Sure, let's break down the steps to calculate the finance charge and the new balance using the previous balance method.
### Given Data:
- Previous balance = [tex]$179.32
- Annual interest rate = 16%
- New purchases = $[/tex]117.42
- Payments/credits = [tex]$85.00
### Steps:
#### 1. Calculate the Monthly Interest Rate
The annual interest rate must be converted to a monthly interest rate since credit card interest is typically compounded monthly.
\[
\text{Monthly interest rate} = \frac{\text{Annual interest rate}}{12} = \frac{16\%}{12} = 1.33\%
\]
In decimal form, 1.33% is 0.0133.
#### 2. Calculate the Finance Charge
The finance charge is calculated based on the previous month's balance.
\[
\text{Finance charge} = \text{Previous balance} \times \text{Monthly interest rate}
\]
\[
\text{Finance charge} = 179.32 \times 0.0133 = 2.39
\]
This has been calculated as \(2.3909333333333334\) dollars.
#### 3. Calculate the New Balance
Now, to find the new balance, we need to add new purchases and the finance charge to the previous balance and then subtract any payments or credits.
\[
\text{New balance} = \text{Previous balance} + \text{Finance charge} + \text{New purchases} - \text{Payments/credits}
\]
Substituting the known values:
\[
\text{New balance} = 179.32 + 2.3909333333333334 + 117.42 - 85.00
\]
\[
\text{New balance} = 214.1309333333333
\]
### Answer:
- The finance charge is $[/tex]2.3909333333333334
- The new balance is $214.1309333333333
Hope this clarifies the steps to achieve the solution!
