To determine the finance charge on the credit card over the given month, we follow several steps starting with computing the average daily balance and then applying the given Annual Percentage Rate (APR). Here is the detailed, step-by-step solution:
### Step 1: Determine the Total Days and Corresponding Balances
The table provides the balances for different periods within the month:
- For days 1 to 3, the balance is \[tex]$200.
- For days 4 to 20, the balance is \$[/tex]300.
- For days 21 to 30, the balance is \[tex]$150.
First, let's determine the number of days each balance was maintained:
1. From days 1 to 3: 3 days with a balance of \$[/tex]200.
2. From days 4 to 20: 17 days with a balance of \[tex]$300 (20 - 4 + 1 = 17 days).
3. From days 21 to 30: 10 days with a balance of \$[/tex]150 (30 - 21 + 1 = 10 days).
### Step 2: Calculate the Weighted Sum of Balances
Next, we calculate the weighted sum of the balances by multiplying each balance by the number of days it was maintained:
- For \[tex]$200 over 3 days: \(200 \times 3 = 600\)
- For \$[/tex]300 over 17 days: [tex]\(300 \times 17 = 5100\)[/tex]
- For \[tex]$150 over 10 days: \(150 \times 10 = 1500\)
Summing these amounts gives:
\[ 600 + 5100 + 1500 = 7200 \]
### Step 3: Calculate the Total Number of Days
The total number of days in the month is:
\[ 3 + 17 + 10 = 30 \]
### Step 4: Compute the Average Daily Balance
The average daily balance is found by dividing the weighted sum of the balances by the total number of days:
\[ \text{Average Daily Balance} = \frac{7200}{30} = 240.0 \]
### Step 5: Calculate the Monthly Finance Charge
The APR given is 15.5%. To convert this annual rate to a monthly rate, we divide by 12 (since there are 12 months in a year):
\[ \text{Monthly Interest Rate} = \frac{15.5\%}{12} = \frac{0.155}{12} \approx 0.0129167 \]
The finance charge for the month is then calculated by multiplying the average daily balance by the monthly interest rate:
\[ \text{Finance Charge} = 240.0 \times 0.0129167 \approx 3.1 \]
### Step 6: Round the Finance Charge
Finally, we round the finance charge to the nearest cent:
\[ \text{Finance Charge} \approx \$[/tex]3.10 \]
Therefore, the finance charge for the credit card over the one month period is:
[tex]\[ \boxed{3.10} \][/tex]
