Consumer Finance Unit
(Level IV Graduate Math)
Draft
(NSSAL)
C. David Pilmer
©2008
(Last Update: Dec 2011)
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The following are permitted to use and reproduce this resource for classroom purposes.
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• Canadian public school teachers delivering public school curriculum
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The following are not permitted to use or reproduce this resource without the written
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Individuals, not including teachers or instructors, are permitted to use this resource for their own
learning. They are not permitted to make multiple copies of the resource for distribution. Nor
are they permitted to use this resource under the direction of a teacher or instructor at a learning
institution.
Acknowledgments
The Adult Education Division would also like to thank the following NSCC instructors for
piloting this resource and offering suggestions during its development.
Eileen Burchill (IT Campus)
Elliott Churchill (Waterfront Campus)
Barbara Leck (Pictou Campus)
Suzette Lowe (Lunenburg Campus)
Floyd Porter (Strait Area Campus)
Brian Rhodenizer (Kingstec Campus)
Joan Ross (Annapolis Valley Campus)
Tanya Tuttle-Comeau (Cumberland Campus)
Jeff Vroom (Truro Campus)
Table of Contents
Introduction………………………………………………………………………………… ii
Track Your Progress……………………………………………………………………….. ii
Negotiated Completion Date………………………………………………………………. ii
The Big Picture…………………………………………………………………………….. iii
Course Timelines…………………………………………………………………………... iv
Simple Interest……………………………………………………………………………... 1
Compound Interest………………………………………………………………………… 9
Using the TVM Solver…………………………………………………………………….. 17
Loans with Equal Payments…………………………………………………………… 18
Investments with Equal Payments…………………………………………………….. 27
Using the Formulas……………………………………………………………………. 35
Putting It Together………………………………………………………………………… 37
Consumer Finance Reading Assignment………………………………………………….. 42
Post-Unit Reflections………………………………………………………………………. 43
Answers……………………………………………………………………………………. 44
Online Supports……………………………………………………………………………. 49
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Introduction
We all want to live a good life which includes good health, fulfilling work, loving relationships,
and financial security. Financial security is difficult to define because it changes from individual
to individual. Some desire excessive amounts of material goods, world travel, multiple
dwellings, and fine dining. Others are content with a simpler life that is not cluttered with
excesses. Regardless of how you define financial security, the ability to obtain this security is
directly connected to your understanding of the financial options that exist for consumers. You
must be an educated consumer when deciding to invest, buy items on credit, or select a
mortgage.
In this unit, you will be provided with the information and skills so that you can make proper
financial decisions. You will initially learn about simple and compound interest. The
calculations for these types of problems will be completed using pencil and paper. Later in the
unit you will look at loans and investments that involve regular equal payments. With these
situations you will be using technology (The TVM Solver on the Graphing Calculator) to solve
related problems.
Track Your Progress
Date
Started
Simple Interest…………………….…………………….……
Compound Interest…………..……………………..…………
Loans with Equal Payments…………………………………..
Investments with Equal Payments……………………………
Putting It Together……………………………………………
Consumer Finance Reading Assignment……………………..
Date
Completed
1
9
18
27
37
42
Negotiated Completion Date
After working for a few days on this unit, sit down with your instructor and negotiate a
completion date for this unit.
Start Date:
_________________
Completion Date:
_________________
Instructor Signature: __________________________
Student Signature:
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The Big Picture
The following flow chart shows the five required units and the four optional units (choose two of
the four) in Level IV Graduate Math. These have been presented in a suggested order.
Math in the Real World Unit (Required)
• Fractions, decimals, percents, ratios, proportions, and
signed numbers in real world applications
• Career Exploration and Math
Solving Equations Unit (Required)
• Solve and check equations of the form Ax + B = Cx + D ,
A = Bx 2 + C , and A = Bx 3 + C .
Consumer Finance Unit (Required)
• Simple Interest and Compound Interest
• TVM Solver (Loans and Investments)
• Credit and Credit Scores
Graphs and Functions Unit (Required)
• Understanding Graphs
• Linear Functions and Line of Best Fit
Measurement Unit (Required)
• Imperial and Metric Measures
• Precision and Accuracy
• Perimeter, Area and Volume
Choose two of the four.
Linear
Functions and
Linear Systems
Unit
Trigonometry
Unit
Statistics Unit
ALP Approved
Projects
(Complete 2 of
the 5 projects.)
Note:
You are not permitted to complete four ALP Approved Projects and thus avoid selecting from
the Linear Functions and Linear Systems Unit, Trigonometry Unit, or Statistics Unit.
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Course Timelines
Graduate Level IV Math is a two credit course within the Adult Learning Program. As a two
credit course, learners are expected to complete 200 hours of course material. Since most ALP
math classes meet for 6 hours each week, the course should be completed within 35 weeks. The
curriculum developers have worked diligently to ensure that the course can be completed within
this time span. Below you will find a chart containing the unit names and suggested completion
times. The hours listed are classroom hours.
Unit Name
Minimum
Completion Time
in Hours
24
20
18
28
24
20
20
Total: 154 hours
Math in the Real World Unit
Solving Equations Unit
Consumer Finance Unit
Graphs and Functions Unit
Measurement Unit
Selected Unit #1
Selected Unit #2
Maximum
Completion Time
in Hours
36
28
24
34
30
24
24
Total: 200 hours
As one can see, this course covers numerous topics and for this reason may seem daunting. You
can complete this course in a timely manner if you manage your time wisely, remain focused,
and seek assistance from your instructor when needed.
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Simple Interest
Interest is the money that one earns from an investment or the fee one pays for taking a loan.
Suppose you borrow $50 from a friend. That friend cannot use that $50 to purchase food, go to a
movie, or buy some clothing. Since your friend cannot use the money that has been loaned to
you, it is only fair that you pay your friend a little extra money for the inconvenience. That extra
money is called the interest on the loan.
Simple interest is the interest earned or paid only on the original sum of money that was invested
or borrowed. Most investments and loans today work with compound interest. With compound
interest, the interest is calculated on the original sum of money invested or borrowed plus the
accumulated interest. We’ll look at compound interest in the next section of this unit.
Calculating Simple Interest
Interest = principal × rate × time
I = Prt
•
•
•
P is the principal (also called present value). The principal is the amount of
money borrowed or invested.
r is the interest rate. The rate is expressed as a decimal. The rate is usually per
year, which is also referred to as per annum.
t is the time. Typically the time is expressed in years.
Example 1:
You invest $350 for 2 years at 4% per annum simple interest. How much interest will you earn?
Answer:
I = Prt
I = (350 )(0.04 )(2 )
I = $28.00
You will earn $28 in interest.
Example 2:
You take a simple interest loan from your brother for $800 for 3 months at a rate of 5% per
annum. What is the interest on the loan?
Answer:
I = Prt
I = (800 )(0.05)(0.25)
I = $10.00
Note: 3 months = 0.25 years
You will pay $10 in interest.
It should be noted that with example 2 we are assuming that you will be paying your brother
back using one lump sum payment on the last day of the third month. This would not be
considered an acceptable payment plan by banks or other lending institutions. They would rather
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have you make small monthly payments over the three months until the loan is paid off. You
will learn how to deal with these types of situations later in this unit.
Calculating the Amount (Future Value) for Simple Interest
The amount (also called the future value) is the total value of an investment or loan. The
amount is found by adding the principal and the interest.
Amount = Principal + Interest
A=P+I
(often written as A = P(1 + rt ) )
A = P + Prt
Example 3:
You make a simple interest loan of $1000 at 7.5% per annum for 6 months. How much will you
ultimately pay back at the end of the 6 month period?
Answer:
We need to find A (the amount or future value).
A = P + Prt
Note: 6 months = 0.5 years
A = 1000 + (1000 )(0.075)(0.5)
A = 1000 + 37.5
The person ultimately pays back $1037.50.
A = 1037.5
Example 4:
Marcus invests $700 for 2 years at 6% per annum simple interest. Find the future value of the
investment.
Answer:
We need to find A (the amount or future value).
A = P + Prt
A = 700 + (700 )(0.06 )(2 )
A = 700 + 84
A = 784
The future value of the investment is $784.
Questions:
1. Bashir invested $450 for 2 years at 3% per annum simple interest. How much interest will he
earn?
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2. Brenda takes a simple interest loan for $700 for 3 years at a rate of 8% per annum. What is
the interest on the loan?
3. Dave invests $420 into a simple interest fund that pays 5.5% per annum. If he leaves the
money in the fund for 6 months, how much interest will he earn?
4. Jorell takes a simple interest loan for $270 at 9% per annum. If he pays the loan back after
18 months, how much interest will he have to pay?
5. Tami takes a simple interest loan of $650 has at 12% per annum for 2 years. How much will
Tami ultimately pay back at the end of the 2 year period?
6. June invests $540 for 3 years at 4.5% per annum simple interest. Find the future value of the
investment.
7. Tyrus completed the following calculation.
A = P + Prt
A = 500 + (500 )(0.09 )(3)
A = 500 + 135
A = 635
Create a simple interest question that would use this calculation to find the answer.
8. Kiana takes a simple interest loan of $1100 for 6 months. If the rate of interest is 11% per
annum, how much will Kiana ultimately pay back at the end of the 6 month period?
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Scrambled Answer Key for Questions 1 to 6 and 8.
$806
$168
$1160.50
$36.45
$1206.50
$27
$612.90
$11.55
9. We can use a graphing calculator to work out simple interest. It’s particularly useful if we
need to calculate a lot of future values. In this question, you are going to use the calculator to
solve six future value questions to that you can understand how the size of a loan (or
investment) can affect the future value. We are going to use the calculator’s “list” feature to
accomplish this.
We are going to use principal values of $ 100, $200, $300, $400, $500, and $600. We are
going to take simple interest loans for 3 years at 6% per annum. That means that we will use
the following equation.
A = P + Prt
A = P + (P × 0.06 × 3)
Step 1: Enter the principal values in List 1
STAT > EDIT > Edit > If there are values in L1, > Enter the principal values in
Use the up arrow until
L1.
L1 is highlighted and
press CLEAR.
Step 2: Enter the equation for future values in List 2
STAT > EDIT > Edit > If there are values in L2, > Enter the equation
Use the up arrow until
L2=L1+(L1*0.06*3) in L2.
L2 is highlighted and
When you press ENTER, the
press CLEAR.
future values will appear.
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Step 3: Enter the values in the following table and answer the question.
Principal
L1
100
200
300
400
500
600
Amount (Future Value)
L2=L1+(L1*0.06*3)
How much are the values in List 2 increasing by?
_______
Why are these values increasing? Is this what you expected?
10. In this question, you are going to use the calculator to solve six future value questions so you
can understand how the interest rate of a loan (or investment) can affect the future value.
We are going to use simple interest rates of 3% per annum, 4% per annum, 5% per annum,
6% per annum, 7% per annum, and 8% per annum. We are going to take a simple interest
loan of $400 for 3 years. That means that we will use the following equation.
A = P + Prt
A = 400 + (400 × r × 3)
Step 1: Enter the interest rates in List 1
STAT > EDIT > Edit > If there are values in L1, > Enter the interest rates as
Use the up arrow until
decimal numbers in LI.
L1 is highlighted and
press CLEAR.
Step 2: Enter the equation for future values in List 2
STAT > EDIT > Edit > If there are values in L2, > Enter the equation
Use the up arrow until
L2=400+(400*L1*3) in L2.
L2 is highlighted and
When you press ENTER, the
press CLEAR.
future values will appear.
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Step 3: Enter the values in the following table and answer the accompanying question.
Interest Rate
Amount (Future Value)
L1
0.03
0.04
0.05
0.06
0.07
0.08
L2=400+(400*L1*3)
How much are the values in List 2 increasing by?
_______
Why are these values increasing? Is this what you expected?
11. In this question, you are going to use the calculator to solve six future value questions so you
can understand how the duration of a loan (or investment) can affect the future value.
We are going to use durations of 1 year, 2 years, 3 years, 4 years, 5 years and 6 years. We
are going to take a simple interest loan of $400 at 6% per annum. That means that we will
use the following equation.
A = P + Prt
A = 400 + (400 × 0.06 × t )
Enter the number of years in List 1. Enter the future value equation in List 2. Fill in the
values in the following table and answer the accompanying questions.
Number of Years
Amount (Future Value)
L1
1
2
3
4
5
6
L2=400+(400*0.06*L1)
How much are the values in List 2 increasing by?
_______
Why are these values increasing? Is this what you expected?
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12. In question 9, 10, and 11 you used the List feature on the graphing calculator to help you
calculate multiple simple interest problems. To make sure that you understood what you
were doing, the following questions will ask you to determine what should be entered into
List 1 and List 2 for specific simple interest problems. A sample question and its solution
have been provided.
Sample Question:
You want to use the calculator to see how the interest rate on a simple interest loan can affect
the future value. You are going to use simple interest rates of 1% per annum, 2% per annum,
3% per annum, 4% per annum, 5% per annum, and 6% per annum. We are dealing with a
simple interest loan of $700 for 8 years. What should be entered in List 1 and List 2 of the
calculator?
Answer:
Enter 0.01, 0.02, 0.03, 0.04, 0.05, and 0.06 in List 1
Enter the equation L2 = 700 + (700*L1*8)
(a) You want to use the calculator to see how the duration of a simple interest loan can affect
the future value. You are going to use durations of 2, 4, 6, and 8 years. We are dealing
with a simple interest loan of $900 at 7% interest. What should be entered in List 1 and
List 2 of the calculator?
(b) You want to use the calculator to see how the size of a simple interest loan can affect the
future value. You are going to use principle values of 250, 300, 350, and 400 years. We
are dealing with a simple interest loan at 8% interest for 3 years. What should be entered
in List 1 and List 2 of the calculator?
(c) You want to use the calculator to see how the interest rate on a simple interest loan can
affect the future value. You are going to use simple interest rates of 3% per annum, 3.5%
per annum, 4% per annum, 4.5% per annum, and 5% per annum. We are dealing with a
simple interest loan of $1200 for 2 years. What should be entered in List 1 and List 2 of
the calculator?
13. Why did we use the List feature on the graphics calculator to complete questions 9, 10 and
11?
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Wrap-Up Statement:
In the section “Simple Interest” you learned that simple interest is the interest earned or paid
only on the original sum of money that was invested or borrowed. The total value (i.e. future
value) of the investment or loan is found using the formula A = P + Pr t . Simple interest is
typically not used by lending or investment institutions. They use compound interest.
Simple interest could be used by a friend or family member when they want to lend money to
or borrow money from another friend or family member. In the next section, you will see
how an understanding of simple interest will help you understand compound interest.
Reflect Upon Your Learning
Fill out this questionnaire after you have completed questions 1 to 13. Select your response
to each statement.
1 - strongly disagree
2 - disagree
3 - neutral
4 - agree
5 - strongly agree
(a)
(b)
(c)
(d)
(e)
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I understand all of the concepts covered in the section, “Simple
Interest.”
I do not need any further assistance from the instructor on the
material covered in this section.
I do not need any more practice questions.
I see the difference between questions that are asking me to
find the amount of interest that is generated in a particular time
versus questions that are asking me to find the future value of
the investment or loan.
I can use the list feature on the calculator to solve multiple
simple interest problems.
8
1
2
3
4
5
1
2
3
4
5
1
1
2
2
3
3
4
4
5
5
1
2
3
4
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Compound Interest
With compound interest, the interest is calculated on the original sum of money invested (or
borrowed) plus the accumulated interest. That means that you ultimately made interest on the
principal and the interest itself. With simple interest, you only earn interest on the principal.
For many people, this difference between definitions for compound and simple interest seems
very small and therefore they feel that there is very little difference between the amount of
money that can be generated by these two techniques. You will learn that this is not the case
when money is invested or borrowed over long periods of time.
With compound interest, interest is paid at regular time intervals called the compounding period.
• When compound interest is paid once a year, the compounding period is one year. We
say that the interest is compounded annually.
• When compound interest is paid twice a year, the compounding period is 6 months. We
say that the interest is compounded semiannually.
• When compound interest is paid twelve times a year, the compounding period is one
month. We say that the interest is compounded monthly.
• When compound interest is paid each day, the compounding period is one day. We say
that the interest is compounded daily.
Example 1:
You deposit $1000 in a savings account at 10% compounded annually. If you leave it in the
account for 4 years, how much would you have at the end of that 4 year period?
Answer:
Method 1:
We can use our knowledge of simple interest to solve this problem. We will create a table
and track the growth of the investment on a yearly basis. We choose to do it on a yearly
basis because the interest is compounded annually.
Year
1
2
3
4
Starting
Balance
1000
1100
1210
1331
Amount in Account
at Year’s End
1000 + (1000 × 0.10 × 1) = 1100
1100 + (1100 × 0.10 × 1) = 1210
1210 + (1210 × 0.10 × 1) = 1331
1331 + (1331 × 0.10 × 1) = 1464.10
Explanation
Find the FV when principal = 1000.
Find the FV when principal = 1100.
Find the FV when principal = 1210.
Find the FV when principal = 1331.
Notice that in the second year you make interest on the initial investment of $1000 plus the
$100 interest you accumulated in year 1. In the third year you make interest on the initial
investment of $1000 plus the $210 interest you accumulated in years 1 and 2. In the fourth
year you make interest on the initial investment of $1000 plus the $331 interest you
accumulated in years 1, 2 and 3. You end up with $1464.10 in the account at the end of 4
years.
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Method 2
There is a formula that allows you to calculate the future value (amount in an investment or
amount of money owed) when you are dealing with compound interest.
nt
r

A = P 1 + 
 n
where: A is the future value
P is the present value or principal
r is the interest rate expressed as a decimal
n is the number of times the interest is compounded per year
t is the number of years
1×4
 0.10 
A = 10001 +

1 

A = 1000(1.10 )
A = 1000 × 1.4641
You will have $1464.10 in the account at the end of 4 years.
A = 1464.1
4
Example 2:
You deposit $400 in a savings account at 6% compounded semiannually. If you leave in the
account for 3 years, how much would you have after that 3 year period?
Answer:
Method 1:
We will create a table and track the growth of the investment on a half yearly basis. We
choose to do it on a yearly basis because the interest is compounded semiannually.
Year
0.5
1
1.5
2
2.5
3
Starting Balance
400
412
424.36
437.09
450.20
463.71
Amount in Account at Year’s End
400 + (400 × 0.06 × 0.5) = 412
412 + (412 × 0.06 × 0.5) = 424.36
424.36 + (424.36 × 0.06 × 0.5) = 437.09
437.09 + (437.09 × 0.06 × 0.5) = 450.20
450.20 + (450.20 × 0.06 × 0.5) = 463.71
463.71 + (463.71 × 0.06 × 0.5) = 477.62
Notice that in the first year you make interest on the initial investment of $400 plus the $12
interest you accumulated in the first half of the year. In year 1.5 you make interest on the
initial investment of $400 plus the $24.36 interest you accumulated in year 0.5 and 1. This
process continues every half year. You end up with $477.62 in the account at the end of 3
years.
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Method 2
Use the future value formula for compound interest.

A = P 1 +

r

n
nt
 0.06 
A = 4001 +

2 

2×3
A = 400(1.03)
6
A = 400 × 1.19405
A = 477.62
You will have $477.62 in the account at the end of 3 years.
Example 3:
Serena wants to borrow $3000 from a family member and pay it back in 2 years. She agrees to
borrow the money at 6% compounded monthly. How much will she have to pay the family
member at the end of the 2 year period?
Answer:

A = P 1 +

r

n
nt
12×2
 0.06 
A = 30001 +

12 

A = 3000(1.005)
24
A = 3000 × 1.12716
A = 3381.48
She will pay $3381.48 at the end of the 2 year period.
Example 4:
Kendrick wants to invest $3000 for 6 years. Investment Plan A pays 10% per annum simple
interest. Investment Plan B pays 10% compounded daily. Which investment plan should he
choose?
Answer:
Investment Plan A
A = P + Prt
A = 3000 + (3000 × 0.10 × 6 )
A = 3000 + 1800
A = $4800.00
Investment Plan B:

A = P 1 +

r

n
nt
 0.10 
A = 30001 +

365 

365×6
A = 3000(1.0002739726 )
A = 3000 × 1.821969
A = $5465.91
2190
Kendrick should choose Investment Plan B.
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Questions:
1. Sheila deposits $500 in an investment plan that pays 20% compounded annually. If she
leaves it in the account for 3 years, how much will she have at the end of that 3 year period?
Solve this question using two different methods.
Method 1
Use your knowledge of simple interest and the table below to answer this compound interest
question.
Year
Starting
Balance
1
500
Amount in Account at Year’s End
(Show your calculations.)
2
3
Method 2
Use the compound interest formula for future value.
2. Manish borrows $2000 from his sister and agrees to pay it back in 2 years time. If he agrees
to pay interest at 8% compounded semiannually, how much will he have to pay her at the end
of the 2 year period? Solve this question two different ways.
Method 1
Use your knowledge of simple interest and the table below to answer this compound interest
question.
Year
Starting
Balance
Amount in Account at Year’s End
(Show your calculations.)
0.5
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Method 2
Use the compound interest formula for future value.
For the remaining questions, use the compound interest formula (Method 2) to find the answer.
3. Sarah is going to invest in a plan that pays 7% interest compounded annually. If she invests
$750, how much will she have in the plan after 5 years?
4. Rana has $1250 to invest. She’s going to leave the money in a plan that pays 6% interest
compounded monthly. If the money stays in the plan for 4 years, how much money will she
have in the plan?
5. Jorell completed the following calculation regarding a particular investment he was making.
r

A = P 1 + 
 n
nt
 0.09 
A = 25001 +

2 

2×7
A = 2500(1.045)
A = 2500 × 1.851945
A = 4629.86
14
Based on Jorell’s calculation,
(a) how much money did he invest?
(b) how long did he invest the money for?
(c) what was the interest rate?
(d) how often was the interest compounded?
(e) how much money did he ultimately end up with?
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6. Hamid completed the following calculation regarding a particular investment he was making.
r

A = P 1 + 
 n
nt
12×6
 0.08 
A = 9501 +

12 

A = 950(1.00666666667 )
A = 950 × 1.613502
A = 1532.83
72
Based on Hamid’s calculation,
(a) how long did he invest the money for?
(b) how much money did he invest?
(c) how much money did he ultimately end up with?
(d) what was the interest rate?
(e) how often was the interest compounded?
____________
____________
____________
____________
____________
7. Keith has $1200 to invest for a 3 year period. He can choose an investment plan whose
interest rate is 6% compounded annually, or a plan whose rate is 6% compounded monthly.
Which plan should he choose? Justify your answer by showing your calculations.
8. Meera wants to invest $2100 for 4 years. The first investment plan’s interest rate is 6%
compounded annually. The second plan’s interest rate is 5% compounded daily.
(a) How much money will Meera have in the first plan after 4 years?
(b) How much money will Meera have in the second plan after 4 years?
(c) Which plan would you choose?
NSSAL
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C. D. Pilmer
9. Brian wants to invest $1600 for 5 years. The first investment plan pays 8% per annum
simple interest. The second investment plan pays 8% compounded monthly. Which plan has
a better return and by how much?
10. Nashi is going to invest $2000 for 3 years. She has two investment plans to choose from.
The first plan pays 6% compounded semiannually. The second plan pays 6.5% per annum
simple interest. Which plan should she choose? Justify your answer by showing your
calculations.
11. In this section and the last section, you have explored simple interest and compound interest.
(a) How are these two types of interest different?
(b) In terms of investments, how does the interest rate (simple or compound) affect the
amount of money earned from that investment?
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C. D. Pilmer
(c) In terms of investments, how does the length of time that the money is invested in a
simple or compound interest plan affect the amount of money earned from that
investment?
Wrap-Up Statement:
In the section “Compound Interest” you learned that compound interest is the interest
calculated on the original sum of money invested (or borrowed) plus the accumulated
interest. The total value (i.e. future value) of the investment or loan can be found using the
nt
 r
formula A = P1 +  . This compound interest formula is used by investing institutions
 n
when you are making one lump payment into an investment plan that has a fixed interest rate
(i.e. Guaranteed Investment Certificate). If you are making multiple payments on a loan or to
an investment, then this formula does not work. You will deal with this in the next section.
Reflect Upon Your Learning
Fill out this questionnaire after you have completed questions 1 to 11. Select your response
to each statement.
1 - strongly disagree
2 - disagree
3 - neutral
4 - agree
5 - strongly agree
(a)
(b)
(c)
(d)
(e)
NSSAL
©2008
I understand all of the concepts covered in the section,
“Compound Interest.”
I do not need any further assistance from the instructor on the
material covered in this section.
I do not need any more practice questions.
In questions 1 and 2, I used my understanding of simple
interest and a table to solve questions concerned with
compound. Although this is a time consuming process, I
understand it.
I know the different compounding periods and how to use them
when solving compound interest problems
16
1
2
3
4
5
1
2
3
4
5
1
1
2
2
3
3
4
4
5
5
1
2
3
4
5
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C. D. Pilmer
Using the TVM Solver
The Time Value Money (TVM) Solver on the TI-83 graphics calculator is a powerful application
that can save you a lot of time with questions involving loans and investments. The TVM Solver
can be accessed by pressing the APPS key, selecting Finance and then selecting TVM Solver.
When you obtain the appropriate screen, you will see the following fields.
N
Total Number of Payments
I%
Annual Rate of Interest
PV
Present Value
PMT Payment Amount (You will always enter a negative number in this field.)
FV
Future Value
P/Y Number of Payment Periods per Year
C/Y Number of Compounding Periods per Year
PMT:END BEGIN Payments at the End or Beginning of Period
(For all of the questions you will encounter in this section, you will
select END.)
IMPORTANT:
All the fields, with the exception of the one you are solving for, require a value. Once entered,
move the cursor to the missing value and press SOLVE. SOLVE is written in green therefore
you need to press ALPHA (the green button), then ENTER to access this command.
TVM Cheat Sheet
With the permission of your instructor, you can tape the following cheat sheet on the cover of
your graphing calculator (TI-83 or TI-84).
N
I%
PV
PMT
FV
P/Y
C/Y
Total Number of Payments
Annual Interest Rate
Present Value
Payment Amount (negative)
Future Value
Number of Payments per Year
Number of Compounding
Periods per Year
PMT (always select END)
NSSAL
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C. D. Pilmer
Loans with Equal Payments
A loan is a contract that defines repayment of a sum of money lent at interest. We’re going to
focus on loans that involve equal repayments of money over equal intervals of time. For
example, you may take a car loan of $10 000 for 4 years at a rate of 8% compounded monthly.
The monthly payments will be $244.13. The present value of this loan is $10 000 because
that’s the initial amount you owed. The future value is $0 because you’ll have the loan paid off
at the end of the 4 year period. A mortgage is a special type of loan where the lending
institution uses the property as security for the repayment of the loan.
Examples:
1. Stewart purchases a new leather sofa using a credit card that charges 18% compounded
monthly. If he wants to pay off the $1300 sofa by making equal monthly payments over 2
years, what will his monthly payments be? How much would he have ultimately paid for the
sofa?
Answer:
• We need to find the payment amount (PMT).
• The number of payments is 24 ( 2 years × 12 payments per year ).
• The interest rate (I%) is 18%.
• The present value (PV) is the amount of money that is borrowed.
• The future value (FV) will be 0 because he will eventually pay off
the loan.
• He’s making a payment every month therefore P/Y equals 12.
• The interest is compounded monthly therefore C/Y equals 12.
Stewart’s monthly payments will be $64.90.
That means that he will ultimately pay $1557.60 ( $64.90 per payment × 24 payments ) for the
sofa.
2. Nasrin wants to buy a car. The bank is prepared to offer her a car loan at 8% compounded
monthly. She figures that she can afford monthly payments of $250 for 4 years. How big of
loan can she afford?
Answer:
• We need to find the present value (PV) because we need to find
how much money she can borrow.
• The number of payments is 48 ( 4 years × 12 payments per year ).
• The interest rate (I%) is 8%.
• She’s making payments of $250. The PMT is negative because an
“out-of-pocket” payment is negative.
• The future value (FV) will be 0 because she’ll ultimately pay off the loan.
• She’s making monthly payments therefore P/Y equals 12.
• If it’s compounded monthly, then C/Y equals 12.
She can afford a loan of $10 240.48.
NSSAL
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C. D. Pilmer
3. Deangelo took a car loan for $8000 at 12% compounded monthly. He was making monthly
payments of $265.71. He is now 2 years into his 3 year loan and wants to sell the car to buy
a motorcycle. If he has only made payments for 2 years, how much will he still owe on the
car loan?
Answer:
• We need to find the future value (FV) because we need to know
much he will still owe after 2 years. In this case, it wouldn’t be 0
because the loan isn’t paid off in 2 years.
• The total number of payments in that 2 year period is 24
( 2 years × 12 payments per year ).
• The interest rate (I%) is 12%.
• He’s borrowing $8000 so the present value (PV) is 8000.
• He’s making payments of $265.71. The PMT is negative because an “out-of-pocket”
payment is negative.
• The P/Y equals 12 because he’s making monthly payments.
• If it’s compounded monthly, then C/Y equals 12.
Deangelo still owes $2990.76 after 2 years.
Note:
If you want to see the pencil and paper techniques for solving the examples 1, 2, and 3, you
can turn to the section titled “Using the Formulas”. It should be stressed that you are not
expected to learn these pencil and paper techniques. We’d rather have you learn how to use
the TVM Solver to solve these types of questions.
4. Renu is taking a $150 000 mortgage on a house. She’d like to pay it off in 20 years making
weekly payments. If she assumes that her interest rate over the 20 years will be 7%
compounded annually, what will her weekly payments be?
Answer:
• We need to find the payment amount (PMT).
• The number of payments is 1040
( 20 years × 52 payments per year ).
• The interest rate (I%) is 7%.
• She’s borrowing $150 000 so the present value (PV) is 150 000.
• The future value (FV) will be 0 because he will eventually pay off the loan.
• There will be 52 payments per year (P/Y) because she’s making weekly payments.
• If it’s compounded annually, then C/Y equals 1.
Renu’s weekly payments will be $263.35.
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C. D. Pilmer
5. Bobbi is taking a $133 000 mortgage on a house. She assumes that the interest rate over the
life of the mortgage will be 6% compounded annually. If her monthly payments are $844,
how long will it take her to pay off the mortgage?
Answer:
• We need to find the number of payments (N) and then convert that
to the number of years.
• The interest rate (I%) is 6%.
• The present value is the amount of money she’s borrowing.
• If she’s making payments of $844, then PMT equals -844.
• The future value is 0 because the mortgage will eventually be paid off.
• The P/Y equals 12 because she’s making monthly payments.
• If it’s compounded annually, then C/Y equals 1.
Bobbi will make a total of 300 payments.
If she’s making 12 payments per year, then that converts to 25 years.
Questions:
Solve the following questions using the TVM Solver on a graphics calculator. In each case, also
provide the numbers that you entered into each of the fields on the calculator.
1. Meredith is taking a $15 000 car loan over 5 years. If the
bank is charging 8% interest compounded monthly, what
will her monthly payments be? How much would she have
ultimately paid for the car at the end of the five year
period?
N=
_________
I% =
_________
PV = _________
PMT = _________
Your Answers:
Meredith’s monthly payments will be ___________.
FV = _________
P/Y = _________
When you consider that Meredith made 60 equal payments,
you can conclude that she ultimately paid
_________________ for the car.
NSSAL
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C/Y = _________
PMT: END BEGIN
Draft
C. D. Pilmer
2. Jeremy is purchasing a flat screen television using a credit
card from a particular electronics store. The credit card
charges 28% compounded monthly. If he wants to pay off
the $2200 television by making equal monthly payments
over 2 years, what will his monthly payments be? How
much would he have ultimately paid for the television?
N=
_________
I% =
_________
PV = _________
PMT = _________
Your Answers:
Jeremy’s monthly payments will be __________.
FV = _________
P/Y = _________
When you consider that Jeremy made 24 equal payments,
you can conclude he ultimately paid ___________ for the
television.
3. Jeremy has another option for purchasing the same flat
screen television. Since he owns a home, he can use his
line of credit which only charges 6% compounded monthly.
If he still plans to pay the $2200 television off by making
equal monthly payments over 2 years, what will his
monthly payments be? How much would he have
ultimately paid for the television?
C/Y = _________
PMT: END BEGIN
N=
_________
I% =
_________
PV = _________
PMT = _________
FV = _________
Your Answers:
Jeremy’s monthly payments will be __________.
P/Y = _________
When you consider that Jeremy made 24 equal payments,
you can conclude he ultimately paid ___________ for the
television.
PMT: END BEGIN
C/Y = _________
4. Look at the answers you got for questions 2 and 3. Were you surprised by the difference?
Do you think that it’s appropriate to buy a “big-ticket” item like a flat screen television using
a credit card if you plan to pay it off gradually?
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C. D. Pilmer
5. The bank is prepared to offer Meera a car loan at 9%
compounded monthly. If she can make monthly payments
of $325 over 5 years, what size of loan can she afford to
take?
Your Answer:
Meera can afford a car loan of ______________.
N=
_________
I% =
_________
PV = _________
PMT = _________
FV = _________
P/Y = _________
C/Y = _________
PMT: END BEGIN
6. A dealership is prepared to offer Meera a car loan at 2%
compounded monthly if she’s willing to purchase their
brand of automobile. If she can still only afford monthly
payments of $325 over 5 years, what size of loan can she
afford to take?
N=
_________
I% =
_________
PV = _________
PMT = _________
Your Answer:
Meera can afford a car loan of ______________.
FV = _________
P/Y = _________
C/Y = _________
PMT: END BEGIN
7. Many consumers use rent-to-own because they do not have
enough cash to pay the full purchase price or cannot obtain
financing from the merchant, banks or credit unions. Rentto-own transactions can also be appealing because they
allow a low weekly or monthly payment, no credit checks,
the ability to cancel the transaction at any time and provide
immediate use of a product.
N=
_________
I% =
_________
PV = _________
Suzanne decided to purchase a new video game console for
her son using rent-to-own. The $450 unit could be hers for
twelve monthly payments of $80. How much did she
ultimately pay for the console? If the interest was
compounded monthly, what interest rate was she paying?
PMT = _________
Your Answers:
Suzanne ultimately paid _________ for the game console.
PMT: END BEGIN
FV = _________
P/Y = _________
C/Y = _________
The interest rate was ______% compounded monthly.
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C. D. Pilmer
8. Paul decided to purchase a video camera using rent-to-own.
The $1100 camera could be his for 90 weekly payments of
$23. How much did he ultimately pay for the camera? If
the interest was compounded monthly, what interest rate
was he paying?
Your Answers:
Paul ultimately paid _________ for the camera.
The interest rate was ______% compounded monthly.
N=
_________
I% =
_________
PV = _________
PMT = _________
FV = _________
P/Y = _________
C/Y = _________
PMT: END BEGIN
9. (a) Do you think it’s reasonable for the rent-to-own agencies described in questions 7 and 8
to charge these rates of interest? Remember that 28% compounded monthly is typically
the highest rate of interest that even the most expensive credit card agencies charge.
(b) What have you learned about the rent-to-own option? Would you use it? Why or why
not?
10. Elliot is buying a house and needs to take a mortgage of $95 000. He figures that the interest
rate over the life of the mortgage will be 7% compounded annually. He debates two different
payment options. He can make monthly payments of $1000 or make weekly payments of
$250. How many monthly payments will he make to pay off the mortgage and how many
years will this take? How many weekly payments will he make to pay off the mortgage and
how many years will this take?
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C. D. Pilmer
Your Answers:
It will take ______ payments
over ______ years to pay off
the mortgage with monthly
payments of $1000.
It will take ______ payments
over ______ years to pay off
the mortgage with weekly
payments of $250.
Weekly Payments
Monthly Payments
N=
_________
N=
_________
I% =
_________
I% =
_________
PV = _________
PV = _________
PMT = _________
PMT = _________
FV = _________
FV = _________
P/Y = _________
P/Y = _________
C/Y = _________
C/Y = _________
PMT: END BEGIN
PMT: END BEGIN
11. What sort of advice would you give a friend regarding payment options on a mortgage?
12. Yemon is taking a loan for $6000 at 10% compounded
monthly. He’s going to be making monthly payments of
$152.18. If he makes payments for 3 years of the 4 year
loan, how much will he still owe on the loan?
Your Answer:
Yemon still owes ____________ after 3 years.
N=
_________
I% =
_________
PV = _________
PMT = _________
FV = _________
P/Y = _________
C/Y = _________
PMT: END BEGIN
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C. D. Pilmer
13. Tammy is taking a loan for $11000 at 9% compounded
monthly. She’s going to be making monthly payments of
$228.34. If she makes payments for 2 years of the 5 year
loan, how much will she still owe on the loan?
N=
_________
I% =
_________
PV = _________
Your Answer:
Tammy still owes ____________ after 2 years.
PMT = _________
FV = _________
P/Y = _________
C/Y = _________
PMT: END BEGIN
14. Janice and her husband agreed that they could afford to buy
a pickup truck if its price is $22 000 or less. Her husband
spends a Saturday at the different used-car dealerships. He
returns and says that he has found a truck. The bank is
prepared to loan him the money even though they don’t
have a down payment. Her husband reports that the loan
will be at 8% compounded monthly for 6 years and that the
monthly payments will be $368.20. He does not tell her
how much the pickup truck costs but Janice wants to know.
She wants to make sure that he did not exceed the $22 000
they budgeted for the vehicle. What is the price of the
vehicle before one factors in the interest charges associated
with the loan?
N=
_________
I% =
_________
PV = _________
PMT = _________
FV = _________
P/Y = _________
C/Y = _________
PMT: END BEGIN
Your Answer:
The price of the truck is ________________.
15. A dealership tells you that they will finance the purchase of
a $18 500 vehicle where the monthly payments for 5 years
will be $384.03. If the loan is paid off in 5 years and the
loan is compounded monthly, what rate of interest is being
charged?
Your Answer:
The interest rate is ______% compounded monthly.
N=
_________
I% =
_________
PV = _________
PMT = _________
FV = _________
P/Y = _________
C/Y = _________
PMT: END BEGIN
NSSAL
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C. D. Pilmer
Scrambled Answers (They are not in any particular order.)
$18542.02
$120.75
$2340.24
524.7
$97.51
170%
10 years
9%
$7180.67
$2070
$15656.35
84%
$21 000.11
$304.15
$18 249
11.4 years
136.6
$960
$2898
$1730.73
Think about This
Payday Loans
Some individuals use payday loans as a way of accessing monies that they will not receive
until their next paycheck. With a typical payday, a borrower writes a postdated check to the
lender for the amount of the loan plus a fee - usually $20 for every $100 borrowed. The lender
agrees not to cash the check for a short period, often two weeks, or in theory, until the
borrower's next payday. Payday lenders say they provide a valuable service and that
borrowers understand the cost. The lenders contend that it's better than paying a $30 penalty
to a bank and having a blot on their financial record for writing a bad check.
The borrower pays $120 to get $100. The lender gets a 20% return on the money in only two
weeks. Anyone investing in the stock market, GICs, or mutual funds would be thrilled to get
a 20% return in an entire year. The payday lender is getting that return, not in one year, but in
only two weeks. The lender would contend that some of that return covers managerial
expenses and loans that not paid back. What are your feelings about payday loans?
Your Response:
NSSAL
©2008
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C. D. Pilmer
Investments with Equal Payments
We’re going to focus on investments that involve equal payments of money over equal intervals
of time into savings accounts or an investment fund. For example, you may want to invest $100
every month for the next 5 years at a rate of 6% compounded monthly. If you do so, you’ll end
up with $6977. The present value of this investment would be $0 because there was nothing in
the investment when you started. The future value of this investment would be $6977 because
that’s what you’d end up with at the end of the 5 year period.
Examples:
1. Every month Manish is going to deposit $30 into an investment fund that pays 5%
compounded annually. If he does this for 15 years, how much will he have in the fund?
Answer:
• We need to find the future value (FV) because we want to know
how much he’ll eventually have in the fund.
• The number of payments is 180 ( 15 years × 12 payments per year ).
• The interest rate (I%) is 5%.
• Initially there is no money in the fund so the present value (PV)
equals 0.
• He’s making payments of $30. The PMT is negative because an “out-of-pocket” payment
is negative.
• The P/Y equals 12 because he’s making monthly payments.
• If it’s compounded annually, then C/Y equals 1.
Manish will have $7944.74 in the fund.
2. Tanya initially deposits $500 into a fund that pays 6% interest compounded semi-annually.
She also deposits an additional $75 into the fund at the end of each month. If she does this
for 10 years, how much will she have in the fund?
Answer:
• We need to find the future value (FV) because we want to know
how much she’ll eventually have in the fund.
• The number of payments is 120 ( 10 years × 12 payments per year ).
• The interest rate (I%) is 6%.
• The present value (PV) is -500 because there was an initial “outof-pocket” investment of $500.
• If she’s making payments of $75, then PMT equals -75.
• The P/Y equals 12 because she’s making monthly payments.
• If it’s compounded semi-annually, then C/Y equals 2.
Tanya will have $13 145.00 in the fund.
NSSAL
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C. D. Pilmer
3. Jacque initially invests $200 into a high interest savings account. He also deposits an
additional $25 into the account at the end of each month. If he does this for 4 years, what
interest rate compounded daily would he need to accumulate $1650 in the account at the end
of the 4 year period?
Answer:
• We need to find the rate of interest (I%).
• The number of payments is 48 ( 4 years × 12 payments per year ).
• The present value (PV) is -200 because there is an initial “out-ofpocket” investment of $200.
• If he’s making payments of $25, then PMT equals -25.
• The future value (FV) will be $1650 because that’s how much money he will have after 4
years.
• If it’s compounded daily, then C/Y equals 365.
Jacque needs an interest rate of 7.1%.
Questions:
Solve the following questions using the TVM Solver on a graphics calculator. In each case, also
provide the numbers that you entered into each of the fields on the calculator.
1. Ranelda makes monthly deposits of $70 into a high interest
account that pays 6.5% compounded monthly. How much
money will she have in the account in 6 years?
Your Answer:
Ranelda will have _____________ in 6 years.
N=
_________
I% =
_________
PV = _________
PMT = _________
FV = _________
P/Y = _________
C/Y = _________
PMT: END BEGIN
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C. D. Pilmer
2. Evan deposits $200 into an account that pays 5%
compounded daily. He then makes monthly deposits of
$30 into the account. If he does this for 7 years, how much
money will be in the account?
Your Answer:
Evan will have ______________ in 7 years.
N=
_________
I% =
_________
PV = _________
PMT = _________
FV = _________
P/Y = _________
C/Y = _________
PMT: END BEGIN
3. Rana deposits $350 into an account that pays 4.5%
compounded daily. She then makes weekly payments of
$15 into the account. If she does this for 2 years, how
much money will be in the account?
N=
_________
I% =
_________
PV = _________
PMT = _________
Your Answer:
Rana will have _____________ in 2 years.
FV = _________
P/Y = _________
C/Y = _________
PMT: END BEGIN
4. In question 3, Rana’s account paid 4.5% compounded
daily. How much would she have after 2 years if the
account paid 4.5% compounded annually?
N=
_________
I% =
_________
PV = _________
Your Answer:
Rana will have _____________ in 2 years.
PMT = _________
FV = _________
P/Y = _________
C/Y = _________
PMT: END BEGIN
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5. Maurita wants to put money away for her new child’s education. The education fund pays
9% compounded monthly. She’s trying to decide between two investment options. With the
first option, she starts investing right now and deposits $40 each month into the fund for the
next 18 years. How much money will be in the fund if she chooses the first option? With the
second option, she waits for 9 years and then invests $80 each month into the fund for the
next 9 years. How much money will be in the fund if she chooses the second option?
Your Answers:
If Maurita chooses the first
investment option ($40
monthly payments over 18
years), there will be
_________________ in the
fund.
If Maurita chooses the
second investment option
($80 monthly payments over
9 years), there will be
_________________ in the
fund.
First Option
Second Option
N=
_________
N=
_________
I% =
_________
I% =
_________
PV = _________
PV = _________
PMT = _________
PMT = _________
FV = _________
FV = _________
P/Y = _________
P/Y = _________
C/Y = _________
C/Y = _________
PMT: END BEGIN
PMT: END BEGIN
6. What did you learn when you completed question 5?
7. Anne wants to take a family vacation in 3 years that will
cost $4000. She’s going to make equal monthly payments
into an account that pays 5% compounded monthly over
the 3 year period. How much should the monthly payments
be to insure that she has enough money for the trip?
Your Answer:
Anne’s monthly payments should be __________.
N=
_________
I% =
_________
PV = _________
PMT = _________
FV = _________
P/Y = _________
C/Y = _________
PMT: END BEGIN
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8. Kadeer wants to make monthly payments into a plan that
pays 6% compounded daily for 4 years. If he wants to
have $2800 in the plan at the end of the 4 year period, how
much should pay into the plan each month?
Your Answer:
Kadeer’s monthly payments should be __________.
N=
_________
I% =
_________
PV = _________
PMT = _________
FV = _________
P/Y = _________
C/Y = _________
PMT: END BEGIN
9. Angela is going to make monthly payments of $70 into a
plan for 5 years with the hope that the investment will be
worth $5000 at the end of the 5 year period. Assuming
that the interest rate is compounded monthly, what interest
rate should the plan offer so that Angela can reach her
target of $5000?
Your Answer:
Angela needs an interest rate of _______% compounded
monthly.
N=
_________
I% =
_________
PV = _________
PMT = _________
FV = _________
P/Y = _________
C/Y = _________
PMT: END BEGIN
10. Akira wants to have $4300 in 3 years time so that she and
her partner can go on a cruise for the fifth wedding
anniversary. She can afford to make monthly payments of
$110 into an investment plan. Assuming that the interest
rate is compounded monthly, what interest rate should the
plan offer so that Akira and her partner can afford the
cruise?
Your Answer:
Akira needs an interest rate of _______% compounded
monthly.
N=
_________
I% =
_________
PV = _________
PMT = _________
FV = _________
P/Y = _________
C/Y = _________
PMT: END BEGIN
Scrambled Answers (They are not in any particular order.)
$21454.07
$3294.77
$13238.66
$2012.25
$2014.60
5.6%
$103.22
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$51.74
6.9%
$6143.98
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C. D. Pilmer
11. With the last ten questions, you have been investigating a variety of investment options.
Using the internet, look up the definitions of RRSP, RESP, GIC, TFSA and Canada Savings
Bond. Which investment option do you prefer and why?
Here are some websites that might be useful when attempting to answer this question.
• Google Search: InvestorED Kinds of Investments
• Google Search: RRSP Advisor
• Google Search: CBC News RRSPs in Volatile Times
• Google Search: RESP Advisor
• Google Search: Government of Canada Tax Free Savings Account
• Google Search: Government of Canada Canada Savings Bonds
• YouTube: Jean-Paul Beran on BCTV News: RESPs
• YouTube: Jean-Paul Beran on BCTV News: RRSPs
• YouTube: Finance & Investment Tips What Is a GIC?
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Why Bother? I Don’t Own a Graphing Calculator
Sometimes learners wonder why they need to learn about the TVM Solver when they do not own
a graphing calculator. The calculator allows us to explore a variety of loan and investment
options so that we can make more informed decisions in our lives. Even though most of us do
not own or have access to a graphing calculator in our personal lives, there are many online
calculators that we can use. Although most are not as versatile as the TVM Solver, they can
educate us as to the best loan and investment options. You may wish to try a few of the ones
listed below.
Canadian Banks Loan Calculator
http://www.canadabanks.net/Loan-Calculator.aspx
Canada Mortgage Amortization Schedule Calculator
http://www.canadamortgage.com/webcalcs/realtorlink/amortschedule.cgi
Canada Trust Mortgage How Much of a Home can I Afford
http://calc.tdcanadatrust.com/HMCIA/Input
Citizens Bank of Canada Loan Calculator
https://www.citizensbank.ca/Personal/Calculators/Loan/
Citizens Bank of Canada Mortgage Loan Calculator
https://www.citizensbank.ca/Personal/Calculators/Mortgage/
CMHC Mortgage Affordability Calculator
http://www.cmhc-schl.gc.ca/en/co/buho/buho_007.cfm
Digital Mortgage Calculator Canada
http://www.mortgagecalculatorcanada.com/#
HSBC Loan Payments Calculator
http://www.hsbc.ca/1/2/en/calculators/loan-payments-calculator
Lending Max Mortgage and Loan Calculator
http://www.lendingmax.ca/calculator.php
Mortgage Calculator Canada Free Tool
http://mortgagecalculatorcanada.net/
RBC Mortgage Payment Calculator
https://www.rbcroyalbank.com/cgi-bin/mortgage/mpc/start.cgi
RBC Personal Lending Centre Loan Payment Calculator
http://www.rbcroyalbank.com/cgi-bin/personalloans/payment/calc.cgi
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Wrap-Up Statement:
In the sections “Loans with Equal Payments” and “Investments with Equal Payments”, you
learned to use the TVM Solver on the graphing calculator to solve questions where one has to
make regular equal payments on a loan or to an investment. This is a very important topic
because most adults will have to take loans or mortgages where they are required to make
monthly, biweekly, or weekly payments.
Reflect Upon Your Learning
Fill out this questionnaire after you have completed questions in both sections (Loans with
Equal Payments and Investments with Equal Payments). Select your response to each
statement.
1 - strongly disagree
2 - disagree
3 - neutral
4 - agree
5 - strongly agree
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
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©2008
I understand all of the concepts covered in the section, “Loans
with Equal Payments.”
I understand all of the concepts covered in the section,
“Investments with Equal Payments.”
I do not need any further assistance from the instructor on the
material covered in this section.
I do not need any more practice questions.
I understand how to use the TVM Solver on a graphing
calculator.
I understand that the interest rate charged on a loan can greatly
effect the amount of money one has to pay back on that loan.
I understand why one should not use rent-to-own agencies
when attempting to purchase an item.
I understand that weekly payments, versus monthly payments,
on a mortgage can significantly reduce the amount of time it
takes to pay the mortgage off.
When investing money, it is important to invest early so that
you can take full advantage of the compound interest over a
long period of time.
I am familiar with the variety of investment options (RRSP,
RESP, GIC, Canada Savings Bonds) that are available to
people.
34
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2
2
3
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4
4
5
5
1
2
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2
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Using the Formulas
The first three examples found on pages 18 and 19 can be worked out by hand. The solutions
can be found here. You are not required to know how to do this.
1. Stewart purchases a new leather sofa using a credit card that charges 18% compounded
monthly. If he wants to pay off the $1300 sofa by making equal monthly payments over 2
years, what will his monthly payments be? How much would he have ultimately paid for the
sofa?
Answer:
P=
P=
i× A
1 − (1 + i )
0.015 × 1300
−N
1 − (1 + 0.015)
P = $64.90
i=
− 24
r 0.18
=
n
12
N = nt = (12)(2) = 24
Stewart’s monthly payments will be $64.90. That means that he will ultimately pay
$1557.60 ( 64.90 × 24 ) for the sofa.
2. Nasrin wants to buy a car. The bank is prepared to offer her a car loan at 8% compounded
monthly. She figures that she can afford monthly payments of $250 for 4 years. How big of
loan can she afford?
Answer:
1 − (1 + i )
× (PMT )
i
− 48
1 − (1 + 0.006667 )
× 250
PV =
0.006667
PV = $10240.48
−N
PV =
i=
r 0.08
=
n
12
N = nt = (12)(4) = 48
She can afford a loan of $10 240.48.
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3. Deangelo took a loan for $8000 at 12% compounded monthly. He’s making monthly
payments of $265.71. This means he’ll have the loan paid off in 3 years. If he’s been
making payments for 2 years, how much does he still have owing on the loan?
Answer:
FV = PV (1 + i ) n −
FV
(1 + i )N
i
−1
× (PMT )
24
(
1 + 0.01) − 1
= 8000(1 + 0.01) −
× 265.71
24
0.01
N = nt = (12)(2) = 24
i=
r 0.12
=
n
12
FV = 10157.88 − 7167.12
FV = $2990.76
Deangelo still owes $2990.76 after 2 years.
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Putting It Together
Up to this point, you have looked at questions concerned with:
• simple interest (I = Prt and A = P + Prt),
nt

 r  

• compound interest A = P1 +  ,

 n  

• loans with equal payments (TVM Solver), and
• investments with equal payments (TVM Solver)
In this section, we will not be introducing any new concepts. We are reviewing previously
learned concepts. The most challenging aspect for you will be deciding what type of question
you are dealing with and whether you should be working out the answer with paper and pencil
(i.e. formulas) or with the TVM Solver.
If your answer requires that you use a formula, show all your calculations. If your answer
requires that you use the TVM Solver, record the numbers that you entered in each of the
calculator’s fields (N, I%, PV, PMT,…).
Questions:
1. Angela takes a simple interest loan of $850 has at 6% per annum for 2 years. How much will
she ultimately pay back at the end of the 2 year period?
2. Ryan has $750 to invest. He is going to leave the money in a plan that pays 8% interest
compounded semiannually. If the money stays in the plan for 3 years, how much money will
he have in the plan?
3. The bank is prepared to offer Yoshi a car loan at 11% compounded monthly. If she can
make monthly payments of $400 over 5 years, what size of loan can she afford to take?
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C. D. Pilmer
4. Every month Renu is going to deposit $50 into an investment fund that pays 6% compounded
annually. If she does this for 10 years, how much will she have in the fund?
5. You deposit $800 in a savings account at 5% compounded monthly. If you leave in the
account for 4 years, how much would you have after that 4 year period?
6. Kiana initially deposits $300 into a fund that pays 6% interest compounded semi-annually.
She also deposits an additional $70 into the fund at the end of each month. If she does this
for 6 years, how much will she have in the fund?
7. Tom invests $650 for 4 years at 7% per annum simple interest. Find the future value of the
investment.
8. Marcus needs to purchase new windows for his cottage. The windows will cost $2800. He
decides to use his line of credit that charges 5% compounded semiannually to purchase the
windows. If he wants to pay off the line of credit by making equal monthly payments over 2
years, what will his monthly payments be?
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9. Deangelo wants to make a long term investment. Here are his three choices.
• Plan A: Make one lump sum investment of $1000. He will make 8.5% compounded
annually. It will remain in this plan for 5 years.
• Plan B: Make one lump sum investment of $1000. He will make 9% per annum
simple interest. It will remain in this plan for 5 years.
• Plan C: Make monthly payments of $20 for 5 years. He will make 8% compounded
semiannually.
(a) How much would Deangelo make on each of these plans?
(b) Which plan would you choose? Why?
10. Bobbi is taking a $125 000 mortgage on a house. She assumes that the interest rate over the
life of the mortgage will be 7% compounded annually. If her monthly payments are $931.81,
how long will it take her to pay off the mortgage?
11. Tami invested $920 for 2 years at 5% per annum simple interest. How much interest will she
earn?
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C. D. Pilmer
12. Jenny completed the following calculation regarding a particular investment she was making.
r

A = P 1 + 
 n
nt
 0.10 
A = 17501 +

2 

2×6
A = 1750(1.05)
A = 1750 × 1.795856
A = 3142.75
12
Based on Jenny’s calculation,
(a) what was the interest rate?
(b) how often was the interest compounded?
(c) how much money did she invest?
(d) how long did she invest the money for?
(e) how much money did she ultimately end up with?
____________
____________
____________
____________
____________
13. Montez is taking a $15 000 car loan over 4 years. If the bank is charging 9% interest
compounded monthly, what will his monthly payments be? How much would he have
ultimately paid for the car at the end of the four year period?
14. Evan and Lei are buying a house and needs to take a mortgage of $150 000. They figure that
the interest rate over the life of the mortgage will be 8% compounded annually. They debate
two different payment options. They can make monthly payments of $1130.12 or make
weekly payments of $282.53.
(a) How many monthly payments will they make to pay off the mortgage and how many
years will this take?
(b) How many weekly payments will they make to pay off the mortgage and how many years
will this take?
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Wrap-Up Statement:
In the section “Putting It Together”, you reviewed concepts learned in previous sections.
Ther were a variety of questions and had to decide if they required the simple interest
formula, the compound interest formula, or the TVM Solver. If the loan or investment
required regular equal payments, then you knew that you had to use the TVM Solver.
Reflect Upon Your Learning
Fill out this questionnaire after you have completed questions 1 to 14. Select your response
to each statement.
1 - strongly disagree
2 - disagree
3 - neutral
4 - agree
5 - strongly agree
(a)
(b)
(c)
(d)
NSSAL
©2008
I understand all of the concepts covered in the section, “Putting
It Together.”
I do not need any further assistance from the instructor on the
material covered in this section.
I do not need any more practice questions.
I was able to figure out which questions required that I use the
simple interest formula or compound interest formula versus
those questions that required the TVM Solver.
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C. D. Pilmer
Consumer Finance Reading Assignment
You have been provided with four brochures from the Financial Consumer Agency of Canada.
Their titles are as follows.
• Understanding Your Credit Report and Credit Score
• Playing It Safe; How to Protect Your Credit Card and Credit History
• Your Rights and Responsibilities; The Cost of Borrowing with a Credit Card
• Managing Your Money; How to Save with a Credit Card
There are also a series of videos on YouTube that compliment the material found in many of the
FCAC brochures.
• Get It On Credit - Investor Education Fund
• Credit Score
• How to Improve Your Credit Score
• How Credit Scores Impact Mortgage Applications
• KayDacus Debt and Simple vs Compound interest
• Debt Management Credit Counseling Corp
• Tackling Credit Card Fraud
• Fake Waiter-Credit Card Fraud
• Prevent Credit Card Fraud
Choose the brochure that is of the greatest interest to you. Read the brochure. Also view two or
more YouTube videos that compliment your brochure selection. Write a one or two page report
on the important information found in the brochure and videos. Although it is not required, you
can include personal experiences and/or opinions that are related to the information found in the
brochure.
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Post-Unit Reflections
What is the most valuable or important
thing you learned in this unit?
What part did you find most interesting or
enjoyable?
What was the most challenging part, and
how did you respond to this challenge?
How did you feel about this math topic
when you started this unit?
How do you feel about this math topic
now?
Of the skills you used in this unit, which
is your strongest skill?
What skill(s) do you feel you need to
improve, and how will you improve them?
How does what you learned in this unit fit
with your personal goals?
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Answers:
Simple Interest (pages 1 to 8)
1. $27
2. $168
3. $11.55
4. $36.45
5. $806
6. $612.90
7. Sample Answer: If you invested $500 for 3 years at a rate of 9% per annum simple interest,
how much would you have after that 3 year period?
8. $1160.50
9.
Principal
L1
100
200
300
400
500
600
Amount (Future Value)
L2=L1+(L1*0.06*3)
118
236
354
472
590
708
As the principal goes up, the future value also goes up.
10.
Interest Rate
Amount (Future Value)
L1
0.03
0.04
0.05
0.06
0.07
0.08
L2=400+(400*L1*3)
436
448
460
472
484
496
As the interest rate goes up, the future value also goes up.
11.
Number of Years
Amount (Future Value)
L1
1
2
3
4
5
6
L2=400+(400*0.06*L1)
424
448
472
496
520
544
As the number of years goes up, the future value also goes up.
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12. (a) Enter 2, 4, 6, and 8 in List 1. Enter the equation L2 = 900 + (900*0.07*L1) in List 2.
(b) Enter 250, 300, 350, and 400 in List 1. Enter L2 = L1 + (L1*0.08*3) in List 2.
(c) Enter 0.03, 0.035, 0.04, 0.045, and 0.05 in List 1. Enter L2 = 1200 + (1200*L1*2) in List
2.
13. If we had to do these individual simple interest calculations by hand it would take too long.
The calculator allows us to explore trends when we adjust the interest rates, principal, or
duration of loan or investment without having to do numerous calculations by hand.
Compound Interest (pages 9 to 16)
1. Method 1
Year
1
2
3
Starting
Balance
500
600
720
Amount in Account at Year’s End
(Show your calculations.)
500 + (500 × 0.20 × 1) = 600
600 + (600 × 0.20 × 1) = 720
720 + (720 × 0.20 × 1) = $864
Method 2

A = P 1 +

r

n
nt
 0.20 
A = 5001 +

1 

1×3
A = 500(1.20 )
A = $864
3
2. Method 1.
Year
0.5
1.0
1.5
2.0
NSSAL
©2008
Starting
Balance
2000
2080
2163.20
2249.73
Amount in Account at Year’s End
(Show your calculations.)
2000 + (2000 × 0.08 × 0.5) = 2080
2080 + (2080 × 0.08 × 0.5) = 2163.20
2163.20 + (2163.20 × 0.08 × 0.5) = 2249.73
2249.73 + (2249.73 × 0.08 × 0.5) = $2339.72
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Method 2
 r
A = P 1 + 
 n
nt
 0.08 
A = 20001 +

2 

A = 2000(1.04 )
A = $2339.72
2×2
4
3. $1051.91
4. $1588.11
5. (a) $2500
(d) semiannually
6. (a) 6 years
(d) 8%
(b) 7 years
(c) 9%
(e) $4629.86
(b) $950
(c) $1532.83
(e) monthly
7. $1429.22, $1436.02, Second Plan.
8. (a) $2651.20
(b) $2564.91
(c) First Plan
9. $2240, $2383.75, Second Plan, $143.75
10. $2388.10, $2390, Second Plan
Loans with Equal Payments (pages 18 to 26)
1. $304.15 and $18249
2. $120.75 and $2898
3. $97.51 and $2340.24
5. $15 656.35
6. $18 542.02
7. $960 and 170%
8. $2070 and 84%
10. 136.6 payments and 11.4 years, 524.7 payments and 10 years
12. $1730.73
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13. $7180.67
14. $21 000.11
15. 9%
Investments with Equal Payments (pages 27 to 34)
1. $6143.98
2. $3294.77
3. $2014.60
4. $2012.25
5. $21 454.07 and $13 238.66
7. $103.22
8. $51.74
9. 6.9%
10. 5.6%
Putting It Together (pages 37 to 41)
1. $952
(simple interest formula)
2. $948.99
(compound interest formula)
3. $18 397.21
(loan with equal payments, TVM Solver, find PV)
4. $8123.67
(investment with equal payments, TVM Solver, find FV)
5. $976.72
(compound interest formula)
6. $6462.46
(investment with equal payments, TVM Solver, find FV)
7. $832
(simple interest formula)
8. $122.78
(loan with equal payments, TVM Solver, find PMT)
9. (a) Plan A: $1503.66
(compound interest formula)
Plan B: $1450
(simple interest formula)
Plan C: $1464.56
(investment with equal payments, TVM Solver, find FV)
(b) Pan A or Plan C
Plan A gives you the best return.
Plan C is easier to budget. Putting away $20 per month is easier than trying to save
$1000 for one lump sum payment.
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10. 21 years
(loan with equal payments, TVM Solver, find N, N/12)
11. $92
(simple interest formula)
12. (a) 10%
(b) semiannually
(d) 6 years
13. $373.28, $17 917.44
(c) $1750
(e) $3142.75
(loan with equal payments, TVM Solver, find PMT, PMT × 48)
14. (loan with equal payments, TVM Solver, find N)
(a) 300 payments, 25 years
(b) 1042.8 payments, 20 years
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Online Supports
Simple and Compound Interest
Google Search: Interactives Math in Daily Life Savings and Credit
Google Search: Slideshare 7.8 Simple and Compound Interest
Google Search: FinanceProfessor Simple Interest vs Compound Interest
Google Search: EPSB Simple and Compound Interest
YouTube: Watch Video on Simple Interest Formula - Math Help
YouTube: FA 8 7 Simple and Compound Interest
TVM Solver
Using the TI-83/84 series TVM Solver for loan calculation
TMCC Financial Calculations on the TI-83
Investments
Google Search: InvestorED Kinds of Investments
Google Search: RRSP Advisor
Google Search: CBC News RRSPs in Volatile Times
Google Search: RESP Advisor
Google Search: Government of Canada Canada Savings Bonds
Google Search: Government of Canada Tax Free Savings Account
YouTube: Jean-Paul Beran on BCTV News: RESPs
YouTube: Jean-Paul Beran on BCTV News: RRSPs
YouTube: Finance & Investment Tips What Is a GIC?
Credit Cards and Credit Scores
YouTube: Get It On Credit - Investor Education Fund
YouTube: Credit Score
YouTube: How to Improve Your Credit Score
YouTube: How Credit Scores Impact Mortgage Applications
YouTube: KayDacus Debt and Simple vs Compound interest
YouTube: Debt Management Credit Counseling Corp
YouTube: Tackling Credit Card Fraud
YouTube: Fake Waiter-Credit Card Fraud
YouTube: Prevent Credit Card Fraud
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