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:
Step 1: Determine the average daily balance.
To find the average daily balance, we need to calculate the balance at the end of each day and then divide it by the number of days in the billing cycle.
Given:
Starting balance = $3,000
Payment = $1,500
Number of days in the billing cycle = 30
To calculate the average daily balance, we need to consider the balance for each day of the billing cycle.
Initially, the balance is $3,000. Then, after 10 days, a payment of $1,500 is made. This leaves a balance of $1,500 for the remaining 20 days of the billing cycle.
For the first 10 days: $3,000 x 10 = $30,000
For the next 20 days: $1,500 x 20 = $30,000
Total balance over the entire billing cycle = $30,000 + $30,000 = $60,000
Average daily balance = $60,000 / 30 = $2,000
Step 2: Calculate the daily interest rate.
The yearly interest rate is given as 21%. To find the daily interest rate, we divide this by the number of days in a year.
Daily interest rate = 21% / 365 = 0.0575%
Step 3: Calculate the monthly finance charge.
The monthly finance charge is calculated by multiplying the average daily balance by the daily interest rate and the number of days in the billing cycle.
Monthly finance charge = $2,000 x 0.0575% x 30
= $34.50 (rounded to the nearest cent)
Therefore, the monthly finance charge for this credit card transaction is $34.50.