Calculate the interest on a $1700 credit card bill that shows a 22% APR, using the average daily balance method. Assume you sent a payment of $375 on the first day of a month that has 30 days and it takes 5 days for this payment to be received and recorded. Round to the nearest penny.
a.$27.04
b.$25.09
c.$28.56
d.$28.60
To calculate the interest on a credit card bill using the average daily balance method, you need to follow a few steps:
Step 1: Calculate the Average Daily Balance (ADB)
The Average Daily Balance is calculated by adding up the balances each day and then dividing by the number of days in the billing cycle.
In this scenario:
- The balance before the payment was made is $1700.
- The payment of $375 is made on day 1 of a 30-day billing cycle.
- It takes 5 days for the payment to be received and recorded.
So, for the first 5 days, the balance is $1700.
For the remaining 25 days, the balance is $1700 - $375 = $1325.
ADB = [(5 days * $1700) + (25 days * $1325)] / 30 days
Step 2: Calculate the interest using the ADB and the Annual Percentage Rate (APR)
To calculate the interest, you multiply the ADB by the APR, and then divide it by 365 (the number of days in a year).
Interest = (ADB * APR) / 365
In this scenario:
- The APR is 22%.
- ADB is calculated as shown above.
Interest = (ADB * 22%) / 365
Step 3: Round the interest to the nearest penny
After performing the calculation, round the interest to the nearest penny.
Let's calculate:
ADB = [(5 * $1700) + (25 * $1325)] / 30
= ($8500 + $33125) / 30
= $41625 / 30
= $1387.50
Interest = ($1387.50 * 0.22) / 365
= $304.25 / 365
= $0.8342 (rounded to 4 decimal places)
Rounding to the nearest penny: $0.83
Therefore, the correct answer is not provided in the options given.