Sure! Let's break down the solution step-by-step to determine Abby's January finance charge using the adjusted balance method.
### Step 1: Understand the Adjusted Balance Method
Using this method, the balance for finance charge calculations is determined after all credits (payments) and debits (purchases) have been posted for the billing cycle.
### Step 2: Initial Balance and Transactions
Abby's initial balance on January 1st is \[tex]$722.10. There are several transactions throughout the month:
- Jan 6: \$[/tex]18.12 purchase
- Jan 7: \[tex]$65.00 payment
- Jan 14: \$[/tex]18.00 purchase
- Jan 20: \[tex]$44.79 purchase
- Jan 23: \$[/tex]34.25 purchase
- Jan 27: \[tex]$40.00 payment
### Step 3: Calculate the Final Balance
We need to adjust the initial balance by adding purchases and deducting payments throughout the billing cycle to find the final balance.
- Starting balance (Jan 1): \$[/tex]722.10
- Jan 6: \[tex]$722.10 + \$[/tex]18.12 = \[tex]$740.22 (purchase)
- Jan 7: \$[/tex]740.22 - \[tex]$65.00 = \$[/tex]675.22 (payment)
- Jan 14: \[tex]$675.22 + \$[/tex]18.00 = \[tex]$693.22 (purchase)
- Jan 20: \$[/tex]693.22 + \[tex]$44.79 = \$[/tex]738.01 (purchase)
- Jan 23: \[tex]$738.01 + \$[/tex]34.25 = \[tex]$772.26 (purchase)
- Jan 27: \$[/tex]772.26 - \[tex]$40.00 = \$[/tex]732.26 (payment)
Final balance by the end of January: \[tex]$732.26
### Step 4: Determine the Daily Rate
The APR (Annual Percentage Rate) given is 11.83%. To find the daily rate, we divide the APR by 365 (the number of days in a year).
\[ \text{Daily Rate} = \frac{11.83\%}{365} = \frac{11.83}{36500} ≈ 0.0003241 \]
### Step 5: Calculate the Finance Charge
To find the finance charge for January, we multiply the final balance by the daily rate and then by the number of days in the billing cycle (30 days).
\[ \text{Finance Charge} = 732.26 \times 0.0003241 \times 30 \]
### Step 6: Compute the Result
Let's compute the finance charge:
\[ \text{Finance Charge} ≈ 732.26 \times 0.0003241 \times 30 \]
\[ ≈ 732.26 \times 0.009723 \]
\[ ≈ 7.12 \]
### Step 7: Identify the Correct Option
Among the given options:
a. \$[/tex]6.08
b. \[tex]$7.12
c. \$[/tex]7.22
d. \[tex]$8.25
The correct finance charge for Abby's account for January is \$[/tex]7.12.
Hence, the answer is:
b. \$7.12
