To determine the finance charge on the average daily balance for the credit card over the 1-month period, follow these detailed steps:
### Step 1: Understand the Given Data
- APR (Annual Percentage Rate): 20% or 0.20
- Days in a year: 365
- Days in the month: 30
### Step 2: Calculate the Daily Interest Rate
The daily interest rate is obtained by dividing the APR by the number of days in a year.
[tex]\[ \text{Daily Interest Rate} = \frac{\text{APR}}{\text{Days in a year}} = \frac{0.20}{365} \approx 0.0005479452 \][/tex]
### Step 3: Record the Balances and Duration
From the table:
- Balance of [tex]$200 for 3 days (Days 1-3)$[/tex]
- Balance of [tex]$300 for 17 days (Days 4-20)$[/tex]
- Balance of [tex]$150 for 10 days (Days 21-30)$[/tex]
### Step 4: Calculate the Total Balance Days
For each balance, multiply the balance by the number of days it was held:
[tex]\[ \text{Total Balance Days} = (200 \times 3) + (300 \times 17) + (150 \times 10) \][/tex]
[tex]\[ = 600 + 5100 + 1500 \][/tex]
[tex]\[ = 7200 \][/tex]
### Step 5: Compute the Average Daily Balance
The average daily balance is the sum of the total balance days divided by the number of days in the month.
[tex]\[ \text{Average Daily Balance} = \frac{\text{Total Balance Days}}{\text{Days in the month}} \][/tex]
[tex]\[ = \frac{7200}{30} = 240 \][/tex]
### Step 6: Calculate the Finance Charge
The finance charge is determined by multiplying the average daily balance by the daily interest rate, and then by the number of days in the month:
[tex]\[ \text{Finance Charge} = \text{Average Daily Balance} \times \text{Daily Interest Rate} \times \text{Days in the month} \][/tex]
[tex]\[ = 240 \times 0.0005479452 \times 30 \approx 3.95064 \][/tex]
### Step 7: Round the Finance Charge to the Nearest Cent
The final step is to round the finance charge to the nearest cent:
[tex]\[ \text{Finance Charge} \approx \$3.95 \][/tex]
Therefore, the finance charge on the average daily balance for the credit card over the 1-month period is:
[tex]\[ \boxed{3.95} \][/tex]
