To calculate the monthly finance charge for the credit card transaction, we can use three different methods: the previous balance method, the adjusted balance method, and the average daily balance method. Below are the detailed steps for each method.
### Given:
- Initial balance: \[tex]$200
- Annual interest rate: 15% (0.15 as a decimal)
- Monthly interest rate: \(\frac{15\%}{12}\)
- Payment: \$[/tex]50
- Days late: 10 days
- Length of the month: 30 days
### Monthly interest rate:
[tex]\[ \text{Monthly interest rate} = \frac{0.15}{12} = 0.0125 \][/tex]
### (a) Previous Balance Method
In this method, the finance charge is calculated based on the balance before the payment.
1. Calculate the finance charge:
[tex]\[ \text{Finance charge} = 200 \times 0.0125 = 2.50 \][/tex]
So, the finance charge using the previous balance method is:
[tex]\[ \text{\$2.50} \][/tex]
### (b) Adjusted Balance Method
In this method, the finance charge is calculated based on the balance after the payment.
1. Calculate the adjusted balance:
[tex]\[ \text{Adjusted balance} = 200 - 50 = 150 \][/tex]
2. Calculate the finance charge:
[tex]\[ \text{Finance charge} = 150 \times 0.0125 = 1.875 \][/tex]
Rounding to the nearest cent, the finance charge using the adjusted balance method is:
[tex]\[ \text{\$1.88} \][/tex]
### (c) Average Daily Balance Method
In this method, the finance charge is calculated based on the average daily balance for the month.
1. Calculate the daily balance for the first 10 days:
[tex]\[ \text{Daily balance for the first 10 days} = 200 \times 10 = 2000 \][/tex]
2. Calculate the adjusted daily balance for the remaining 20 days:
[tex]\[ \text{Adjusted daily balance for the remaining 20 days} = 150 \times 20 = 3000 \][/tex]
3. Total daily balance for the 30 days:
[tex]\[ \text{Total daily balance} = 2000 + 3000 = 5000 \][/tex]
4. Average daily balance:
[tex]\[ \text{Average daily balance} = \frac{5000}{30} = \frac{5000}{30} \approx 166.67 \][/tex]
5. Calculate the finance charge:
[tex]\[ \text{Finance charge} = 166.67 \times 0.0125 \approx 2.083375 \][/tex]
Rounding to the nearest cent, the finance charge using the average daily balance method is:
[tex]\[ \text{\$2.08} \][/tex]
### Summary
The monthly finance charges are:
(a) Previous balance method: \[tex]$2.50
(b) Adjusted balance method: \$[/tex]1.88
(c) Average daily balance method: \$2.08
