To determine the finance charge on the average daily balance, we need to follow these steps:
### Step 1: Calculate the total balance days
We need to take into account the balance for each period and the number of days within that period, then sum the products of balances and days.
1. Days 1-3: Balance = \[tex]$200
- Duration: 3 days
- Total balance days: \(3 \text{ days} \times \$[/tex]200 = \[tex]$600 \text{ balance days}\)
2. Days 4-20: Balance = \$[/tex]300
- Duration: 17 days
- Total balance days: [tex]\(17 \text{ days} \times \$300 = \$5100 \text{ balance days}\)[/tex]
3. Days 21-30: Balance = \[tex]$150
- Duration: 10 days
- Total balance days: \(10 \text{ days} \times \$[/tex]150 = \[tex]$1500 \text{ balance days}\)
Adding these together:
\[ \text{Total balance days} = \$[/tex]600 + \[tex]$5100 + \$[/tex]1500 = \[tex]$7200 \text{ balance days} \]
### Step 2: Calculate the average daily balance
Average daily balance is found by dividing the total balance days by the number of days in the month:
\[ \text{Average daily balance} = \frac{\$[/tex]7200 \text{ balance days}}{30 \text{ days}} = \[tex]$240 \]
### Step 3: Determine the monthly interest rate
The Annual Percentage Rate (APR) is 18%. To find the monthly interest rate, we convert APR to a daily rate and then multiply by the number of days in the month.
1. APR (Annual Percentage Rate) = 18%
2. Days in a year = 365
The daily interest rate is found by dividing APR by the number of days in a year:
\[ \text{Daily interest rate} = \frac{18\%}{365} = 0.049315\% \approx 0.00049315 \text{ (as a decimal)} \]
Then, the monthly interest rate for 30 days:
\[ \text{Monthly interest rate} = 0.00049315 \times 30 = 0.014794520547945205 \]
### Step 4: Calculate the finance charge
Finally, we compute the finance charge by multiplying the average daily balance by the monthly interest rate:
\[ \text{Finance Charge} = \$[/tex]240 \times 0.014794520547945205 = \[tex]$3.55 \]
### Conclusion
The finance charge for the credit card over the 1-month period is:
\[
\text{Finance Charge} = \$[/tex]3.55
\]
