Calculate the monthly finance charge for the following 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. Assume 365 days in a year. (Round your answer to the nearest cent.)
$3,000 balance, 21% rate, $1,500 payment, adjusted balance method
To calculate the monthly finance charge using the adjusted balance method, we need to follow these steps:
Step 1: Calculate the average daily balance
To calculate the average daily balance, we need to determine the number of days the balance was at the old (unpaid) balance and the number of days the balance was at the new (paid) balance.
Days at old balance = 20 days (30 days in a month - 10 days for payment processing)
Days at new balance = 10 days (payment processing time)
Average daily balance = (Old balance × Days at old balance + New balance × Days at new balance) / Total days in the billing cycle
Old balance = $3,000
New balance = $3,000 - $1,500 (payment) = $1,500
Total days in the billing cycle = 30 days
Average daily balance = ($3,000 × 20 + $1,500 × 10) / 30 = $66,666.67
Step 2: Calculate the monthly interest rate
The monthly interest rate is determined by the annual interest rate and dividing it by 12 months.
Annual interest rate = 21%
Monthly interest rate = 21% / 12 = 0.0175
Step 3: Calculate the monthly finance charge
To calculate the monthly finance charge, we multiply the average daily balance by the monthly interest rate.
Monthly finance charge = Average daily balance × Monthly interest rate
Monthly finance charge = $66,666.67 × 0.0175 = $1,166.67
Therefore, the monthly finance charge for the credit card transaction is approximately $1,166.67.
To calculate the monthly finance charge using the adjusted balance method, you need to follow these steps:
1. Calculate the Adjusted Balance: Subtract the payment amount from the balance.
Adjusted Balance = $3,000 - $1,500 = $1,500
2. Determine the Daily Periodic Rate: Divide the annual interest rate by 365 to get the daily periodic rate.
Daily Periodic Rate = 21% / 365 = 0.0575%
3. Calculate the Average Daily Balance: Multiply the adjusted balance by the number of days in the billing cycle (30 days in this case).
Average Daily Balance = $1,500 * 30 = $45,000
4. Determine the Monthly Interest Rate: Multiply the daily periodic rate by the number of days in a month (30 days).
Monthly Interest Rate = 0.0575% * 30 = 1.725%
5. Calculate the Monthly Finance Charge: Multiply the average daily balance by the monthly interest rate.
Monthly Finance Charge = $45,000 * 1.725% = $776.25
So, the monthly finance charge for this credit card transaction is approximately $776.25.