10.4 Installment Buying 625 Anyone purchasing a car or other costly items should consider a number of different sources for a loan. Example 11 illustrates one method of making a comparison. Example 11 Comparing Loan Sources Franz purchased carpeting costing $2400 with his credit card. When the bill comes due on February 1, Franz realizes that he can pay $350 per month until the debt is paid off. His credit card charges a 1.5% interest rate per month. a) Assuming Franz makes no other purchases with this credit card, how many payments are necessary to retire this debt? b) What is the total interest Franz will pay? c) How much money could Franz have saved by obtaining a fixed installment loan of $2400 with an annual percentage rate of 6% interest with six equal monthly payments? Solution a) Franz would make his first monthly payment of $350 on February 1, resulting in a new balance of $2400 $350 $2050. − = His next bill reflects the $2050 balance plus the monthly interest. He continues to make payments until the debt is retired. For each date indicated, the amount on the far right represents the amount due on that date. February 1 $2400 $350 $2050 − = March 1 $2050 0.015($2050) $2080.75; $2080.75 $350 + = − $1730.75 = April 1 $1730.75 0.015($1730.75) $1756.71; $1756.71 $350 + = − $1406.71 = May 1 $1406.71 0.015($1406.71) $1427.81; $1427.81 $350 + = − $1077.81 = June 1 $1077.81 0.015($1077.81) $1093.98; $1093.98 $350 + = − $743.98 = July 1 $743.98 0.015($743.98) $755.14; $755.14 $350 + = − $405.14 = August 1 $405.14 0.015($405.14) $411.22; $411.22 $350 + = − $61.22 = September 1 $61.22 0.015($61.22) $62.14 + = After eight payments — seven for $350 and one for $62.14 — Franz has paid off his credit card bill for his carpeting. b) To calculate the total interest paid, we add up all his payments and then subtract the cost of the carpeting: Total of all payments 7($350) $62.14 $2512.14 Total interest $2512.14 $2400 $112.14 = + = = − = c) To determine the interest that Franz pays with the installment loan, we will use Table 10.2. From Table 10.2, we see that a fixed installment loan with an APR of 6% for 6 months corresponds to a finance charge of $1.757 per $100 of the amount financed. So the interest, or finance charge, is Finance charge 1.757 2400 100 1.757(24) $42.17 = ⎛ ⎝ ⎞ ⎠ = ≈ Therefore, Franz would save $112.14 $42.17 $69.97 − = in interest by using an installment loan instead of a credit card. 7 Now try Exercise 45 Instructor Resources for Section 10.4 in MyLab Math • Objective-Level Videos 10.4 • PowerPoint Lecture Slides 10.4 • MyLab Exercises and Assignments 10.4 Did You Know? Identity Theft I dentity theft, where one person uses another person’s identity for financial gains, is on the rise. The most important thing you can do to prevent identity theft is to secure your personal data. Below are some things that can be done to prevent your identity from being stolen. Secure your data: Use electronic statements rather than paper statements. Shred important documents. Resist giving out your Social Security number or your mother’s maiden name. Do not give or receive important information when using public Wi-Fi. Do not share important personal information on social media. Change your passwords often and consider using a password manager. Do not use the same password for all important accounts. When using a credit card, check that the credit card machine does not look like it has been tampered with. Phone scams: Phone scams are used to gather data on people or to trick them into paying money. Be careful what information you provide over the phone. Do not answer calls from numbers you do not recognize. If you answer your phone and hear a recorded voice, don’t say anything—just hang up. Tetra Images/Getty Images
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