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, previous balance method
To calculate the monthly finance charge using the previous balance method, follow these steps:
Step 1: Determine the Average Daily Balance
To find the average daily balance, consider the balance at different points during the billing cycle. In this case, there are two balances to consider: the starting balance and the new balance after the payment is made.
1. Starting Balance: $3,000
2. New Balance after Payment: $3,000 - $1,500 = $1,500
Now, we need to calculate the number of days each balance was in effect during the billing cycle.
3. Days with Starting Balance: 30 days
4. Days with New Balance: 20 days (30 days - 10 days)
To calculate the average daily balance:
(Average Daily Balance = (Starting Balance x Days with Starting Balance) + (New Balance x Days with New Balance)) / Total Days
= ($3,000 x 30) + ($1,500 x 20) / 30
= $90,000 + $30,000 / 30
= $120,000 / 30
= $4,000
Step 2: Calculate the Daily Rate
To find the daily rate, divide the annual percentage rate (APR) by 365:
Daily Rate = 21% / 365
= 0.057534%
Step 3: Calculate the Monthly Finance Charge
To find the monthly finance charge, multiply the average daily balance by the daily rate and then by the number of days in the billing cycle:
Monthly Finance Charge = Average Daily Balance x Daily Rate x Number of Days in the Billing Cycle
= $4,000 x 0.00057534 x 30
= $6.90408
Rounding to the nearest cent:
= $6.90
Therefore, the monthly finance charge for this credit card transaction is approximately $6.90.
To calculate the monthly finance charge using the previous balance method, follow these steps:
1. Determine the previous balance: The previous balance is the outstanding balance on the credit card before the current payment was made. In this case, the previous balance is $3,000.
2. Determine the average daily balance: To calculate the average daily balance, you need to know how many days in the billing cycle the balance was at the previous balance and how many days the balance is at zero after the payment is made.
- The previous balance is outstanding for the entire billing cycle, which is 30 days.
- The payment is made after 10 days, so the balance is zero for the remaining 20 days of the billing cycle.
Calculate the average daily balance as follows:
Average Daily Balance = (Previous Balance * Days Balance is Outstanding in Billing Cycle + Zero Balance * Days Balance is Zero in Billing Cycle) / Number of Days in Billing Cycle
Average Daily Balance = ($3,000 * 30 + $0 * 20) / 30
Average Daily Balance = $3,000
3. Determine the daily periodic rate: The daily periodic rate is the interest rate divided by the number of days in a year. In this case, the interest rate is 21% and the number of days in a year is 365.
Daily Periodic Rate = Interest Rate / Number of Days in a Year
Daily Periodic Rate = 21% / 365
Daily Periodic Rate = 0.0575%
4. Calculate the monthly finance charge: The monthly finance charge is the average daily balance multiplied by the daily periodic rate and then multiplied by the number of days in the billing cycle.
Monthly Finance Charge = Average Daily Balance * Daily Periodic Rate * Number of Days in Billing Cycle
Monthly Finance Charge = $3,000 * 0.0575% * 30
Monthly Finance Charge = $5.48 (rounded to the nearest cent)
Therefore, the monthly finance charge for this credit card transaction is approximately $5.48.