To calculate Yolanda's finance charges using different methods, we'll go through each method step-by-step:
### 1. Previous Balance Method
According to the previous balance method, the finance charge is based on the beginning balance at the start of the billing cycle. Here, the Annual Percentage Rate (APR) is 16.22%.
First, we need to convert the APR to a monthly rate:
[tex]\[
\text{Monthly Rate} = \frac{16.22\%}{12} = \frac{0.1622}{12} \approx 0.01351667
\][/tex]
Next, we compute the finance charge using the beginning balance:
[tex]\[
\text{Previous Balance Finance Charge} = 857.14 \times 0.01351667 \approx 11.5857
\][/tex]
### 2. Adjusted Balance Method
For the adjusted balance method, the finance charge is calculated based on the balance after all payments (but before new purchases) are taken into account.
First, we determine the adjusted balance:
[tex]\[
\text{Adjusted Balance} = \text{Beginning Balance} - \text{Payments} = 857.14 - 50.00 = 807.14
\][/tex]
Then, we compute the finance charge using the adjusted balance:
[tex]\[
\text{Adjusted Balance Finance Charge} = 807.14 \times 0.01351667 \approx 10.9098
\][/tex]
### 3. Daily Balance Method
The daily balance method involves calculating an average daily balance for the billing cycle and then computing the finance charge based on that average.
First, we track the balance changes day-by-day:
[tex]\[
\begin{align*}
1-2 & : 857.14 \\
3-9 & : 857.14 + 76.95 = 934.09 \\
10-23 & : 934.09 - 50.00 = 884.09 \\
24-30 & : 884.09 + 43.19 = 927.28 \\
\end{align*}
\][/tex]
Next, we calculate the daily balances and then average them:
[tex]\[
\begin{align*}
\text{Sum of Daily Balances} & = (857.14 \times 2) + (934.09 \times 7) + (884.09 \times 14) + (927.28 \times 7) \\
& = 1714.28 + 6538.63 + 12377.26 + 6490.96 = 27121.13
\end{align*}
\][/tex]
[tex]\[
\text{Average Daily Balance} = \frac{27121.13}{30} \approx 904.0377
\][/tex]
Then, we compute the finance charge using this average balance:
[tex]\[
\text{Daily Balance Finance Charge} = 904.0377 \times 0.01351667 \approx 12.2154
\][/tex]
### Comparing the Finance Charges
We've computed the following finance charges:
- Previous Balance Finance Charge: \[tex]$11.5857
- Adjusted Balance Finance Charge: \$[/tex]10.9098
- Daily Balance Finance Charge: \[tex]$12.2154
The finance charge that is neither the lowest nor the highest among these values is \$[/tex]11.5857. Thus, the correct answer is:
b. [tex]\( \$11.59 \)[/tex]
