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, average daily balance method
To calculate the monthly finance charge using the average daily balance method, we need to follow these steps:
1. Determine the number of days in the billing cycle: In this case, the billing cycle is 30 days.
2. Determine the average daily balance: The average daily balance is calculated by adding up the daily balances for each day in the billing cycle, then dividing that total by the number of days in the cycle.
To find the daily balance, we need to consider the balance at the start and end of each day, as well as any transactions made during the billing cycle.
Here's how we can calculate it:
Day 1: Balance = $3,000
Day 2-10: No change in balance
Day 11-30: Balance = $3,000 - $1,500 (payment) = $1,500
Next, calculate the sum of the daily balances:
Sum of daily balances = (30 x $3,000) + (20 x $1,500) = $90,000 + $30,000 = $120,000
Finally, calculate the average daily balance:
Average daily balance = Total balance / Number of days = $120,000 / 30 = $4,000
3. Calculate the monthly interest rate: To convert the annual interest rate to a monthly rate, divide it by 12. In this case, the annual rate is 21%, so the monthly rate is 21% / 12 = 1.75% (or 0.0175 as a decimal).
4. Calculate the monthly finance charge: Multiply the average daily balance by the monthly interest rate to find the finance charge.
Monthly finance charge = Average daily balance x Monthly interest rate = $4,000 x 0.0175 = $70
Therefore, the monthly finance charge for this credit card transaction is $70.