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Sagot :
Let's find Yolanda's finance charge in November using three different methods: the previous balance method, the adjusted balance method, and the daily balance method. We will then determine which of these is neither the lowest nor the highest.
### 1. Previous Balance Method
The previous balance method calculates the finance charge based on the balance at the beginning of the billing cycle.
- APR: 16.22%
- Monthly Period Rate: [tex]\( \frac{16.22\%}{12} = 0.01622 / 12 = 0.00135166667 \)[/tex]
- Previous Balance: \[tex]$857.14 The finance charge is then calculated as follows: \[ \text{Finance Charge} = \text{Previous Balance} \times \text{Monthly Period Rate} \] \[ \text{Finance Charge} = 857.14 \times 0.00135166667 \] \[ \text{Finance Charge} \approx 11.585675666666665 \] So, the finance charge using the previous balance method is approximately \$[/tex]11.59.
### 2. Adjusted Balance Method
The adjusted balance method calculates the finance charge based on the balance after payments are subtracted within the billing cycle.
- Adjusted Balance: [tex]\( 857.14 - 50.00 = 807.14 \)[/tex]
The finance charge is then calculated as follows:
[tex]\[ \text{Finance Charge} = \text{Adjusted Balance} \times \text{Monthly Period Rate} \][/tex]
[tex]\[ \text{Finance Charge} = 807.14 \times 0.00135166667 \][/tex]
[tex]\[ \text{Finance Charge} \approx 10.909842333333332 \][/tex]
So, the finance charge using the adjusted balance method is approximately \[tex]$10.91. ### 3. Daily Balance Method The daily balance method calculates the finance charge based on the average daily balance over the billing cycle. We need to determine the daily balance for each day and then find the average daily balance. 1. Balances per Day: - Nov 1 - Nov 2: \$[/tex]857.14
- Nov 3 - Nov 9: \[tex]$857.14 + \$[/tex]76.95 = \[tex]$934.09 - Nov 10 - Nov 23: \$[/tex]934.09 - \[tex]$50.00 = \$[/tex]884.09
- Nov 24 - Nov 30: \[tex]$884.09 + \$[/tex]43.19 = \[tex]$927.28 2. Sum of Daily Balances: - \[ 2 \times 857.14 + 7 \times 934.09 + 14 \times 884.09 + 7 \times 927.28 \] - \[ 1714.28 + 6538.63 + 12377.26 + 6490.96 \approx 27121.13 \] 3. Average Daily Balance: - \[ \text{Average Daily Balance} = \frac{\text{Sum of Daily Balances}}{30} = \frac{27121.13}{30} \approx 904.0376666666667 \] The finance charge is then calculated as follows: \[ \text{Finance Charge} = \text{Average Daily Balance} \times \text{Monthly Period Rate} \] \[ \text{Finance Charge} = 904.0376666666667 \times 0.00135166667 \] \[ \text{Finance Charge} \approx 12.219575794444443 \] So, the finance charge using the daily balance method is approximately \$[/tex]12.22.
### Comparing Finance Charges
We have the finance charges from three methods:
- Previous Balance Method: \[tex]$11.59 - Adjusted Balance Method: \$[/tex]10.91
- Daily Balance Method: \[tex]$12.22 Among these, the value that is neither the lowest nor the highest is \$[/tex]11.59.
### Answer
The finance charge that is neither the lowest nor the highest is:
b. \$11.59.
### 1. Previous Balance Method
The previous balance method calculates the finance charge based on the balance at the beginning of the billing cycle.
- APR: 16.22%
- Monthly Period Rate: [tex]\( \frac{16.22\%}{12} = 0.01622 / 12 = 0.00135166667 \)[/tex]
- Previous Balance: \[tex]$857.14 The finance charge is then calculated as follows: \[ \text{Finance Charge} = \text{Previous Balance} \times \text{Monthly Period Rate} \] \[ \text{Finance Charge} = 857.14 \times 0.00135166667 \] \[ \text{Finance Charge} \approx 11.585675666666665 \] So, the finance charge using the previous balance method is approximately \$[/tex]11.59.
### 2. Adjusted Balance Method
The adjusted balance method calculates the finance charge based on the balance after payments are subtracted within the billing cycle.
- Adjusted Balance: [tex]\( 857.14 - 50.00 = 807.14 \)[/tex]
The finance charge is then calculated as follows:
[tex]\[ \text{Finance Charge} = \text{Adjusted Balance} \times \text{Monthly Period Rate} \][/tex]
[tex]\[ \text{Finance Charge} = 807.14 \times 0.00135166667 \][/tex]
[tex]\[ \text{Finance Charge} \approx 10.909842333333332 \][/tex]
So, the finance charge using the adjusted balance method is approximately \[tex]$10.91. ### 3. Daily Balance Method The daily balance method calculates the finance charge based on the average daily balance over the billing cycle. We need to determine the daily balance for each day and then find the average daily balance. 1. Balances per Day: - Nov 1 - Nov 2: \$[/tex]857.14
- Nov 3 - Nov 9: \[tex]$857.14 + \$[/tex]76.95 = \[tex]$934.09 - Nov 10 - Nov 23: \$[/tex]934.09 - \[tex]$50.00 = \$[/tex]884.09
- Nov 24 - Nov 30: \[tex]$884.09 + \$[/tex]43.19 = \[tex]$927.28 2. Sum of Daily Balances: - \[ 2 \times 857.14 + 7 \times 934.09 + 14 \times 884.09 + 7 \times 927.28 \] - \[ 1714.28 + 6538.63 + 12377.26 + 6490.96 \approx 27121.13 \] 3. Average Daily Balance: - \[ \text{Average Daily Balance} = \frac{\text{Sum of Daily Balances}}{30} = \frac{27121.13}{30} \approx 904.0376666666667 \] The finance charge is then calculated as follows: \[ \text{Finance Charge} = \text{Average Daily Balance} \times \text{Monthly Period Rate} \] \[ \text{Finance Charge} = 904.0376666666667 \times 0.00135166667 \] \[ \text{Finance Charge} \approx 12.219575794444443 \] So, the finance charge using the daily balance method is approximately \$[/tex]12.22.
### Comparing Finance Charges
We have the finance charges from three methods:
- Previous Balance Method: \[tex]$11.59 - Adjusted Balance Method: \$[/tex]10.91
- Daily Balance Method: \[tex]$12.22 Among these, the value that is neither the lowest nor the highest is \$[/tex]11.59.
### Answer
The finance charge that is neither the lowest nor the highest is:
b. \$11.59.
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