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, follow these steps:
1. Determine the Average Daily Balance (ADB) for the billing cycle. ADB is calculated by adding up the daily balances and dividing the total by the number of days in the billing cycle.
First, we need to find the daily balance for each day in the billing cycle. Here's a breakdown of the transaction:
- Starting balance: $3,000
- Payment: -$1,500 (credited 10 days later)
- Interest rate: 21%
To determine the daily balance:
- For the initial 20 days, the daily balance remains $3,000.
- For the next 10 days (after the payment), the daily balance is reduced by the payment amount: $3,000 - $1,500 = $1,500.
Next, let's calculate the ADB:
- Total daily balance for the first 20 days = $3,000 * 20 = $60,000.
- Total daily balance for the next 10 days = $1,500 * 10 = $15,000.
- ADB = (Total daily balance for the first 20 days + Total daily balance for the next 10 days) / 30 days
= ($60,000 + $15,000) / 30
= $75,000 / 30
= $2,500
So, the Average Daily Balance (ADB) is $2,500.
2. Calculate the Monthly Interest Rate (MIR). The MIR is the annual interest rate divided by 365 to get the daily interest rate, and then multiplied by 30 to get the monthly interest rate.
MIR = (Annual Interest Rate / 365) * 30
Given an annual interest rate of 21%, we can calculate the MIR as follows:
- MIR = (0.21 / 365) * 30
= 0.00057534 * 30
≈ 0.01726
So, the Monthly Interest Rate (MIR) is approximately 0.01726.
3. Compute the Monthly Finance Charge. The Monthly Finance Charge is calculated by multiplying the ADB by the MIR.
Monthly Finance Charge = ADB * MIR
= $2,500 * 0.01726
≈ $43.15
Therefore, the monthly finance charge for this credit card transaction, using the adjusted balance method, is approximately $43.15.
To calculate the monthly finance charge using the adjusted balance method, you need to find the average daily balance for the billing cycle.
1. Find the average daily balance:
Average Daily Balance = (Starting Balance * Number of Days) - (Payment * Payment Days) / Number of Days in the Billing Cycle
Starting Balance = $3,000
Number of Days = 30
Payment = $1,500
Payment Days = 10
Number of Days in the Billing Cycle = 30
Average Daily Balance = ($3,000 * 30 - $1,500 * 10) / 30
= ($90,000 - $15,000) / 30
= $75,000 / 30
= $2,500
2. Calculate the finance charge:
Finance Charge = Average Daily Balance * Monthly Interest Rate
Monthly Interest Rate = (Annual Interest Rate / Number of Months) / 100
= (21 / 12) / 100
= 0.0175
Finance Charge = $2,500 * 0.0175
= $43.75 (rounded to the nearest cent)
Therefore, the monthly finance charge for this credit card transaction would be $43.75.