To calculate the average daily balance and the finance charge for the given 30-day billing cycle, follow these steps:
1. Determine the balance before and after each transaction:
- On 7/3, the initial balance is \[tex]$400.
- On 7/18, a payment of \$[/tex]100 is made, reducing the balance:
[tex]\[
\text{Balance on 7/18} = 400 - 100 = \$300
\][/tex]
- On 7/27, a charge of \[tex]$250 is incurred, increasing the balance:
\[
\text{Balance on 7/27} = 300 + 250 = \$[/tex]550
\]
2. Calculate the number of days each balance was held:
- From 7/3 to 7/18:
[tex]\[
\text{Days with balance of \$400} = 18 - 3 = 15 \text{ days}
\][/tex]
- From 7/18 to 7/27:
[tex]\[
\text{Days with balance of \$300} = 27 - 18 = 9 \text{ days}
\][/tex]
- From 7/27 to 7/30 (end of cycle):
[tex]\[
\text{Days with balance of \$550} = 30 - 27 = 3 \text{ days}
\][/tex]
3. Calculate the total balance for each period:
- For balance of \[tex]$400 over 15 days:
\[
\text{Total balance sum} = 400 \times 15 = 6000
\]
- For balance of \$[/tex]300 over 9 days:
[tex]\[
300 \times 9 = 2700
\][/tex]
- For balance of \[tex]$550 over 3 days:
\[
550 \times 3 = 1650
\]
4. Sum the products of balances and their respective days:
\[
\text{Total of all balances} = 6000 + 2700 + 1650 = 10350
\]
5. Calculate the average daily balance:
\[
\text{Average daily balance} = \frac{\text{Total of all balances}}{\text{Number of days in the billing cycle}} = \frac{10350}{30} = 345.0
\]
6. Calculate the finance charge, applying the 2% finance charge on the average daily balance:
\[
\text{Finance charge} = 345.0 \times 0.02 = 6.9
\]
Therefore, the:
- Average daily balance is: \$[/tex]345.0
- Finance charge is: \$6.90
