10.4 Installment Buying 623 Many lending institutions use the average daily balance method of calculating the finance charge because they believe that it is fairer to the customer. With the average daily balance method, a balance is determined each day of the billing period for which there is a transaction in the account. The average daily balance method is illustrated in Example 9. a) Determine the finance charge due on December 5, Peter’s next billing date, using the previous balance method. Assume that the interest rate charged is 1.3% per month. b) Determine the new account balance on December 5. Solution a) The finance charge is based on the $275 balance due on November 5. To determine the finance charge due on December 5, we used the simple interest formula with a time of 1 month. i $275 0.013 1 $3.58 = × × ≈ The finance charge due on December 5 is $3.58. b) The balance due on December 5 is determined by adding the costs of the new purchases and the calculated interest to the balance due on November 5, and then subtracting the payment made from this sum. $275 $320 $3.58 $145 $453.58 + + − = The balance due on December 5 is $453.58. The finance charge on January 5 is based on the December 5 balance of $453.58. 7 Now try Exercise 35 MATHEMATICS TODAY “What’s in Your Wallet?” In 2023, Americans used over one billion credit cards to finance a total of over $1 trillion in credit card debt. The average credit card debt per household was about $5133, and the average annual percentage rate (APR) was about 24.76%. Most credit cards are issued by a bank or other lending institution. The individual institutions are responsible for paying the merchants for the money charged by the consumer, but they also reap the benefit of the interest charged to the cardholders. As of 2023, the largest credit card–issuing banks in the United States were Chase, Bank of America, Citibank, and Capital One. Why This Is Important Although credit cards are an important part of the modern financial world, the overuse of credit cards can lead to financial problems and even bankruptcy. When borrowing money for longer than one month, it is usually better to seek alternatives other than using your credit cards. Other, 1% American Express, 6% Discover, 8% Mastercard, 32% Visa, 53% U.S. Credit Card Market Share 2023 Source: Forbes.com Example 9 Finance Charges Using the Average Daily Balance Method The balance on Min’s credit card account on July 1, the billing date, was $375.80. The following transactions occurred during the month of July. July 5 Payment $150.00 July 10 Charge: Toy store 74.35 July 18 Charge: Garage 123.50 July 28 Charge: Restaurant 42.50 a) Determine the average daily balance for the billing period. b) Determine the finance charge to be paid on August 1, Min’s next billing date. Assume that the interest rate is 1.3% per month. c) Determine the balance due on August 1. Solution a) To determine the average daily balance, we do the following. (i) Determine the balance due for each transaction date. July 1 $375.80 July 5 $375.80 − $150 = $225.80 July 10 $225.80 + $74.35 = $300.15 July 18 $300.15 + $123.50 = $423.65 July 28 $423.65 + $42.50 = $466.15
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