# 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: Alex savings =$333.34 monthly payment × 3 months = $1000.02. Alex credit card =$333.34 monthly payment × 3 months = $1000.02. Both the accounts have the same amount for 3 months. Question 2. How much less did Barry’s loan, at an interest rate of 9%, cost than Alex’s loan at 21%? Answer: Barry’s loan at an interest rate of 9 % =$1015.05
Alex’s loan at 21% = $1035.21. Therefore$1035.21 – $1015.05 =$20.16
Barry’s loan is $20.16 less. 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: Barry cost of repaying an easy access loan =$1000.
Cost of a loan is 3% for every $20. Therefore 20 × 10 = 200 2% of 20 = 0.6. 0.6 × 50 =$30.
Jess will owe at the end of a loan = $1000. Jess’s total payment is$1000 + $1000 +$30 = $2030. 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: _______________
Loan amount = $5000. Loan term = 2 years. Interest rate = 7% The formula for the simple interest is PTR/100. Here P = principle. T = time. R = interest rate. Interest for 2 years =$5000 × 2 × 7/100 = $700. Total payment for 2 years =$5000 + $700 =$5700.
Monthly payment = $2700/24 =$112.5.
Interest paid = $700 Question 5. Loan amount:$5000 Monthly payment: _______________
Loan term: 2 years Total repayment: _______________
Interest rate: 21% Interest paid: _______________
Loan amount = $5000. Loan term = 2 years. Interest rate = 21% The formula for the simple interest is PTR/100. Here P = principle. T = time. R = interest rate. Interest for 2 years =$5000 × 2 × 21/100 = $2100. Total repayment for 2 years =$5000 + $2100 =$7100.
Monthly payment = $7100/24 =$295.8
Interest paid = $2100. 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.

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.
Susan saves each month in her savings account =$20. Save a total$ 1000 = 1000/20 = 50 months.
Time she took to pay the credit card loan = 93 months.
The savings account has fewer months.

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?
Laura paid off her debt in 36 months interest = $301.40. Susan paid off her debt in 93 months interest =$860.93.
Therefore $860.93 –$301.40 = $559.53.$559.53 less did laura pay in interest than susan paid.

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: Using online calculator: Loan amount:$5000 Monthly payment: $270.8 Loan term: 2 years Total repayment:$6500
Interest rate: 15% Interest paid: $1500 Explanation: Loan amount =$5000.
Loan term = 2 years.
Interest rate = 15%
The formula for the simple interest is PTR/100.
Here P = principle.
T = time.
R = interest rate.
Interest for 2 years = $5000 × 2 × 15/100 =$1500.
Total repayment for 2 years = $5000 +$1500 = $6500. Monthly payment =$6500/24 = $27.8. Interest paid =$1500.
Question 9.
Loan amount: $5000 Monthly payment: _______________ Loan term: 4 years Total repayment: _______________ Interest rate: 15% Interest paid: _______________ Answer: Using online calculator Loan amount:$5000 Monthly payment: $166.6 Loan term: 4 years Total repayment:$8000
Interest rate: 15% Interest paid: $3000 Explanation: Loan amount =$5000.
Loan term = 4 years.
Interest rate = 15%
Formula for the simple interest is PTR/100.
Here P = principle.
T = time.
R = interest rate.
Interest for 4 years = $5000 × 4 × 15/100 =$3000.
Total payment for 2 years = $5000 +$3000. = $8000. 4 years = 42 months. Monthly payment =$8000/48 = $166.6 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: Credit card loan: Using online calculator: Loan amount:$1500
Loan term: 24 months
Interest rate: 20% per year
Monthly payment: $76.34$76.34 × 24 months = 1832.16
Total repayment: $1832.16 Interest paid:$332.25
Bank loan:
Using online calculator
Loan amount: $1500 Loan term: 24 months Interest rate: 11% per year Monthly payment:$76.25
$76.25 × 24 months =$1830
Total repayment: $1830 Interest paid:$330
Credit card interest – bank interest = $332.25 –$330 = $2.25 Kyle pays$2.25 less in interest if he borrows from the bank than if he borrows using his credit card.

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.
Using online calculator:
Monthly payment: $138.75$138.75 × 12 months = Total repayment: 1665
Interest paid: $165 Kyle will pay$165 less for a loan that lasts 1 year instead of 2.
Explanation:
Loan money = $1500. Time = 1 year = 12 months. Interest = 11% Formula for simple interest = PTR/100 Interest =$1500 × 1 × 11/100 = $165. Total replacement =$1500 + $165 =$1665.
Monthly payment = $1665/12 = 138.75 2 year interest – 1 year interest =$330 – $165 =$165.

Essential Question Check-In

Question 3.
How do you calculate the cost of repaying a loan using an online calculator?
Answer: The cost of repaying a loan using an online calculator is multiplying the monthly payment with the number of months.

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. Question 4. Find the amount of Claudia’s monthly payment for these choices. a. 14% for 3 years: _________ Answer: Loan money =$10,000
Number of years = 3
Interest rate = 14%
Formula = PTR/100 = $10,000 × 3 × 14/100 =$4200.
The total money for 3 years = $10,000 +$4200 = $14200. 1 year = 12 months 3 years = 36 months For monthly payment =$14200/36 = $394.4. b. 14% for 5 years: __________ Answer: Loan money =$10,000
Number of years = 5
Interest rate = 14%
Formula = PTR/100 = $10,000 × 5 × 14/100 =$7000.
The total money for 5 years = $10,000 +$7000 = $17000. 1 year = 12 months 5 years = 5 × 12 = 45 months For monthly payment =$17000/45 = $377.7. c. 8% for 3 years: ____________ Answer: Loan money =$10,000
Number of years = 3
Interest rate = 8%
Formula = PTR/100 = $10,000 × 3 × 8/100 =$2400.
The total money for 3 years = $10,000 +$2400 = $12400. 1 year = 12 months 3 years = 3 × 12 = 36 months For monthly payment =$12400/36 = $344.4. Question 5. Find the amount of Claudia’s total repayment for these choices. a. 14% for 3 years: ____________ Answer: Loan money =$10,000
Number of years = 3
Interest rate = 14%
Formula = PTR/100 = $10,000 × 3 × 14/100 =$4200.
The total repayment money for 3 years = $10,000 +$4200 = $14200. b. 14% for 5 years: ____________ Answer: Loan money =$10,000
Number of years = 5
Interest rate = 14%
Formula = PTR/100 = $10,000 × 5 × 14/100 =$7000.
The total repayment money for 5 years = $10,000 +$7000 = $17000. c. 8% for 3 years: ____________ Answer: Loan money =$10,000
Number of years = 3
Interest rate = 8%
Formula = PTR/100 = $10,000 × 3 × 8/100 =$2400.
The total repayment money for 3 years = $10,000 +$2400 = $12400. Question 6. Find the amount that Claudia would pay in interest for these choices. a. 14% for 3 years: ____________ Answer: Loan money =$10,000
Number of years = 3
Interest rate = 14%
Formula = PTR/100 = $10,000 × 3 × 14/100 =$4200.

b. 14% for 5 years: ____________
Loan money = $10,000 Number of years = 5 Interest rate = 14% Formula = PTR/100 =$10,000 × 5 × 14/100 = $7000. The total interest for 5 years =$7000.

c. 8% for 3 years: ____________
Loan money = $10,000 Number of years = 3 Interest rate = 8% Formula = PTR/100 =$10,000 × 3 × 8/100 = $2400. The interest for 3 years =$2400.

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?
Car dealer loan at 14% of 3 years.
Loan money = $10,000 Number of years = 3 Interest rate = 14% Formula = PTR/100 =$10,000 × 3 × 14/100 = $4200. The total interest for 3 years =$4200.
Bank loan at 8% of 3 years.
Loan money = $10,000 Number of years = 3 Interest rate = 8% Formula = PTR/100 =$10,000 × 3 × 8/100 = $2400. The interest for 3 years =$2400.
The interest on the bank loan is less compared to the dealer loan.

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?
Car dealer loan at 14% of 3 years.
Loan money = $10,000 Number of years = 3 Interest rate = 14% Formula = PTR/100 =$10,000 × 3 × 14/100 = $4200. The total interest for 3 years =$4200.
Car dealer loan at 14% of 5 years.
Loan money = $10,000 Number of years = 5 Interest rate = 14% Formula = PTR/100 =$10,000 × 5 × 14/100 = $7000. The total interest for 5 years =$7000.
The interest rate is more for the 5 years loan compared to the 3 years loan.

Question 9.
If Claudia wants the lowest possible monthly payment, which option should she choose?
8% of a 3 years bank loan is the best option. Compared to all the options its amount is less.
Loan money = $10,000 Number of years = 3 Interest rate = 8% Formula = PTR/100 =$10,000 × 3 × 8/100 = $2400. The total money for 3 years =$10,000 + $2400 =$12400.
1 year = 12 months
3 years = 3 × 12 = 36 months
For monthly payment = $12400/36 =$344.4.

Question 10.
If Claudia wants the lowest possible cost for the loan, which option should she choose?
She can choose the 8% of 3 years bank loan. Because it is the lowest possible cost.
Loan money = $10,000 Number of years = 3 Interest rate = 8% Formula = PTR/100 =$10,000 × 3 × 8/100 = $2400. The total repayment money for 3 years =$10,000 + $2400 =$12400.

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.
Here loan length means the duration. When the duration increases you have a lower interest rate. But you affect the monthly payments because the duration increases the monthly payments increases.

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?
Jess takes an easy access loan = $200. The cost of a loan is 2% for every$20.
Therefore 20 × 10 = 200
2% of 20 = 0.4.
0.4 × 10 = $4. Jess will owe at the end of a loan =$200.
Jess’s total payment is $200 +$200 + $4 =$404.

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? Answer: Changing a computer =$2000.
Interest =21%
Months = m
Using online calculator
$44.30 per month Christopher paid twice the original price =$4000.
Repaying money = monthly payment × number of months.
4000 = monthly payment × m
4000 = $44.30 × m M = 4000/$44.30 = 90.2
Therefore m = 90.2 months.

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.
The cost of the machine = $1500. She saves in each month =$200.
Therefore $1500/$200 = 7.5
To buy a machine you can save $200 for 7 and half months. Or take a loan from the bank and buy a machine and later may have$200 in the bank with interest.

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: Pat can get a student loan =$10,000.
Number of years = 10.
Interest rate = 7%.
Formula for the simple interest = PTR/100 =$10,000 × 10 × 7/100 = 7000. Total amount for 10 years =$10,000 + $7000 =$17000.
And the same amount of 5 years and 4%.
Simple interest = PTR/100 =$10,000 × 5 × 4/100 =$2000.
Pat should do the %5 years at an interest rate of 4%. Because it interest is less than the 10 years at an interest of 7%.

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?