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. (Round your answer to the nearest cent.)
$300 balance, 18% rate, $50 payment, average daily balance method
$____
To calculate the monthly finance charge for this credit card transaction, you will need to use the average daily balance method.
The average daily balance is calculated by adding up the daily balances for each day in the billing cycle and then dividing it by the number of days in the billing cycle.
In this case, we have the following information:
- $300 starting balance
- 18% annual interest rate (0.18 in decimal form)
- $50 payment
- Billing cycle of 30 days
- 10 days for a payment to be received and recorded
To calculate the average daily balance, we need to take into account the effect of the payment made during the billing cycle. Since the payment is made after 10 days, we need to deduct the payment amount from the balance for those 10 days.
Therefore, the average daily balance can be calculated as follows:
Average Daily Balance = (($300 * 20) - ($50 * 10)) / 30
Now let's calculate:
Average Daily Balance = ($6000 - $500) / 30
Average Daily Balance = $5500 / 30
Average Daily Balance ≈ $183.33
Now that we have the average daily balance, we can calculate the monthly finance charge using the following formula:
Monthly Finance Charge = Average Daily Balance * Monthly Interest Rate
The monthly interest rate can be calculated by dividing the annual interest rate by 12 (since there are 12 months in a year).
Monthly Interest Rate = Annual Interest Rate / 12
In this case, the monthly interest rate would be:
Monthly Interest Rate = 0.18 / 12
Monthly Interest Rate ≈ 0.015
Now, let's calculate the monthly finance charge:
Monthly Finance Charge = $183.33 * 0.015
Monthly Finance Charge ≈ $2.75
Therefore, the monthly finance charge for this credit card transaction is approximately $2.75.