10.4 Installment Buying 621 Open-End Installment Loans A credit card is a popular way of making purchases or borrowing money. Use of a credit card is an example of an open-end installment loan. A typical credit card charge account with a bank or store may have the terms given in Table 10.3. Table 10.3 Credit Card Terms Type of Charge Daily Periodic Rate* Annual Percentage Rate* Purchases 0.05614% 20.49% Cash advances 0.08285% 30.24% *These rates vary with different credit card accounts and localities. Typically, credit card monthly statements contain the following information: balance at the beginning of the period, balance at the end of the period (or new balance), the transactions for the period, statement closing date (or billing date), payment due date, and the minimum payment due. In addition, the Credit Card Accountability Responsibility and Disclosure (CARD) Act of 2009 required credit card companies to provide additional information to their customers on their monthly statements (see Mathematics Today on page 620). For purchases, there is no finance or interest charge if there is no previous balance due and you pay the entire new balance by the payment due date. The period between when a purchase is made and when the credit card company begins charging interest is called the grace period and is usually 20 to 25 days. However, if you use a credit card to borrow money, called a cash advance, there generally is no grace period and a finance charge is applied from the date you borrowed the Solution a) Recall from Example 5 that Tino’s monthly payments are $237.00. After 30 payments have been made, 18 payments remain. Thus, n 18 = and P $237. = To determine V, use the APR table (Table 10.2). In the Number of Payments column, find the number of remaining payments, 18, and then look to the right until you reach the column headed by 7.5%, the APR. This row and column intersect at 6.0423. Thus, V 6.0423. = Now use the actuarial method formula to determine the unearned interest, u. u n P V V 100 (18)(237)(6.0423) 100 6.0423 243.08 = ⋅ ⋅ + = + ≈ By paying off the loan early, Tino will save $243.08 in interest by the actuarial method. b) Because the remaining payments total 18($237) $4266, = Tino’s remaining balance, excluding his 30th monthly payment, is $4266.00 243.08 $4022.92 − Total of remaining payments (which includes interest) Interest saved (unearned interest) Balance due (excluding the 30th monthly payment) A payment of $4022.92 plus the 30th monthly payment of $237 will terminate Tino’s installment loan. $4022.92 237.00 $4259.92 + Balance due (excluding the 30th monthly payment) 30th monthly payment Total amount due The total amount due is $4259.92. 7 Now try Exercise 27
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