Updated 11/15/21Course Information
Course Scope and Sequence
Semester A
Student Name:
________________________________________________
1. Gross Income
Math Teacher Information:
2. Net Income & Recordkeeping
________________________________________________
3. Checking Accounts
________________________________________________
Tutor Information:
4. Savings Accounts
________________________________________________
5. Cash Purchases
________________________________________________
Semester B
1. Charge Accounts & Credit Cards
Math Schedule (Days/Time)
2. Loans
MON
TUE
WED
THU
FRI
3. Vehicle Transportation
4. Housing Costs
Credit Materials
Pencil
This Learning Events Packet (LEP)
McGraw Hill Mathematics of Business and
Personal Finance (2016) Student Textbook
Internet (optional)
Calculator (optional)
5. Investments
Personal Finance B
Credit 2 LEP
Page |2
Grading Components
Scale
Grade
A
B
C
D
Incomplete
Value
100-90%
89-80%
79-70%
69-60%
59-0%
Learning Events Packet (Mandatory)
Complete all the activities, and show all your thinking
in the space provided in the packet or on separate
paper.
Credit Components
Credit Checkpoint (15%)
Complete the Credit Checkpoint and show all your
thinking.
Quiz
70%
Homework (15%)
All homework is to be completed inside this packet or on
separate paper. Show organization and show all your
thinking.
Homework
15%
Credit
Checkpoint
15%
Quiz (70%)
Use the Credit Checkpoint to review concepts and
prepare for the Quiz.
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Vocabulary
The Vocabulary icon will focus on math vocabulary words that will help you with the
concepts you are learning.
Personal Finance B
Credit 2 LEP
Page |3
Credit Instructions
➢
Make sure to read each entire lesson inside this
Learning Events Packets (LEP) and study the
given examples before attempting the activities
that immediately follow.
➢
Use the instructional videos for each lesson to help
you work independently and determine where you
may need extra support from your teacher and/or
tutor.
➢
Write neatly and show as much of your thinking
as possible. You may complete your work inside
this packet or on separate paper.
➢
You may use a calculator when completing
the activities and quiz for this credit, but
you should always verify with your teacher,
as they will make the final decision on.
Digital Resources
L4L Virtual Tutoring
Visit our Virtual Tutoring Site and work with a tutor
virtually from your home Monday – Friday 9:30am to 6pm
http://tutoring.learn4life.org/
L4L Student Math Resource Website
Home to all of our math instructional videos!
http://learn4.life/math
or
http://bit.ly/L4Lmath
Personal Finance B
Credit 2 LEP
Page |4
Pacing Guide
Due Date
Completion Date
Due Date
Completion Date
Lesson 8.1 – Single-Payment Loans
Learning Goal: I can compute the maturity value and interest rate of a
single-payment loan.
Lesson 8.2 – Installment Loans – Amount Financed
Learning Goal: I can calculate the down payment and the amount financed
on an installment loan.
Lesson 8.3 – Installment Loans – Monthly Payment & Finance
Charge
Learning Goal: I can calculate the monthly payment, total amount repaid,
and finance charge on an installment loan.
Lesson 8.4 – Installment Loans – Monthly Payment Allocation
Learning Goal: I can calculate the payment to interest, payment to principal,
and new balance.
Lesson 8.5 – Paying Off Installment Loans
Learning Goal: I can compute the final payment when paying off an
installment loan.
Lesson 8.6 – Determining the APR
Learning Goal: I can determine the annual percentage rate of a loan using a
table and a formula.
Summative Assessments
Credit Checkpoint
Quiz
Personal Finance B
Credit 2 LEP
Page |5
Lesson 8.1
Single-Payment Loans
Learning Goal: I can compute the maturity value and interest rate
of a single-payment loan.
L4L Math Resource Center
learn4.life/Math
Video Instruction Available!
Read the section below and complete the following activity.
Single-Payment Loans – A single-payment loan is a loan that you repay with one payment after a specified
period of time. A business may be short of funds and need to borrow money to meet its payroll or pay for
inventory and supplies. The business owner could sign a promissory note with its financial institution. A
promissory note is a written promise to pay a certain sum of money on a specific date in the future. The
maturity value of the loan is the total amount you must repay. It includes both the principal and the interest
owed. Remember that principal is the amount borrowed.
A loan’s term is the amount of time for which the loan is granted. For example, a single-payment loan may be
granted for a number of years, months, or days. When the term is a specific number of days, the lending agency
may calculate interest in one of two ways:
1. Ordinary interest is based on a 360-day year.
2. Exact interest is based on a 365-day year.
The following formulas are used:
Interest = Principal ∙ Rate ∙ Time
Ordinary Interest = Principal ∙ Rate ∙
Exact Interest = Principal ∙ Rate ∙
Time
360
Time
365
Maturity Value = Principal + Interest
Example 1
Anita Sloane’s bank granted her a single-payment loan of $7,200 for 91 days to pay for new merchandise for her
candle shop. Determine the maturity value of the loan if the rate is (a) 6% ordinary interest or (b) 6% exact
interest.
Step 1:
Step 2:
Step 3:
Step 4:
Find the ordinary interest owed.
Ordinary Interest
=
Principal
∙
Rate
∙
$𝟏𝟎𝟗. 𝟐𝟎
=
$7,2000
∙
0.06
∙
time
360
91
360
Find the maturity value with ordinary interest.
+ Interest
Maturity Value = Principal
$𝟕, 𝟑𝟎𝟗. 𝟐𝟎
= $7,2000.00 + $109.20
Find the exact interest owed.
Principal
∙
Rate
∙
$7,200.00
∙
0.06
∙
Time
365
91
365
= $107.704 = $𝟏𝟎𝟕. 𝟕𝟎 Exact Interest
Find the maturity value with exact interest.
+ Interest
Maturity Value = Principal
$𝟕, 𝟑𝟎𝟕. 𝟕𝟎
= $7,2000.00 + $107.70
Personal Finance B
Credit 2 LEP
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Example 2 – Real-world Algebra Connection
Claudia Valdez took out a single-payment loan for $1,500.00 at 7.8% ordinary interest to pay her federal income
tax bill. If the loan’s maturity value is $1,529.25, when would Claudia have to pay back the loan?
Step 1:
Step 2:
Find the interest, 𝐼.
Maturity
=
Value
$1,529.25
=
$29.25
=
Principal
+
Interest
$1,500.00
𝐼
+
𝐼
Substitute given values.
Subtract $1,500.00 on both sides.
Find the time of the loan in days, 𝑡.
Ordinary Interest
=
Principal
∙
Rate
∙
$29.25
=
$1,500.00
∙
0.078
∙
t
360
𝑡
360
$10,530
=
$117𝑡
90
=
𝑡
Claudia would have to pay back the loan in 𝟗𝟎 days.
Substitute given values.
Multiply both sides by 360.
Divide both sides by $117.
Concept Check
Compute the a) interest and b) maturity value for each loan. (From Example 1)
1. Parker Logan purchased a new surfboard costing $600 and financed it at 9% ordinary interest for 90 days.
a) $13.50
b) $613.50
2. Holmes Ostendorf added a tack room to his barn costing $4,850 financed at 7% exact interest for 120 days.
a) $111.62
b) $4,961.62
Complete the problem. (From Example 2)
3. How long would it take a construction loan for $548,048 to earn interest of $50,000 at 9% exact interest?
370 days
Personal Finance B
Credit 2 LEP
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EVALUATE
Independent Practice
Lesson 8.1 Homework
Complete problems 1-3 below for independent practice.
HW
When you are finished, check the solutions with your teacher.
Calculate the interest and maturity value in each row.
1.
Row 1: a) $4.50; b) $904.50
Row 2: a) $9.67; b) $1,969.67
Row 3: a) $164; b) $4,964.00
Row 4: a) $656.04; b) $10,331.04
Determine the a) interest owed, and b) maturity value.
2. Sari Tagore obtains a $1,000 loan to purchase a laser printer. Her interest rate is 7% ordinary interest for 108
days.
a) $21
b) $1,021
Solve the problem below.
3. On April 14, Mikos Souvakis borrowed $100,000 to remodel his restaurant kitchen with a single payment loan
at 10.5% ordinary interest. If his loan’s maturity value was $104,375, how many days does Mikos have to pay
it back? 153 days
Personal Finance B
Credit 2 LEP
Page |8
Learning Goal
Lesson Reflection (Circle one)
I can compute the maturity value and interest rate of a single-payment
loan.
Starting…
Getting there…
Got it!
Lesson 8.1 Checkpoint
Once you have completed the above problems and checked your solutions, complete the Lesson Checkpoint
below.
Complete the Lesson Reflection above by circling your current understanding of the Learning Goal.
Determine the a) interest owed and b) maturity value.
1. Helio Silver obtains a loan to buy a piano for $8,400. His interest rate is 12% exact interest for 146 days.
a) $403.20
b) $8,803.20
Solve the problem below.
2. Suppose that your bank has a minimum loan charge of $48 when you borrow at 6% ordinary interest for 90
days. What principal borrowed will result in a $48 interest charge?
$3,200
Personal Finance B
Credit 2 LEP
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Lesson 8.2
Installment Loans – Amount Financed
Learning Goal: I can calculate the down payment and the amount
financed on an installment loan.
L4L Math Resource Center
learn4.life/Math
Video Instruction Available!
Read the section below and complete the following activity.
Installment Loans – You could apply for an installment loan to finance the purchase of a new or used vehicle,
such as a car, truck, or motorcycle. You repay an installment loan in equal payments over a specified period
of time. Usually, when you purchase an item with an installment loan, you must make a down payment. The
down payment is a portion of the cash price of the item you are purchasing before financing the rest on credit.
It could be a dollar amount or a percent of the cash price. The amount financed is the portion of the cash price
that you owe after making the down payment. The formulas to calculate the amount financed are:
Amount Financed = Cash Price − Down Payment
Down Payment = Cash Price ∙ Percent
Example 1
Trudy Quintero is buying gym equipment for $1,399. She makes a $199 down payment and finances the
remainder. How much does she finance?
Find the amount financed.
Cash Price − Down Payment
$1,399 − $199 = $𝟏, 𝟐𝟎𝟎 amount financed
Trudy financed $𝟏, 𝟐𝟎𝟎.
Example 2 – Real-world Algebra Connection
Roslyn Clay purchased a previously owned piano for $1,140 using the store’s installment credit plan. She made a
20% down payment and financed the remaining amount. What amount did she finance?
Step 1:
Step 2:
Find the 20% down payment.
Down Payment = Cash Price ∙ Percent
Down Payment = $1,140 ∙ 20%
Down Payment = $1,140 ∙ 0.20
Down Payment = $𝟐𝟐𝟖
Find the amount financed.
Amount Financed = Cash Price − Down Payment
$𝟗𝟏𝟐
= $1,140 −
$228
Substitute given values.
Convert percent 20% to decimal 0.20.
Multiply $1,140 and 0.20.
Substitute given values and simplify.
Roslyn financed $𝟗𝟏𝟐.
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Concept Check
Complete the problems by determining the amount financed. (From Example 1)
1. Melinda Vardalos purchased season concert tickets for $1,999.99. The down payment is $199.99. $1,800
2. Bertellini Dentistry purchased new equipment for $3,950. The down payment is $150. $3,800
Find the a) down payment, and b) amount financed. (From Example 2)
3. Antonio Reyes purchased an antique chest for a $1,360 cash price. He made a 20% down payment.
a) $272
b) $1,088
4. Maya DiNardo purchased a diamond bracelet for $1,725. The down payment was 30%.
a) $517.50
b) $1,207.50
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EVALUATE
Independent Practice
Lesson 8.2 Homework
Complete problems 1-5 below for independent practice.
HW
When you are finished, check the solutions with your teacher.
Find the a) down payment and b) amount financed in each row.
1.
Row 1: a) $120; b) 520
Row 2: a) $1,400; b) $3,460
Row 3: a) $1,500; b) $8,274
Row 4: a) $1,440; b) $2,160
Row 5: a) $1,422; b) $8,058
Row 6: a) $1,341; b) $4,023
Find the amount financed.
2. Owen Hawkins purchased carpentry equipment for $1,265 with a $100 down payment.
$1,165
3. Megan Barnes purchased photography equipment for $4,100 with a $1,000 down payment.
$3,100
Find the a) down payment, and b) amount financed.
4. Laurenz Huber financed the purchase of an $8,371.39 used car with a 15% down payment.
a) $1,255.71
b) $7,115.68
5. Linda Cusak purchased a $279.50 DVD player/stereo for her car. Using the store’s credit plan, she made a
$50.00 down payment.
a) $50
b) $229.50
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Learning Goal
Lesson Reflection (Circle one)
I can calculate the down payment and the amount financed on an
installment loan.
Starting…
Getting there…
Got it!
Lesson 8.2 Checkpoint
Once you have completed the above problems and checked your solutions, complete the Lesson Checkpoint
below.
Complete the Lesson Reflection above by circling your current understanding of the Learning Goal.
Find the amount financed.
1. Audrey Copeland purchased a used car for $14,470 with a $3,000 down payment.
$11,470
Find the a) down payment, and b) amount financed.
2. Bailey Ruffin bought a new motorcycle for $18,936.50 and made a 30% down payment.
a) $5,680.95
b) $13,255.55
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Installment Loans – Monthly Payment &
Finance Charge
Lesson 8.3
Learning Goal: I can calculate the monthly payment, total amount
repaid, and finance charge on an installment loan.
L4L Math Resource Center
learn4.life/Math
Video Instruction Available!
Read the section below and complete the following activity (adapted from Lesson 8.3).
Installment Loans – When you obtain an installment loan, you must pay finance charges for the use of the
money. You repay the loan with equal monthly payments over a specified period of time. Part of each payment
pays the interest on the loan’s unpaid balance. The remaining part of the payment is used to reduce the balance
of the loan principal.
The amount of each monthly payment depends on the amount financed, the number of payments, and the
annual percentage rate. The annual percentage rate (APR) is an index showing the cost of borrowing money
on a yearly basis, expressed as a percent. You will need to refer to the Monthly Payment on a Simple Installment
Loan of $100 table listed below to calculate related amounts. You will also need to use the following formulas:
Monthly Payment =
Amount of Loan
$100
∙ Monthly Payment for a $100 Loan
Total Amount Repaid = Number of Payments ∙ Monthly Payment
Finance Charge = Total Amount Repaid − Amount Financed
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Example 1
Blake and Jacqueline Toepfer are purchasing a $1,399.99 side-by-side refrigerator with an installment loan that
has an APR of 12%. The store financing requires a 10% down payment and 12 monthly payments. What is the
finance charge?
Step 1:
Step 2:
Find the amount financed.
Amount Financed = Selling Price − Down Payment
Amount Financed = $1,399.99 − (0.10 ∙ $1,399.99)
Amount Financed = $1,399.99 −
$140.00
Amount Financed = $𝟏, 𝟐𝟓𝟗. 𝟗𝟗
Find the monthly payment. (Refer to the Monthly Payment on a Simple Installment Loan of $100
table on the previous page.)
Monthly Payment =
Monthly Payment
Step 3:
Step 4:
Amount of Loan
$100
$1,259.99
$100
∙ Monthly Payment for a $100 Loan
∙
$8.88
Monthly Payment = $111.887
Monthly Payment = $𝟏𝟏𝟏. 𝟖𝟗
Find the total amount repaid.
Total Amount Repaid = Number of Payments ∙ Monthly Payment
Total Amount Repaid =
12
∙
$111.89
Total Amount Repaid = $𝟏, 𝟑𝟒𝟐. 𝟔𝟖
Find the finance charge.
Finance Charge = Total Amount Repaid − Amount Financed
Finance Charge =
$1,342.68
−
$1,259.99
Finance Charge = $𝟖𝟐. 𝟔𝟗
The finance charge is $𝟖𝟐. 𝟔𝟗.
Concept Check
Complete the problem.
1. Ingrid Nilsen purchased a $4,000 hydroponic system for her garden. The down payment is 20%, and the
installment loan has an APR of 10% for 36 months. Find the a) down payment, b) amount financed, c) monthly
payment, d) total amount repaid, and e) finance charge.
a) $800
b) $3,200
c) $103.36
d) $3,720.96
e) $520.96
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EVALUATE
Independent Practice
Lesson 8.3 Homework
Complete problems 1-6 below for independent practice.
HW
When you are finished, check the solutions with your teacher.
Determine the a) down payment, b) amount of the loan, c) monthly payment, and d) finance charge.
1. Jason Wagner obtains an installment loan to buy a $12,000 Honda Accord. His down payment is 25%, and the
APR is 9% for 36 months.
a) $3,000
b) $9,000
c) $286.20
d) $1,303.20
2. Shelly Lemony obtains a small business equipment loan for $120,000. Her down payment is 20% and the APR
is 8% for 12 months.
a) $24,000
b) $96,000
c) $8,352
d) $4,224
Find the finance charge.
3. Patrick Woracek obtains an installment loan of $6,400 to buy a professional digital camera and lenses. The
APR is 12%. The loan is to be repaid in 36 monthly payments.
$1,249.28
4. Adolfo LaRosa obtained an installment loan of $6,800 to help pay his college tuition. Student loans do not
require a down payment. He obtained the loan from a local bank and agreed to repay the loan in 24 monthly
payments at an 18% APR.
$1,343.68
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Complete the following problems.
5. Andrew and Ruth Bacon would like to obtain an installment loan of $1,850 to repaint their home. They can
get the loan at an APR of a) 8% for 24 months or b) 11% for 18 months. Which loan has the lower finance
charge? Lower finance charge is APR of 8% for 24 months at $156.88 compared to APR of 11% for 18 months
at $164.65
6. Lucy and Don Pflum need an installment loan of $12,900 to remodel their hair salon. City Loan will lend the
money at 10% for 24 months. Economy Line Finance Company will lend the money at 9% for 30 months.
Which loan costs less? How much will they save by taking the loan that costs less?
City Loan = $1,372.56
Economy Line = $1,535.10
City Loan costs $162.54 less
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Learning Goal
Lesson Reflection (Circle one)
I can calculate the monthly payment, total amount repaid, and finance
charge on an installment loan.
Starting…
Getting there…
Got it!
Lesson 8.3 Checkpoint
Once you have completed the above problems and checked your solutions, complete the Lesson Checkpoint
below.
Complete the Lesson Reflection above by circling your current understanding of the Learning Goal.
Find the finance charge.
1. Herb and Marci Jordan obtained an installment loan that has a 10% APR to purchase a dishwasher that
sells for $699.95. They agree to make a down payment of 20% and to make 12 monthly payments. What is
the finance charge?
$30.69
Complete the following problem.
2. Lola Segal needs to take out an installment loan of $1,200 to pay for auto repairs. Walton Savings and Loan
will lend her the money at 9% for 12 months. Horton finance company at 12% for 24 months. How much will
she save by taking the loan with the lower finance charge?
$96.48 saved by using Walton Savings
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Credit 2 LEP
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Lesson 8.4
Installment Loans – Monthly Payment
Allocation
Learning Goal: I can calculate the payment to interest, payment to
principal, and new balance.
L4L Math Resource Center
learn4.life/Math
Video Instruction Available!
Read the section below and complete the following activity (adapted from Lesson 8.4).
Allocation of Payment on Installment Loans – As you learned in the last lesson, Lesson 8.3, an installment
loan is repaid in equal monthly payments. Part of each payment is allocated to pay the interest on the unpaid
balance of the loan, and the remaining part is used to reduce the balance. The interest is calculated each month
on the unpaid balance using the simple interest formula. The amount of principal that you owe decreases with
each monthly payment. The formulas follow:
Interest = Principal ∙ Rate ∙ Time
Payment to Principal = Monthly Payment − Interest
New Principal = Previous Principal − Payment to Principal
A repayment schedule shows the distribution of interest and principal over the life of a loan. The repayment
schedule below shows the interest and principal on an $1,800 installment loan for 6 months at 8%.
Example 1
Melinda and Xavier Garza obtained a loan for a used pickup truck. See the loan of $1,800 at 8% for 6 months in
the repayment schedule in the table above. She the calculation for the first payment. What are the (𝐚) interest,
(𝐛) payment to principal, and (𝐜) new principal after they make the first payment?
Step 1:
Find the interest.
Interest = Principal ∙ Rate ∙ Time
$𝟏𝟐
Step 2:
Step 3:
= $1,800 ∙ 8% ∙
1
12
Find the payment to principal.
Payment to Principal = Monthly Payment − Interest
$𝟐𝟗𝟓. 𝟎𝟖
=
$307.08
− $12.00
Find the new principal.
New Principal = Previous Principal − Payment to Principal
$𝟏, 𝟓𝟎𝟒. 𝟗𝟐 =
$1,800.00
−
295.08
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Example 2
Anton Grindenko obtained a $6,000 loan to update his café’s kitchen equipment at 8% for 36 months. The
monthly payment is $187.80. The balance of the loan after 20 payments is $2,849.08. What is the interest for the
first payment? What is the interest for the 21st payment? Why is the interest so much different for the two
payments?
Step 1:
Find the interest for the first payment.
Interest for First Payment = Principal ∙ Rate ∙ Time
$𝟒𝟎. 𝟎𝟎 = $6,000.00 ∙ 8% ∙
1
12
Anton pays $𝟒𝟎. 𝟎𝟎 interest in the first payment.
Step 2: Find the interest for the 21st payment.
Interest for 21st Payment = Principal ∙ Rate ∙ Time
$𝟏𝟖. 𝟗𝟗 = $2,849.08 ∙ 8% ∙
1
12
Anton pays $𝟏𝟖. 𝟗𝟗 interest in the 𝟐𝟏st payment.
The interest is reduced by more than half because the principal on which the interest is calculated for the first
payment is much higher than the principal on which the interest for the 21st payment is calculated.
Concept Check
Complete the problem. (From Example 1)
1. Use the loan information from the Garzas in Example 1 to compute the second month values for:
a) The interest $10.03
b) The payment to principal $297.05
c)
The new balance $1,207.87
Complete the problem. (From Example 2)
2. You take out an $8,000 loan on a new motorcycle at 12% for 24 months. The monthly payment is $376.80. The
balance of the loan after 15 payments is $3,222.44. What is the interest for the a) first payment and b) 16th
payment?
a) $80
b) $32.22
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EVALUATE
Independent Practice
Lesson 8.4 Homework
Complete problems 1-3 below for independent practice.
HW
When you are finished, check the solutions with your teacher.
Determine the missing amounts in the following table.
1.
Row 1: a) $1,105.44
Row 2: a) $28.83; b) $179.12; c) $3280.88
Row 3: a) $54; b) $275.04; c) $6,924.96
Complete the repayment schedule for a $2,400 loan at 12% for 12 months.
2.
Row 1: a) $1,236.53
Row 2: a) $200.75; b) $1,035.78
Row 3: a) $10.36; b) $202.76; c) $833.02
Row 4: a) $8.33; b) $204.79; c) $628.23
Row 5: a) $6.28; b) $206.84; c) $421.39
Row 6: a) $4.21; b) $208.91; c) $212.48
Row 7: a) $213.12; b) $2.12; c) $211; d) $1.48
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Complete the problem.
3. Emma Jarmel obtained a $6,000 loan at 10% for home improvements. The monthly payment is $276.60. What
is the amount of the a) interest for the first payment, b) payment to principal, and c) new principal?
a) $50
b) $226.60
c) $5,773.40
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Learning Goal
Lesson Reflection (Circle one)
I can calculate the payment to interest, payment to principal, and new
balance.
Starting…
Getting there…
Got it!
Lesson 8.4 Checkpoint
Once you have completed the above problems and checked your solutions, complete the Lesson Checkpoint
below.
Complete the Lesson Reflection above by circling your current understanding of the Learning Goal.
Complete the following problems.
1. Don Stone obtained an $8,500 installment loan at 14% for 42 months. The loan’s balance after 26 payments is
$3,733.55. What is the interest for payment 27?
$43.56
2. Demarrio Kibbe obtained a loan for $4,500 at 10%. The monthly payment is $270.45. What is the amount of
the a) interest for the first payment, b) payment to principal, and c) new principal?
a) $37.50
b) $232.95
c) $4,267.05
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Lesson 8.5
Paying Off Installment Loans
Learning Goal: I can compute the final payment when paying off
an installment loan.
L4L Math Resource Center
learn4.life/Math
Video Instruction Available!
Read the section below and complete the following activity.
Determining the Final Payment – When you have an installment loan, you pay interest on the unpaid
balance. You might have a simple interest installment loan for a car and sell the car before the end of the loan
term. If so, you pay only the previous balance plus the current month’s interest. This is known as the final
payment. Note that there may be a penalty for paying off a loan early.
One motive to pay off a loan before the end of the term is to pay less interest. The amount of interest saved
depends on the total payback minus the sum of the previous payments and the final payment. You will need to
use three formulas:
Interest = Principal ∙ Rate ∙ Time
Final Payment = Previous Balance + Current Month′ s Interest
Interest Saved = Total Payback − (Sum of Previous Payments + Final Payment)
Example 1
See the figure below for the first 3 months of the repayment schedule for Darlene and Hayden Grant’s home
repair loan of $1,800 at 12% interest for 6 months. What is the final payment if they pay the loan off with the
fourth payment?
Step 1:
Step 2:
Find the previous balance.
Read the repayment schedule above for the balance after the third payment. It is $913.70.
Find the interest for the fourth month.
Principal ∙ Rate ∙ Time
$913.70 ∙ 12% ∙
Step 3:
1
12
= $9.137 = $𝟗. 𝟏𝟒 Interest (fourth month)
Find the final payment.
Final Payment = Previous Balance + Current Month′ s Interest
$𝟗𝟐𝟐. 𝟖𝟒
=
= $913.70
+
$9.14
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Example 2 – Real-world Algebra Connection
How much would the Grants in Example 1 save by paying off the loan early?
Find the interest saved.
Interest Saved = Total Payback − (Sum of Previous Paymetns + Final Payment)
(3 ∙ $310.50)
= (6 ∙ $310.50) − [
+ $922.84]
=
$1,863.00 − [
$931.50
+ $922.84]
$𝟖. 𝟔𝟔 =
$1,863.00 − $1,854.34
They saved $𝟖. 𝟔𝟔.
Substitute given values.
Multiply 3 ∙ $310.50.
Add inside brackets.
Concept Check
Complete the problem. (From Example 1)
1. You plan to finance the purchase of a $1,200 electric scooter with a 12-month loan at 12% interest with a balance
of $816.04 after the fourth payment. What is the final payment amount if you pay off the loan with the fifth
payment? $824.20
Complete the problem. (From Example 2)
2. In problem 1 above, you had a 12-month loan of $1,200 at 12% interest to purchase an electric scooter. The
balance after the fourth payment of $106.56 is $816.04. How much do you save by paying off the loan with the
fifth payment? $28.28
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EVALUATE
Independent Practice
Lesson 8.5 Homework
Complete problems 1-3 below for independent practice.
HW
When you are finished, check the solutions with your teacher.
Find the interest and final payment.
1.
Row 1: a) $48; b) $4,848
Row 2: a) $20; b) $3,020
Row 3: a) $12.17; b) $1,472.97
Row 4: a) $29.91; b) $4,017.51
Row 5: a) $29.94; b) $3,295.81
Complete the following problems.
2. Jean-Claude Bubose will be the best man at his friend’s wedding. To pay for plane fare, gifts, and other
expenses, he took a $1,800 installment loan. The loan is for 12 months at 8% interest with a $156.60 monthly
payment. After 8 months, the balance is $615.87, and he pays off the loan when the next payment is due. a)
What is the amount of the final payment? b) How much does he save by paying the loan off early?
a) $619.98
b) $6.42
3. Nancy Parker has a $12,000 simple-interest installment loan at 12% for 36 months. The monthly payment is
$398.52. The balance after the sixth payment is $10,286.53. a) What is the final payment if the loan is paid off
with the seventh payment? b) How much will Nancy save by paying off the loan with payment number 7?
a) $10,389.40
b) $1,566.20
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Learning Goal
Lesson Reflection (Circle one)
I can compute the final payment when paying off an installment loan.
Starting…
Getting there…
Got it!
Lesson 8.5 Checkpoint
Once you have completed the above problems and checked your solutions, complete the Lesson Checkpoint
below.
Complete the Lesson Reflection above by circling your current understanding of the Learning Goal.
Complete the following problem.
1. Willard Hudson paid for a shipment of bicycles with a $6,000 installment loan at 10% interest for 24 months.
His monthly payment is $276.60. After 4 payments, the balance is $5,082.21. He pays off the loan when the
next payment is due. What is the amount of a) interest, b) final payment, and c) savings if Willard pays off
the loan with the fifth payment?
a) $42.35
b) $5,124.56
c) $407.44
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Lesson 8.6
Determining the APR
Learning Goal: I can determine the annual percentage rate of a
loan using a table and a formula.
L4L Math Resource Center
learn4.life/Math
Video Instruction Available!
Read the section below and complete the following activity.
Determining the APR – You should know that a lender who gives you an installment must tell you the annual
percentage rate (APR). If you know the number of monthly payments and the finance charge per $100 of the
amount financed, you can determine the loan’s APR. You can use a table such as the one below to find the
APR. With this information, you can compare the cost related to different loans. The full table can be found at
the end of this LEP on pages 36-37 and should be used to help you solve the homework problems.
Example 1
Paul Norris obtained a $1,500 installment loan to buy a racing bicycle. The finance charge is $146.25, and he will
repay the loan in 18 monthly payments. What is the APR?
Step 1:
Find the finance charge per $100.
Finance Charge per $100
=
$100.00
∙
=
$100.00
∙
Finance Charge
Amount Financed
$146.25
$1,500.00
$𝟗. 𝟕𝟓 = $100.00 ∙
0.0975
For every $𝟏𝟎𝟎 Paul borrows, he will pay a $𝟗. 𝟕𝟓 finance charge.
Step 2: Find the APR. (Refer to the Annual Percentage Rate for Monthly Payment Plans table.)
In the row for 18 payments, find the number closest to $9.75.
It is $9.77.
Read the APR at the top of the column.
The APR is 𝟏𝟐. 𝟎𝟎%.
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Concept Check
Complete the problem by finding the a) finance charge per $100, and b) APR.
1. Francesa Santorelli took a 6-month loan of $800 to buy art supplies. The finance charge is $24.64.
a) $3.08
b) 10.50%
EVALUATE
Independent Practice
Lesson 8.6 Homework
Complete problems 1–3 below for independent practice.
HW
When you are finished, check the solutions with your teacher.
11111
Complete the table. Using the Annual Percentage Rate for Monthly Payment Plans on page 36 & 37,
find the finance charge per $100 and the APR.
1.
Row 1: a) $3.31; b) 11.25%
Row 2: a) $6.64; b) 6.25%
Row 3: a) $3.60; b) 4.50%
Row 4: a) $12.81; b) 8.00%
Determine the APR.
2. Melissa Costouras obtains a $3,000 loan for darkroom equipment. She makes six monthly payments of
$511.18
7.75%
3. Jorge Alonso obtained an installment loan for $3,500 to finance his new invention. The bank requires a down
payment of 20% and 36 monthly payments of $85.18 each.
6.00%
4
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Learning Goal
Lesson Reflection (Circle one)
I can determine the annual percentage rate of a loan using a table and a
formula.
Starting…
Getting there…
Got it!
Lesson 8.6 Checkpoint
Once you have completed the above problems and checked your solutions, complete the Lesson Checkpoint
below.
Complete the Lesson Reflection above by circling your current understanding of the Learning Goal.
Determine the APR.
1. Helen Olson needs an installment loan of $999.00. She must repay the loan in 24 months. The monthly
payment is $44.96.
7.50%
2. Oneta Correy wants to obtain an installment loan of $9,900.00 to purchase a used truck. The bank has agreed
to a loan for 24 months at $439.89 per month.
6.25%
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When all bulleted points below are met, check the box to the right.
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• 1 to 8 points
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60% accuracy.
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the Credit Checkpoint
and/or demonstrate at
least 60% accuracy.
• 1 to 49 points
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the Quiz.
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higher.
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complete the Credit
Checkpoint with an
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complete the Credit
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I scored between 70% to
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• 60 to 70 points
I scored 85% or higher on
the Quiz.
15
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Add the points to approximate the Total Credit Score.
Total Credit Score
=
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Name _____________________________________________________________
Comment:
Personal Finance B Credit 2
Credit Checkpoint
ASSESSMENT Credit Checkpoint
Complete the following problems to help you prepare for your Quiz.
Learning Goal from Lesson 8.1
How I Did (Circle one)
I can compute the maturity value and interest rate of a single-payment
loan.
I got it!
I’m still learning it.
Compute the loan’s maturity value.
1. Jamie Tavare’s bank granted him a $3,500 single payment loan for 80 days at 11% ordinary interest. What is
the loan’s maturity value? (2 points)
$3,585.56
Learning Goal from Lesson 8.2
How I Did (Circle one)
I can calculate the down payment and the amount financed on an
installment loan.
I got it!
I’m still learning it.
Find the a) down payment and b) amount financed.
2. Devin Gallagher purchased home entertainment equipment for $4,020.19 using the store’s credit plan. He made
a 20% down payment. (2 points)
a) $804.04
b) $3,216.15
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Learning Goal from Lesson 8.3
How I Did (Circle one)
I can calculate the monthly payment, total amount repaid, and finance
charge on an installment loan.
I got it!
I’m still learning it.
Determine the finance charge.
3. Jill Paa obtained a $1,450 installment loan to pay for a new laptop computer for her classwork. She agreed to
repay the loan in 18 monthly payments at an APR of 8%. (2 points)
$92.51
Learning Goal from Lesson 8.4
How I Did (Circle one)
I can calculate the payment to interest, payment to principal, and new
balance.
I got it!
I’m still learning it.
4. Daniela Nanz obtained a $2,500 loan at 12.5% to buy furniture for her apartment. The monthly payment is
$118.23. What is the amount of the a) interest for the first payment, b) payment to principal, and c) new
principal? (3 points)
a) $26.04
b) $92.19
c) $2,407.81
Learning Goal from Lesson 8.5
How I Did (Circle one)
I can compute the final payment when paying off an installment loan.
I got it!
I’m still learning it.
Complete the following problem.
5. Lillian Hartwick paid for her summer college tuition with an installment loan of $3,600 at 8% for 12 months
with a $313.20 monthly payment. After 6 payments, the balance was $1,835.62. She paid off the loan with the
next payment. What is the amount of a) interest, b) final payment, and c) savings by paying the loan off early?
(3 points)
a) $12.24
b) $1,847.86
c) $31.34
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Learning Goal from Lesson 8.6
How I Did (Circle one)
I can determine the annual percentage rate of a loan using a table and a
formula.
I got it!
I’m still learning it.
Determine the APR.
6. Jeff Stapleton acquired a $1,995 installment loan to pay for a new laptop computer. He will repay the loan in 12
monthly payments of $174.70. (3 points)
9.25%
Checkpoint Score
Total
=
Personal Finance B
Credit 2 LEP
15
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Full Table for Lesson 8.6
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