To determine the finance charge on the average daily balance for this credit card over a 1-month period, we will follow these steps:
1. Identify the number of days the balance was at each value:
- Days 1-5: \[tex]$200 (Initial Balance)
- Days 6-20: \$[/tex]350 (After a \[tex]$150 purchase)
- Days 21-30: \$[/tex]150 (After a \[tex]$200 payment)
2. Calculate the total number of days in the month:
- Total days = \(5 + 15 + 10 = 30\)
3. Calculate the weighted balance for each period and sum them:
- Days 1-5: \(5 \text{ days} \times \$[/tex]200 = \[tex]$1000\)
- Days 6-20: \(15 \text{ days} \times \$[/tex]350 = \[tex]$5250\)
- Days 21-30: \(10 \text{ days} \times \$[/tex]150 = \[tex]$1500\)
- Total weighted balance = \( \$[/tex]1000 + \[tex]$5250 + \$[/tex]1500 = \[tex]$7750 \)
4. Determine the average daily balance:
- Average daily balance = Total weighted balance / Total days
- \( \text{Average daily balance} = \$[/tex]7750 / 30 = \[tex]$258.33 \) (rounded to two decimal places)
5. Calculate the monthly interest rate from the APR:
- APR = 15.5\%
- Monthly interest rate = APR / 12
- \( \text{Monthly interest rate} = 0.155 / 12 ≈ 0.01291667 \)
6. Calculate the finance charge:
- Finance charge = Monthly interest rate × Average daily balance
- \( \text{Finance charge} = 0.01291667 \times 258.33 ≈ 3.34 \) (rounded to two decimal places)
Hence, the finance charge on the average daily balance for this credit card over this 1-month period is approximately \$[/tex]3.34.
