Texas Go Math Grade 8 Lesson 16.1 Answer Key Repaying Loans

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Texas Go Math Grade 8 Lesson 16.1 Answer Key Repaying Loans

Example 1

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.

Use an online calculator. Enter these numbers
Loan amount: $1000
Loan term: 3 months
Interest rate: 21% per year
The calculator converts to 0.25 year.

Click CALCULATE.
Monthly payment: $345.07

What is Alex’s total repayment?
$345.07 monthly payment × 3 months = $1035.21

The credit card company loaned Alex $1000, and he paid $1035.21 back to the credit card company. What was the cost of this loan?
Interest paid = $1035.21 – $1000 = $35.21 The cost of the loan

B. 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.

What is Barry’s total repayment and the cost of his loan?
$338.35 monthly payment × 3 months = $1015.05
Interest paid = $1015.05 – $1000 = $15.05 The cost of the loan

Reflect

Question 1.
What If? If Alex had saved $333.34 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?
Answer:

Question 2.
How much less did Barry’s loan, at an interest rate of 9%, cost than Alex’s loan at 21%?
Answer:

Question 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?
Answer:

Your Turn

Use an online calculator to fill in the blanks for the easy access loans.

Question 4.
Loan amount: $5000 Monthly payment: _______________
Loan term: 2 years Total repayment: _______________
Interest rate: 7% Interest paid: _______________
Answer:

Question 5.
Loan amount: $5000 Monthly payment: _______________
Loan term: 2 years Total repayment: _______________
Interest rate: 21% Interest paid: _______________
Answer:

Example 2

A. Susan has a balance of $1000 on her credit card. She stops using her card and pays the minimum monthly amount until the loan ¡s paid off.
Texas Go Math Grade 8 Lesson 16.1 Answer Key 1
Use an online calculator. Enter these numbers:
Loan amount: $1000
Loan term: 93 months
Interest rate: 18% per year
Click CALCULATE. Monthly payment: $20.01

What is Susan’s total repayment?
$20.01 monthly payment × 93 months = $1860.93

What was the cost of this loan?
Interest paid = $1860.93 – $1000 = $860.93 The cost of the loan

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.

Use an online calculator. Enter these numbers:
Loan amount: $1000
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 = $1301.40

What was the cost of this loan?
Interest paid = $1301.40 – $1000 = $301.40 The cost of the loan

Reflect

Question 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 $1000.
Answer:

Question 7.
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?
Answer:

Your Turn

Use an online calculator to fill in the blanks.

Question 8.
Loan amount: $5000 Monthly payment: _______________
Loan term: 2 years Total repayment: _______________
Interest rate: 15% Interest paid: _______________
Answer:

Question 9.
Loan amount: $5000 Monthly payment: _______________
Loan term: 4 years Total repayment: _______________
Interest rate: 15% Interest paid: _______________
Answer:

Texas Go Math Grade 8 Lesson 16.1 Guided Practice Answer Key

Question 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
Loan amount: $________
Loan term: ________ months
Interest rate: ________% per year
Monthly payment: $________
$________ × 24 months =
Total repayment: $________
Interest paid: $_________

Bank Loan
Loan amount: $_________
Loan term: ________ months
Interest rate: ________% per year
Monthly payment: $________
$________ × 24 months =
Total repayment: $________
Interest paid: $_________
Kyle would pay $________ less in interest if he borrows from the bank than if he borrows using his credit card.
Answer:

Question 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 = Total repayment: $__________
Interest paid: $_________
Kyle will pay $_________ less for a loan that lasts 1 year instead of 2.
Answer:

Essential Question Check-In

Question 3.
How do you calculate the cost of repaying a loan using an online calculator?
Answer:

Texas Go Math Grade 8 Lesson 16.1 Independent Practice Answer Key

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.
Texas Go Math Grade 8 Lesson 16.1 Answer Key 2

Question 4.
Find the amount of Claudia’s monthly payment for these choices.
a. 14% for 3 years: _________
Answer:

b. 14% for 5 years: __________
Answer:

c. 8% for 3 years: ____________
Answer:

Question 5.
Find the amount of Claudia’s total repayment for these choices.
a. 14% for 3 years: ____________
Answer:

b. 14% for 5 years: ____________
Answer:

c. 8% for 3 years: ____________
Answer:

Question 6.
Find the amount that Claudia would pay in interest for these choices.
a. 14% for 3 years: ____________
Answer:

b. 14% for 5 years: ____________
Answer:

c. 8% for 3 years: ____________
Answer:

Question 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?
Answer:

Question 8.
What is the difference in interest cost between the car dealer loan for 3 years and the car dealer loan for 5 years?
Answer:

Question 9.
If Claudia wants the lowest possible monthly payment, which option should she choose?
Answer:

Question 10.
If Claudia wants the lowest possible cost for the loan, which option should she choose?
Answer:

Question 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.
Answer:

Question 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. Flow much will Jess’s total payments be?
Answer:

H.O.T. Focus On Higher Order Thinking

Use an online calculator for 13-16.

Question 13.
Persevere in Problem Solving Christopher is thinking about charging a $2000 computer on his credit card at an interest rate of 21%. He realizes that if he takes m months to pay off this debt, he will have paid just over twice the original price. What is the value of m?
Texas Go Math Grade 8 Lesson 16.1 Answer Key 3
Answer:

Question 14.
Make a Conjecture Lara wants to buy a sewing machine so she can sell quilts that she makes. The machine costs $1500. She is able to save $200 each month. What advice would you give Lara about how to pay for the machine? Explain.
Answer:

Question 15.
Multistep Pat can get a student loan of $10,000 for 10 years at an interest rate of 7% or borrow the same amount for 5 years at an interest rate of 4%. Which do you think Pat should do and why?
Answer:

Question 16.
Analyze Relationships What do you need to know in order to decide which choice is better when you are borrowing money? What do you need to consider when you make your choice?
Answer:

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