SOLUTION: Calculate the monthly finance charge for the credit card transaction. Assume that it takes 10 days for a payment to be received and recorded and that the month is 30 days long. (Ro

Question 1201558: Calculate the monthly finance charge for the credit card transaction. Assume that it takes 10 days for a payment to be received and recorded and that the month is 30 days long. (Round your answer to the nearest cent.)
Balance: $300
Rate: 17%
Payment: $50
Method: Adjusted balance

Answer by asinus(45) (Show Source): You can put this solution on YOUR website!
To calculate the monthly finance charge for the credit card transaction using the adjusted balance method, we will follow these steps:
### Step 1: Calculate the Adjusted Balance
1. **Initial Balance**: $300
2. **Payment Made**: $50
3. **Days Until Payment is Processed**: 10 days
4. **Days in the Billing Cycle**: 30 days
Since the payment takes 10 days to process, the adjusted balance for the first 10 days is the full balance of $300. After the payment is processed, the balance will be reduced to $250 for the remaining 20 days.
### Step 2: Calculate the Weighted Average Balance
The weighted average balance can be calculated as follows:
$$
\text{Weighted Average Balance} = \left( \text{Balance}_1 \times \text{Days}_1 + \text{Balance}_2 \times \text{Days}_2 \right) / \text{Total Days}
$$
Where:
- $ \text{Balance}_1 = 300 $ (for the first 10 days)
- $ \text{Days}_1 = 10 $
- $ \text{Balance}_2 = 250 $ (for the remaining 20 days)
- $ \text{Days}_2 = 20 $
Substituting the values:
$$
\text{Weighted Average Balance} = \left( 300 \times 10 + 250 \times 20 \right) / 30
$$
Calculating the numerator:
$$
300 \times 10 = 3000
$$
$$
250 \times 20 = 5000
$$
$$
\text{Total} = 3000 + 5000 = 8000
$$
Now, divide by the total number of days:
$$
\text{Weighted Average Balance} = \frac{8000}{30} \approx 266.67
$$
### Step 3: Calculate the Monthly Finance Charge
The monthly finance charge is calculated using the formula:
$$
\text{Finance Charge} = \text{Weighted Average Balance} \times \left( \frac{\text{Annual Interest Rate}}{12} \right)
$$
Where:
- Annual Interest Rate = 17% = 0.17
Calculating the monthly interest rate:
$$
\text{Monthly Interest Rate} = \frac{0.17}{12} \approx 0.01416667
$$
Now, substituting the values into the finance charge formula:
$$
\text{Finance Charge} = 266.67 \times 0.01416667 \approx 3.78
$$
### Final Result
Rounding to the nearest cent, the monthly finance charge is:
$$
\boxed{3.78}
$$
RELATED QUESTIONS
Calculate the monthly finance charge for the following credit card transaction. Assume... (answered by Theo)

This is a problem I have, I have tried everything to solve it and can't. I have one... (answered by math_tutor2020)

Hello I have a question about trying to find the finance charge. I could not figure out... (answered by greenestamps)

I HAVE TWO QUESTIONS! PLEASE HELP! SUPPOSE THAT YOU WANT TO PURCHASE A HOME FOR... (answered by aprylk25)

Malik purchased a pair of roller blades that were originally priced at $250 for a sale... (answered by KMST)

The following problem is somewhat confusing. The answer I have is $470., but I don't... (answered by josmiceli)

Suppose we have a credit card company that sets the due date every 1st month. If its... (answered by ikleyn)

Calculate the amount financed, the finance charge, and the monthly payments (in $) for... (answered by Theo)

The irrigation system needs about 3 times as long to complete a job as another irrigation (answered by josmiceli)