616 CHAPTER 10 Consumer Mathematics The advantage of installment buying is that the buyer has the use of an article while paying for it. If the article is essential, installment buying may serve a real need. A disadvantage is that some people buy more on the installment plan than they can afford. Another disadvantage is the interest the borrower pays for the loan. To provide the borrower with a way to compare interest rates from various lenders, Congress passed the Truth in Lending Act of 1968. The law requires lending institutions to tell the borrower two things: the annual percentage rate and the finance charge. The annual percentage rate (APR) is the true rate of interest charged for the loan. The APR provides consumers the ability to compare loans without having to do calculations to determine the true interest rate they are being charged. The finance charge is the total amount of money the borrower must pay for borrowing the money. The finance charge includes the interest plus any additional fees charged to obtain the loan. For the rest of this section, we will include the interest only when we refer to the finance charge. In this section we will also discuss the total installment price. The total installment price is the sum of all the monthly payments and the down payment, if any. Fixed Installment Loans We begin our discussion of fixed installment loans with an example in which the finance charge has been provided for us. Example 1 Dre is purchasing a new car that costs $30,000. To obtain an installment loan, he is required to pay 15% of the car cost as a down payment. The finance charge on the loan is $2412.30. The loan amount plus the finance charge will be paid in 48 equal monthly payments. a) Determine the down payment amount. b) Determine the amount financed. c) Determine Dre’s monthly payment. Solution a) To determine the down payment amount, we need to calculate 15% of $30,000. 0.15(30,000) 4500 = Thus, the down payment amount is $4500. b) To determine the amount financed, we subtract the down payment amount, $4500, from the cost of the car, $30,000. 30,000 4500 25,500 − = Thus, the amount financed is $25,500. c) Dre must pay back the amount financed plus the finance charge by making 48 equal monthly payments. To determine the monthly payment, we add the amount financed, $25,500, to the finance charge, $2412.30 and then divide this sum by 48. 25,500 2412.30 48 27,912.30 48 581.51 + = ≈ Thus, Dre’s monthly payments will be $581.51. 7 Now try Exercise 7 In our next example, we will use a table to determine the finance charge on a fixed installment loan.
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