A credit card bill for $856.25 was due on July 15. The next due date was August 15. The table below shows purchases and payments made during that time.
| Date | Purchase or payment | Date | Purchase or payment |
| :----- | :------------------ | :----- | :------------------ |
| 7/19 | 115.54 | 8/6 | 126.94 |
| 7/24 | 29.09 | 8/7 | 60.00 |
| 7/25 | 110.66 | 8/7 | 107.65 |
| 7/26 | 36.02 | 8/8 | 141.25 |
| 7/26 | 53.64 | 8/8 | 51.91 |
| 7/27 | 86.41 | 8/9 | 141.99 |
| 7/29 | -450.00 | 8/10 | 48.14 |
| 7/30 | 29.17 | 8/11 | 85.55 |
| 8/4 | 73.01 | 8/13 | 144.54 |
| 8/5 | 21.72 | 8/14 | 105.59 |
Calculate the finance charge based on the average daily balance and an annual interest rate of 20.5%. (Round your answer to the nearest cent.)
Answer (2)
Calculate the daily balance for each day from July 15 to August 14 based on the given transactions.
Determine the number of days each balance was maintained.
Calculate the average daily balance by summing the product of each daily balance and the number of days it was maintained, then dividing by the total number of days (31).
Calculate the finance charge by multiplying the average daily balance by the monthly interest rate (annual interest rate divided by 12), resulting in $21.61 .
Explanation
Problem Analysis We are given a credit card bill with an initial balance, a series of transactions, and an annual interest rate. Our goal is to calculate the finance charge based on the average daily balance. The due date was July 15, and the next due date was August 15. The annual interest rate is 20.5%.
Calculating Daily Balances First, we need to calculate the daily balance for each day from July 15 to August 14. We will denote July 15 as day 0. We are given the initial balance as $856.25. We need to calculate the balance for each day based on the transactions that occurred on that day.
Table of Daily Balances To simplify the calculation, let's create a table of the daily balances. We will adjust the dates to represent the number of days from July 15.
Date
Days from July 15
Transactions
Balance
7/15
0
856.25
7/19
4
+115.54
971.79
7/24
9
+29.09
1000.88
7/25
10
+110.66
1111.54
7/26
11
+36.02, +53.64
1201.20
7/27
12
+86.41
1287.61
7/29
14
-450.00
837.61
7/30
15
+29.17
866.78
8/4
20
+73.01
939.79
8/5
21
+21.72
961.51
8/6
22
+126.94
1088.45
8/7
23
+60.00, +107.65
1256.10
8/8
24
+141.25, +51.91
1449.26
8/9
25
+141.99
1591.25
8/10
26
+48.14
1639.39
8/11
27
+85.55
1724.94
8/13
29
+144.54
1869.48
8/14
30
+105.59
1975.07
Calculating Days for Each Balance Now, we calculate the number of days each balance was maintained:
$856.25 for 4 days * $971.79 for 5 days
$1000.88 for 1 day * $1111.54 for 1 day
$1201.20 for 1 day * $1287.61 for 2 days
$837.61 for 1 day * $866.78 for 5 days
$939.79 for 1 day * $961.51 for 1 day
$1088.45 for 1 day * $1256.10 for 1 day
$1449.26 for 1 day * $1591.25 for 1 day
$1639.39 for 1 day * $1724.94 for 2 days
$1869.48 for 1 day * $1975.07 for 1 day
Sum of Daily Balances Next, we calculate the sum of (daily balance * number of days):
( 856.25 × 4 ) + ( 971.79 × 5 ) + ( 1000.88 × 1 ) + ( 1111.54 × 1 ) + ( 1201.20 × 1 ) + ( 1287.61 × 2 ) + ( 837.61 × 1 ) + ( 866.78 × 5 ) + ( 939.79 × 1 ) + ( 961.51 × 1 ) + ( 1088.45 × 1 ) + ( 1256.10 × 1 ) + ( 1449.26 × 1 ) + ( 1591.25 × 1 ) + ( 1639.39 × 1 ) + ( 1724.94 × 2 ) + ( 1869.48 × 1 ) + ( 1975.07 × 1 ) = 39203.44
Calculating Average Daily Balance Now, divide the sum by the total number of days (31) to find the average daily balance:
31 39203.44 = 1264.62709677
So, the average daily balance is approximately $1264.63.
Calculating Monthly Interest Rate The monthly interest rate is the annual interest rate divided by 12:
12 0.205 = 0.017083333
Calculating Finance Charge Finally, calculate the finance charge by multiplying the average daily balance by the monthly interest rate:
1264.63 × 0.017083333 = 21.6054
Rounding to the nearest cent, the finance charge is $21.61.
Final Answer Therefore, the finance charge based on the average daily balance and an annual interest rate of 20.5% is $21.61 .
Examples
Credit card companies use the average daily balance method to calculate finance charges. Understanding how these charges are calculated can help consumers manage their credit card usage and avoid unnecessary fees. For example, by making payments more frequently, a consumer can lower their average daily balance and, consequently, reduce the finance charges they incur. This knowledge empowers individuals to make informed financial decisions and maintain better control over their credit card debt.
The finance charge based on the average daily balance from July 15 to August 14, with an annual interest rate of 20.5%, is calculated to be $21.61. This is done by determining daily balances, averaging them over the billing period, and applying the monthly interest rate to the average balance. Thus, the final finance charge is $21.61.
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