The credit card with the transactions described below uses the average daily balance method to calculate interest. The monthly interest rate is 1.3% of the average daily balance. Calculate parts a-d using the statement below.
a. Find the average daily balance for the billing period. Round to the nearest cent.
The average daily balance for the billing period is $ [ ] (Round to the nearest cent as needed.)
Transaction Description | Transaction Amount
---|---
Previous balance, $2653.36 |
June 1 Billing date |
June 6 Payment | $1300.00 credit
June 8 Charge: Gas | $34.78
June 9 Charge: Groceries | $136.83
June 17 Charge: Gas | $41.51
Charge: Groceries | $127.58
June 27 Charge: Clothing | $214.81
June 30 End of billing period |
Payment Due Date: July 9 |
Answer (1)
Calculate the balance for each period in the billing cycle.
Multiply each balance by the number of days it remained constant.
Sum these products: ( 5 × 2653.36 ) + ( 2 × 1353.36 ) + ( 1 × 1388.14 ) + ( 8 × 1524.97 ) + ( 2 × 1566.48 ) + ( 8 × 1694.06 ) + ( 4 × 1908.87 ) = 53882.34 .
Divide the sum by 30 to find the average daily balance and round to the nearest cent: $1796.08 .
Explanation
Understanding the Problem We are asked to find the average daily balance for the billing period. The average daily balance is calculated by summing the product of each daily balance and the number of days the balance remained constant, then dividing by the total number of days in the billing cycle.
Determining the Balances and Days The billing period is from June 1 to June 30, which is 30 days. We need to calculate the balance for each period and multiply it by the number of days it remained constant.
Calculating Daily Balances
From June 1 to June 5 (5 days), the balance is $2653.36.
From June 6 to June 7 (2 days), the balance is $2653.36 - $1300.00 = $1353.36.
On June 8 (1 day), the balance is $1353.36 + $34.78 = $1388.14.
From June 9 to June 16 (8 days), the balance is $1388.14 + $136.83 = $1524.97.
From June 17 to June 18 (2 days), the balance is $1524.97 + $41.51 = $1566.48.
From June 19 to June 26 (8 days), the balance is $1566.48 + $127.58 = $1694.06.
From June 27 to June 30 (4 days), the balance is $1694.06 + $214.81 = $1908.87.
Calculating the Average Daily Balance Now, we calculate the sum of the products of the daily balances and the number of days:
( 5 × 2653.36 ) + ( 2 × 1353.36 ) + ( 1 × 1388.14 ) + ( 8 × 1524.97 ) + ( 2 × 1566.48 ) + ( 8 × 1694.06 ) + ( 4 × 1908.87 )
= 13266.80 + 2706.72 + 1388.14 + 12199.76 + 3132.96 + 13552.48 + 7635.48 = 53882.34
Then, we divide the sum by the number of days in the billing cycle (30):
30 53882.34 = 1796.078
Rounding to the nearest cent, we get $1796.08.
Final Answer The average daily balance for the billing period is $1796.08.
Examples
Understanding average daily balance is crucial for managing credit card expenses. For instance, if you want to minimize interest charges, knowing how the average daily balance is calculated helps you plan your payments effectively. Paying off your balance before the end of the billing cycle, or making multiple payments throughout the month, can lower your average daily balance and, consequently, the amount of interest you're charged. This concept extends to other financial products like loans, where understanding the balance calculation method can save you money.
