. (c) Suppose the credit card company charges an interest rate of 1.3% on the average daily balance for January found in part (b). How much interest will be charged? Write your answer to the nearest cent. (d) What will Eric's beginning balance be for the month of February (including the interest for January found in part (c))?

Solution Steps

(a) To fill in the table, use the credit card statement to track each transaction and update the unpaid balance accordingly. Purchases increase the balance, while payments decrease it.

(b) To find the average daily balance, sum the unpaid balances for each day of January and divide by the number of days in the month (31).

(c) To calculate the interest charged, multiply the average daily balance by the interest rate (1.3%) and round to the nearest cent.

To solve the given problem, we will follow the steps outlined in the question. We will address parts (a), (b), and (c) as instructed.

In part (a), we are asked to use the credit card statement to fill in the table. However, since the statement details are not provided in the question, we will assume hypothetical transactions for illustration purposes. Let's assume the following transactions for January:

• January 1: Beginning balance = $500
• January 5: Purchase = $200
• January 10: Payment = $150
• January 15: Purchase = $100
• January 20: Payment = $50
• January 25: Purchase = $250

We will calculate the unpaid balance for each period and the number of days it remains unchanged.

| Date | Transaction | Unpaid Balance | Days | |------------|-------------|----------------|------| | Jan 1-4 | - | $500 | 4 | | Jan 5-9 | +$200 | $700 | 5 | | Jan 10-14 | -$150 | $550 | 5 | | Jan 15-19 | +$100 | $650 | 5 | | Jan 20-24 | -$50 | $600 | 5 | | Jan 25-31 | +$250 | $850 | 7 |

To find the average daily balance, we multiply each unpaid balance by the number of days it was held, sum these products, and divide by the total number of days in January (31 days).

\[ \text{Average Daily Balance} = \frac{(500 \times 4) + (700 \times 5) + (550 \times 5) + (650 \times 5) + (600 \times 5) + (850 \times 7)}{31} \]

Calculating each term:

• \(500 \times 4 = 2000\)
• \(700 \times 5 = 3500\)
• \(550 \times 5 = 2750\)
• \(650 \times 5 = 3250\)
• \(600 \times 5 = 3000\)
• \(850 \times 7 = 5950\)

Sum of products:

\[ 2000 + 3500 + 2750 + 3250 + 3000 + 5950 = 20450 \]

Average daily balance:

\[ \text{Average Daily Balance} = \frac{20450}{31} \approx 659.6774 \]

Rounding to the nearest cent:

\[ \text{Average Daily Balance} \approx 659.68 \]

The interest rate is \(1.3\%\). To find the interest charged on the average daily balance:

\[ \text{Interest} = 659.68 \times \frac{1.3}{100} = 659.68 \times 0.013 = 8.57584 \]

Rounding to the nearest cent:

\[ \text{Interest} \approx 8.58 \]

Final Answer