ESSENTIAL QUESTION How do you calculate the cost of repaying a loan?
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1 ? LESSON 16.1 Repaying Loans ESSENTIAL QUESTION How do you calculate the cost of repaying a loan? financial literacy 8.12.A Solve real-world problems comparing how interest rate and loan length affect the cost of credit. Also 8.12.B, 8.12.E Comparing Interest Rates How much does it cost to borrow money? When you use a credit card or get a loan from a bank, the cost of borrowing the money depends on two factors. The first is the interest rate that you pay. The second is the time that you take to pay off the total amount. Interest is the money that you pay to borrow money or use credit. The interest rate determines in part the cost of a loan or of purchases on a credit card. Math On the Spot EXAMPLE A, 8.12.B A In September, Alex charged his textbooks, clothes, and some downloads on his credit card. He received a bill from his credit card company for $1000. The interest rate on his card is 21%. He is going to pay in 3 monthly payments. He wants to know how much this loan will cost him in interest. Credit Card Loan term: 3 months The calculator converts to 0.25 year. Interest rate: 21% per year Click CALCULATE. Monthly payment: $ B What is Alex s total repayment? $ monthly payment 3 months = $ The credit card company loaned Alex $1000, and he paid $ back to the credit card company. What was the cost of this loan? Interest paid = $ $1000 = $35.21 Barry takes out a loan from his bank for $1000 to buy a bicycle. The interest rate on his loan is 9%. He is going to pay the total amount in 3 monthly payments. Use an online calculator to find the cost of his loan. Math Talk Mathematical Processes In addition to the interest you pay to borrow money, what other costs may there be when you take out a loan? What is Barry s total repayment and the cost of his loan? $ monthly payment 3 months = $ Interest paid = $ $1000 = $
2 Reflect 1. What If? If Alex had saved $ a month for 3 months, how much money would he have? If he had used his savings instead of his credit card, how much less would his purchases have cost him? 2. How much less did Barry s loan, at an interest rate of 9%, cost than Alex s loan at 21%? 3. Barry looks into the cost of repaying an easy access loan for $1000. The up-front cost of the loan is $3 for every $20 borrowed, plus Barry will owe $1000 at the end of the loan. How much will this loan cost Barry? YOUR TURN Online Assessment and Intervention Math On the Spot Animated Math Use an online calculator to fill in the blanks for the easy access loans. 4. Loan amount: $5000 Monthly payment: Comparing Loan Lengths You saw in Example 1 how the interest rate affects the cost of borrowing money. The time taken to repay the loan also affects the cost. EXAMPLE 2 A Interest rate: 7% 5. Loan amount: $5000 Monthly payment: Interest rate: 21% Susan has a balance of $1000 on her credit card. She stops using her card and pays the minimum monthly amount until the loan is paid off. Loan term: 93 months Interest rate: 18% per year Click CALCULATE. Monthly payment: $ A, 8.12.B Image Credits: BananaStock/ Jupiterimages/Getty Images 442 Unit 7
3 What is Susan s total repayment? $20.01 monthly payment 93 months = $ What was the cost of this loan? Interest paid = $ $1000 = $ B Laura also has a balance of $1000 at 18% interest on her credit card. She stops using her card. She wants to pay as much as she can each month to pay off the loan as quickly as she can. Loan term: 3 years Interest rate: 18% per year Click CALCULATE. Monthly payment: $36.15 What is Laura s total repayment? $36.15 monthly payment 36 months = $ What was the cost of this loan? Interest paid = $ $1000 = $ Reflect 6. What If? If Susan had put $20 in her savings account each month, how long would it take her to save a total of $1000? Compare this to the time she took to pay off her credit card loan of $ Laura paid off her debt in 36 months while Susan took 93 months to pay off her debt of the same amount. How much less did Laura pay in interest than Susan paid? YOUR TURN Use an online calculator to fill in the blanks. 8. Loan amount: $5000 Monthly payment: Interest rate: 15% 9. Loan amount: $5000 Monthly payment: Loan term: 4 years Interest rate: 15% Online Assessment and Intervention 443
4 Guided Practice 1. Kyle is going to take out a loan for $1500 for 2 years. He wants to know how much more it will cost him in interest if he uses his credit card, at 20% interest, instead of borrowing from the bank at 11% interest. Find the difference in the cost of these two choices. (Example 1) Enter the numbers in an online calculator and fill in the blanks. Credit Card Bank Loan Loan amount: $ Loan amount: $ Loan term: months Loan term: months Interest rate: % per year Interest rate: % per year Monthly payment: $ Monthly payment: $ $ 24 months = $ 24 months = $ $ $ $ Kyle would pay $ less in interest if he borrows from the bank than if he borrows using his credit card. 2. How much less will Kyle pay in interest if he borrows $1500 at 11% for 1 year instead of for 2 years? (Example 2) Monthly payment: $ $ months = $ $ Kyle will pay $ less for a loan that lasts 1 year instead of 2.? ESSENTIAL QUESTION CHECK-IN 3. How do you calculate the cost of repaying a loan using an online calculator? 444 Unit 7
5 Name Class Date 16.1 Independent Practice 8.12.A, 8.12.B, 8.12.E Online Assessment and Intervention Claudia is going to buy a used car for $10,000. She can finance it at the car dealer for 14% interest, or she can get a loan from the bank at 8% interest for 3 years. If she chooses to finance with the car dealer, she can choose either a 3-year loan or a 5-year loan. Use an online calculator. 4. Find the amount of Claudia s monthly payment for these choices. 5. Find the amount of Claudia s total repayment for these choices. 6. Find the amount that Claudia would pay in interest for these choices. Image Credits: Tom Kelley Archive/Getty Images 7. What is the difference in interest cost between the car dealer loan at 14% for 3 years and the bank loan at 8% for 3 years? 8. What is the difference in interest cost between the car dealer loan for 3 years and the car dealer loan for 5 years? 9. If Claudia wants the lowest possible monthly payment, which option should she choose? 10. If Claudia wants the lowest possible cost for the loan, which option should she choose? 11. Communicate Mathematical Ideas With Claudia s loan, does loan length or interest rate have the greater effect on the cost of the interest for the loan? Explain. 12. Jess takes out an easy access loan for $200. The up-front cost of the loan is $4 for every $20, plus Jess will owe $200 at the end of the loan. How much will Jess s total payments be? 445
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