Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Name:_______________
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
1
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Grade 11 Essential Math
Course Outline
Course Description: Essential Math will prepare you with the mathematical tools and skills
needed by consumer and active citizens. You will learn how mathematical concepts permeate
daily life, business, industry, government and our thinking about the environment. Cooperative,
interactive and communicative skills will continue to develop as we progress through the course.
Topics of Study: Six units will be covered in the Grade 11 Math course
Interest and Credit
Statistics
Managing Your Money
Trigonometry
Relations and Patterns
Measurement
Evaluation:
Tests
25%
Learning Activities 10%%
Communication Skills
Assignments:
15%
Communication Skills
Projects
15%
(all projects and assignments must be completed to be eligible in earning a credit in this course)
Final Exam 30%
(A minimum score of 40% on the final must be earned to be awarded a credit in this course)
Supplies:
Binder, Loose leaf, Pencils, Eraser, Scientific Calculator, Ruler
Student Responsibilities:
The Grade 11 Essential Math course has a lot of material to cover so it is important that you do
all of your assignments, ask questions and study for tests. This is a self-paced course but the
expectation is that you will work diligently to complete the course in a reasonable time period.
Because there is a lot of material in this course having goals that you can set and achieve will
allow you to move at a reasonable pace. Typically, if you are attending half days, five days a
week you will want to complete one unit every two weeks. It is imperative that you use class
time efficiently so you will want to limit the amount of time you are distracted by others around
you or your phone.
“We sometimes think of being good at mathematics as an innate ability. You either have ‘it’ or
you don’t. But it’s not so much as ability as attitude. You master mathematics if you are willing
to try. Success is a function of persistence and doggedness and willingness to work hard to make
sense of something most people give up on.”
Malcom Gladwell (Outliers)
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Grade 11 Essential Mathematics
Unit 1: Interest and Credit
The Big Picture…
The most important purpose of schooling is to prepare children to participate as citizens in a free
and democratic society. And what kind of citizens does a free and democratic society require:
competent, mature, moral, and noble human beings. Everything else takes a backseat to this
most important aim. In order for this to happen, several basic prerequisites are necessary...
Your first level of commitment is attending every day and on time. Chronic late arrival to class
and missing class for trivial reasons disrespects yourself, education, your classmates, and the
teacher. Why? Because it negatively impacts your personal development, your chances of
earning course credit, earning your high school diploma, studying at a post-secondary
educational institution, finding a meaningful career and well-paying job, and ultimately a life
worth living. It’s also disrespectful because it disrupts the flow of classroom activity, hindering
the delivery of instruction and your classmates' pursuit of their education.
Your second level of commitment is to bring a teachable spirit and a hope and vision for your
own personal future and for the world you will take your place in as an adult. Tune in and turn
on. See every assignment, exercise, test and project you're given as a personal development
opportunity. Education is about so much more than course content and skill development; it's
more about building people, about building the skills, attitudes and aptitudes you need to flourish
and for the maintenance and betterment of the society and ultimately the world you inhabit.
Contribute to making the classroom a positive environment and experience for everyone. Make
every effort to make the classroom a purposeful, work-like environment and to live in peace and
harmony with the people around you. Do what you need to do so that others can do what they
need to do. That includes turning off and tuning out anything that distracts you from getting an
education, like cell phones, mp3 players and the like. If you’re too undisciplined to manage this
yourself, staff will help you manage it (i.e., we'll confiscate it) until you’re disciplined enough to
handle it yourself. Rule of Thumb: “Out of sight, out of mind, focusing on the task at hand.”
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Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Guidelines for Success:
In order to be successful most students require personal habits, behaviours and attitudes that
foster their commitment to class. Listed below are some guidelines that may be helpful in
achieving your success.

Be here every day; on time and prepared with the required materials (pens, pencils, eraser,
etc.)

Be engages and focused.

Work diligently at the assigned tasks; don’t just go through the motions.

Bringing your body to class only guarantees your contribution to carbon dioxide gas and
body heat to the classroom (provided, of course that you’re alive). It does not guarantee
you’re learning anything. Actively participate in learning the material. This means that
while you are copying the notes into your booklet, you are thinking about what you are
writing. Pay attention when you are working through each lesson. Don’t speed through,
skimming the text and passively writing the notes down. Try to figure out where the
formulas and numbers are from and how to progress through the steps to solve the example.
This active participation will prepare you for the Learning Activities and the Assignments.

Learn from your mistakes. Pay attention when your assignments are corrected and be sure
you understand where your mistake was so you don’t make the same mistake again.

Sleep well every night. Sleep will improve your memory and concentration skills, which in
turn may lead to you doing better in school.

Be persistent! Don't only start well and let it fall apart. Keep your study plans active and
working for your success.

Stay focused! One thing to do is to concentrate on getting the job done, don't try to do
several things at once. Rather, focus on doing your homework free of distractions.

Computer distractions, texting, listening to music and watching television are common
distractions for students. Every time you get distracted, you lose your concentration and train
of thought. It takes an extra effort to get back into what you were trying to do in your
homework.
Don't procrastinate. It will just put more stress on you and make the quality of your work
poorer.


Study for tests and exams. Don’t just “look at” your notes and examples actually write out
answers to the questions to practice the steps and help you understand the material.
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Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Unit 1: Interest and Credit
Introduction
In this unit, you will learn to calculate the interest using simple interest and compound interest.
You will also examine various sales promotion techniques, and determine the real cost of these
promotions. You will also learn the pros and cons of credit cards and how credit companies will
charge you interest on your outstanding balance.
Assessment Checklist:
Check off the following as you complete each:
o Lesson 1 Assignment: Gross Income
o Learning Activity 1.1 Simple Interest:
o Learning Activity 1.2: Simple Interest
o Lesson 2 Assignment: Simple Interest
o Learning Activity: 1.3 Compound Interest
o Lesson 3 Assignment: Compound Interest
o Lesson 4 Assignment: Credit Cards
o Lesson 5 Assignment: Sales Tax and On Sale
o Learning Activity 1.4: Instalment Buying
o Learning Activity 1.5: Buy Now Pay Later
o Lesson 6 Assignment: Promotions
o Lesson 7 Assignment: Personal Loans
Test Unit 1: Interest and Credit
5
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
LESSON 1: SALARIES AND WAGES
The pay that people receive for working is determined a number of ways. You can be paid on an
hourly rate (a wage). Some people earn a salary, which is a set amount of money regardless of
how many hours they work. People can earn money by working piecework; they earn money
based on how much they can produce in a day. Finally, people can also earn money by working
on commission which is a certain percentage of what they sell. There are three types of
commission:
a. Straight commission: paid a single percentage of commission on all sales
b. Salary plus commission: paid a salary plus a commission on their sales
c. Graduated commission: the percentage of commission increases as the sales become higher
Some examples of jobs that use these different methods to pay employees are:
1. a day-care worker is paid an hourly wage
2. a member of parliament is paid a salary
3. a car salesman is paid on commission
4. a factory worker could be paid by piecework
Calculating Income:
Income is how much money you earn. Your gross income is what you earn before deductions.
Your net income is what you get after deductions (often called your ‘take home pay’).
Gross Income:
Example:
You work at a local clothing retail store and are paid $8.50 an hour. If your hours for this week
are: M – 5, T – 4, W – 4.5, T – 3.5 F – 3.5, what is your gross pay for the week?
Solution:
ℎ𝑜𝑢𝑟𝑠 𝑤𝑜𝑟𝑘𝑒𝑑 = 5 + 4 + 4.5 + 3.5 + 3.5 = 20.5
𝑔𝑟𝑜𝑠𝑠 𝑝𝑎𝑦 = (ℎ𝑜𝑢𝑟𝑠 𝑤𝑜𝑟𝑘𝑒𝑑)(ℎ𝑜𝑢𝑟𝑙𝑦 𝑟𝑎𝑡𝑒) = (20.5)($8.50) = $174.25
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Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Example:
Tim earns an hourly wage of $8.25 at a local grocery store. His normal work week is 40 hours. If
he works over that, he gets paid time and one half in overtime pay. What is his gross pay for a
week that he works 47 hours this week?
Solution:
𝑅𝑒𝑔:
ℎ𝑜𝑢𝑟𝑠 = 40
ℎ𝑜𝑢𝑟𝑙𝑦 𝑟𝑎𝑡𝑒 = $8.25
𝑅𝑒𝑔 𝑃𝑎𝑦 = (40)($8.25) = $330
𝑂𝑣𝑒𝑟𝑡𝑖𝑚𝑒:
ℎ𝑜𝑢𝑟𝑠 = 7
ℎ𝑜𝑢𝑟𝑙𝑦 𝑟𝑎𝑡𝑒 = ($8.25)(1.5) = $12.38
𝑂𝑇 𝑝𝑎𝑦 = (7)($12.38) = $86.66
𝐺𝑟𝑜𝑠𝑠 𝑃𝑎𝑦 = $330 + $86.66 = $416.66
Example:
Jake works at a popular holiday retail store. To get ready for the holidays, he has been working
an extra hour each day. If Jake normally works 38 hours in a five day work week and gets paid
an hourly wage of $8.45 plus time and one half for any overtime hours, how much did Jake earn?
Solution:
𝑅𝑒𝑔:
ℎ𝑜𝑢𝑟𝑠 = 38
ℎ𝑜𝑢𝑟𝑙𝑦 𝑟𝑎𝑡𝑒 = $8.45
𝑅𝑒𝑔 𝑃𝑎𝑦 = (38)($8.45) = $321.10
𝑂𝑣𝑒𝑟𝑡𝑖𝑚𝑒:
ℎ𝑜𝑢𝑟𝑠 = 5
ℎ𝑜𝑢𝑟𝑙𝑦 𝑟𝑎𝑡𝑒 = ($8.45)(1.5) = $12.68
𝑂𝑇 𝑝𝑎𝑦 = (7)($12.38) = $63.40
𝐺𝑟𝑜𝑠𝑠 𝑃𝑎𝑦 = $321.10 + $63.40 = $384.50
Example:
A friend has a part time job making necklaces for a local artist. If she gets paid $0.40 for each
necklace that she makes, how much does she earn if she can make 20 necklaces in 1 hour and she
worked a total of 32 hours this week?
Solution:
ℎ𝑜𝑢𝑟𝑙𝑦 𝑟𝑎𝑡𝑒 = ($0.40)(20) = $8.00
𝑔𝑟𝑜𝑠𝑠 𝑝𝑎𝑦 = (32)($8.00) = $256
Example:
You are bundling fliers for a newspaper and are paid $0.35 for each bundle. If you are really
good at your job and can bundle 22 fliers an hour:
a. how much would you make in an 8 hour day?
b. how much would you make in a 5 day work week?
Solution:
# 𝑜𝑓 𝑏𝑢𝑛𝑑𝑙𝑒𝑠 𝑖𝑛 8 ℎ𝑜𝑢𝑟𝑠 = (22)(8) = 176
𝑃𝑎𝑦 = (176 𝑏𝑢𝑛𝑑𝑙𝑒𝑠)($0.35)(5 𝑑𝑎𝑦𝑠) = $308
7
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Example:
Bob is a car salesman and earns a straight commission of 7.5% of his total sales. If Bob sold 3
cars this past month and they cost $17,475; $30,330; and $36,715 how much did Bob earn last
month?
Solution:
𝑠𝑎𝑙𝑒𝑠 = $17 475 + $30 330 + $36 715 = $84 520
𝑐𝑜𝑚𝑚𝑖𝑠𝑠𝑖𝑜𝑛 = (𝑡𝑜𝑡𝑎𝑙 𝑠𝑎𝑙𝑒𝑠)(% 𝑐𝑜𝑚𝑚𝑖𝑠𝑠𝑖𝑜𝑛) = ($84 520)(0.075) = $6339
Example:
Sara is also a salesman. She earns $350 each week plus 6% commission on any amount of sales
over $20,000. If she had $62,000 in sales this month, what is her gross pay?
Solution:
Step 1: 𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒 𝑡ℎ𝑒 𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝑠𝑎𝑙𝑎𝑟𝑦 𝑓𝑜𝑟 𝑆𝑎𝑟𝑎.
𝑇ℎ𝑒𝑟𝑒 𝑎𝑟𝑒 𝑛𝑜𝑡 𝑒𝑥𝑎𝑐𝑡𝑙𝑦 4 𝑤𝑒𝑒𝑘𝑠 𝑖𝑛 𝑎 𝑚𝑜𝑛𝑡ℎ 𝑠𝑜 𝑤𝑒 𝑓𝑖𝑟𝑠𝑡 ℎ𝑎𝑣𝑒 𝑡𝑜 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒 ℎ𝑒𝑟 𝑦𝑒𝑎𝑟𝑙𝑦 𝑠𝑎𝑙𝑎𝑟𝑦
𝑦𝑒𝑎𝑟𝑙𝑦 𝑠𝑎𝑙𝑎𝑟𝑦 = ($350)(52) = $18 200
𝑎𝑛𝑑 𝑡ℎ𝑒𝑛 𝑢𝑠𝑒 𝑖𝑡 𝑡𝑜 𝑓𝑖𝑛𝑑 ℎ𝑒𝑟 𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝑠𝑎𝑙𝑎𝑟𝑦.
𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝑠𝑎𝑙𝑎𝑟𝑦 =
Step 2: C𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒 ℎ𝑒𝑟 𝑐𝑜𝑚𝑚𝑖𝑠𝑠𝑖𝑜𝑛:
$18 200
= $1516.67
12
𝑠𝑎𝑙𝑒𝑠 = $62 000 − $20 000 = $42 000
𝑐𝑜𝑚𝑚𝑖𝑠𝑠𝑖𝑜𝑛 = ($42 000)(0.06) = $2520
𝑔𝑟𝑜𝑠𝑠 𝑝𝑎𝑦 = $1516.67 + $2520 = $4036.67
8
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Example:
Mary sells electronics and receives 4% commission on her first $5,000 in sales; 5% on sales
between $5,000 and $15,000; and 6% on any sales over $15,000. Calculate her gross pay if she
sells $32,000 worth of electronics.
Solution:
𝑇𝑜𝑡𝑎𝑙 𝑆𝑎𝑙𝑒𝑠 = $32 000
𝐿𝑒𝑣𝑒𝑙𝑠
𝑀𝑎𝑥𝑖𝑚𝑢𝑚
% 𝑐𝑜𝑚𝑚𝑖𝑠𝑠𝑖𝑜𝑛 𝑎𝑚𝑜𝑢𝑛𝑡𝑜𝑓 𝑆𝑎𝑙𝑒𝑠
𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑆𝑎𝑙𝑒𝑠 𝑙𝑒𝑓𝑡
𝐶𝑜𝑚𝑚𝑖𝑠𝑠𝑖𝑜𝑛
$0 − $5000
4%
$5000
$32 000 − $5 000 = $27 000
($5000)(0.04) = $200
$5000 − $15 000
5%
$10 000
$27 000 − $10 000 = $17 000
($10 000)(0.05) = $500
$15 000 − 𝑜𝑣𝑒𝑟
6%
$17 000
($17 000)(0.06) = $1020
Example:
Henry receives a commission of 3% on the first $2,000 in sales, 4.5% on sales between $2,000
and $6,000, and 5% on any sales over $6,000. What is his gross pay if he has the following in
one month of working?
Weekly Sales
$0 - $2,000
3%
Amount of Sales Left
$2,000 - $6,000
(Max Amount: $4000)
4.5%
Week 1: $1,750
Week 2: $4,880
Week 3: $7,400
Week 4: $8,900
($1750)(0.03)
= $52.50
($2000)(0.03)
= $60
($2000)(0.03)
= $60
($2000)(0.03)
= $60
$0
$4880 − $2000
= $2880
$7400 − $2000
= $5400
$8900 − $2000
= $6900
($2880)(0.045) ($4000)(0.045) ($4000)(0.045)
= $129.60
= $180
= $180
Amount of Sales Left
$5400 − $4000
= $1400
$6900 − $4000
= $2900
Over $6,000
5%
($1400)(0.05)
= $70
($2900)(0.05)
= $145
9
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Example:
At a local furniture store, salespeople are paid a salary of $300 a week plus a commission of 8%
on any sales between $10,000 and $25,000 and a commission of 10% on any sales over $25,000.
Calculate Herb’s monthly income if he sells $38,900 worth of furniture this month.
Solution:
Step 1: Calculate monthly salary
𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝑠𝑎𝑙𝑎𝑟𝑦 =
($300)(52)
= $1300 𝑎 𝑚𝑜𝑛𝑡ℎ
12
Step 2: Calculate commission for the first level:
𝐸𝑎𝑟𝑛𝑠 0% 𝑜𝑛 𝑠𝑎𝑙𝑒𝑠 𝑓𝑟𝑜𝑚 $0 𝑢𝑝 𝑡𝑜 $10 000
𝑐𝑜𝑚𝑚𝑖𝑠𝑠𝑖𝑜𝑛 = $0
𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑆𝑎𝑙𝑒𝑠 𝑙𝑒𝑓𝑡 = $38 900 − $10 000 = $28 900
Step 3: Calculate commission for the second level:
𝐸𝑎𝑟𝑛𝑠 8% 𝑜𝑛 𝑠𝑎𝑙𝑒𝑠 𝑓𝑟𝑜𝑚 $10 000 𝑢𝑝 𝑡𝑜 $25 000 𝑠𝑜 𝑎 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑜𝑓 $15 000 𝑖𝑛 𝑠𝑎𝑙𝑒𝑠
𝑐𝑜𝑚𝑚𝑖𝑠𝑠𝑖𝑜𝑛 = ($15 000)(0.08) = $1200
𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑠𝑎𝑙𝑒𝑠 𝑙𝑒𝑓𝑡 = $28 900 − $15 000 = $13 900
Step 4: Calculate commission for the third level
𝐸𝑎𝑟𝑛𝑠 10% 𝑜𝑛 𝑠𝑎𝑙𝑒𝑠 𝑙𝑒𝑓𝑡
𝐶𝑜𝑚𝑚𝑖𝑠𝑖𝑜𝑛 = ($13 900)(0.10) = $1390
Step 4: Calculate the total pay
𝐺𝑟𝑜𝑠𝑠 𝑃𝑎𝑦 = $1300 + $0 + $1200 + $1390 = $3890
10
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Curriculum Outcomes:
Develop an understanding of managing money
Lesson 1 Assignment: Gross Income
See your Teacher for Lesson 1 Assignment
11
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
LESSON 2: INTEREST
When you invest your money into a bank, the bank pays you interest for using your money to
lend to other bankers. When you borrow money from a bank, you pay the bank interest for the
use of the money.
Two types of interest:
1. Simple interest – interest is calculated on the principal only (principal is the original
amount invested); the interest is NOT added to the principal and reinvested
2. Compound interest – interest is paid on both the principal and on the interest earned;
the interest earned is added back on to the principal and reinvested
SIMPLE INTEREST
Formula:
𝐼 = 𝑃𝑟𝑡
where: I = amount of interest earned
P = principal (original amount of money invested)
r = annual interest rate (as a decimal)
t = time in years
Note: time must be in years
When the length of time is given in months, divide it by 12 to convert it to years
When the length of time is given in days, divide it by 365 to convert it to years
12
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Example:
Olive Branch invests $1500 in a bank that offers her an interest rate of 4% per annum (year).
Calculate the interest that she earns at the end of:
a. three years
b. seven months
c. 100 days
Solution:
a. 𝐼 = 𝑃𝑟𝑡
𝑃 = $1500
𝑟 = 4% = 0.04
𝑡 = 3 𝑦𝑒𝑎𝑟𝑠
b. 𝐼 = 𝑃𝑟𝑡
𝑃 = $1500
𝑟 = 4% = 0.04
𝑡 = 7 𝑚𝑜𝑛𝑡ℎ𝑠
c. 𝐼 = 𝑃𝑟𝑡
𝐼 = ($1500)(0.04)(3) = $180
7
𝑡 = 12 = 0.583 𝑦𝑒𝑎𝑟𝑠
𝐼 = ($1500)(0.04)(0.583) = $35
100
𝑃 = $1500
𝑡 = 365 = 0.274 𝑦𝑒𝑎𝑟𝑠
𝑟 = 4% = 0.04
𝑡 = 100 𝑑𝑎𝑦𝑠
𝐼 = ($1500)(0.04)(0.274) = $16.44
Example:
Ross Quarter deposits $400 into his savings account that earns 3.25% per year. How much
interest does Ross earn at the end of:
a. a year
b. 5 months
c. 76 days
Solution:
a. 𝑃 = $400
𝑟 = 3.25% = 0.0325
𝑡 = 1 𝑦𝑒𝑎𝑟
𝐼 = ($400)(0.0325)(1) = $13
b. 𝑃 = $400
𝑡 = 12 = 0.417 𝑦𝑒𝑎𝑟𝑠
𝑟 = 3.25% = 0.0325
𝑡 = 5 𝑚𝑜𝑛𝑡ℎ𝑠
c. 𝑃 = $400
𝑟 = 3.25% = 0.0325
𝑡 = 76 𝑑𝑎𝑦𝑠
5
𝐼 = ($400)(0.0325)(0.417) = $5.42
76
𝑡 = 365 = 0.208 𝑦𝑒𝑎𝑟𝑠
𝐼 = ($400)(0.0325)(0.208) = $2.71
13
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Example:
Mr. Fontaine invests $20,000 at his bank. If his account earns 6.25%, how much will he have
earned at the end of 2 years and 3 months?
Solution:
3
𝑃 = $20 000
𝑡 = 12 = 0.25 𝑦𝑒𝑎𝑟𝑠
𝐼 = ($20 000)(0.0625)(2.25) = $2812.50
𝑟 = 6.25% = 0.0625
𝑡 = 2 𝑦𝑒𝑎𝑟𝑠 3 𝑚𝑜𝑛𝑡ℎ𝑠
Learning Activity 1.1 Simple Interest:
1. Find the interest earned for each of the following:
Interest
Principal
$1000
$500
$1500
$2540
$12500
Rate
5%
4.75%
7.75%
2.5%
3.25%
Time
2 years
6 months
125 days
18 months
326 days
2. What is the interest earned in an account that you have saved $5000 and you earn 3.25%
interest and have been saving money for 12 years?
3. How much interest has June earned if she saved $1389 in a savings account at the bank
that has a rate of 4.5% and she has had the money in for 285 days?
14
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
MANIPULATING THE SIMPLE INTEREST FORMULA:
We can also use the simple interest formula to calculate the other variables. Using the following
triangle to help us, we can write the formulas for the other variables.
I
P r
t
So, to find
𝑃=
Principal: cover P and write the formula as shown in the triangle.
r=
Interest rate: cover r and write the formula
t=
Time: cover t and write the formula
𝐼
𝑟𝑡
I
Pt
I
Pr
Example:
Mrs. Pine has borrowed a certain sum of money from her bank. She pays $200 in interest after 16
months. If the annual interest rate is 5%, what was the original amount that Mrs. Pine borrowed?
Solution:
𝑃 =?
𝑡=
16
𝑃=
𝐼
𝐼 = $200
𝑡 = 16 𝑚𝑜𝑛𝑡ℎ𝑠
= 1.33 years
12
𝑟𝑡
=
$200
(0.05)(1.33)
=
$200
0.0667
= $3000
𝑟 = 5% = 0.05
Example:
Danny borrows money from his bank and is charged an interest rate of 12.25%. If he pays
$497.50 in interest at the end of 2 years and 4 months, how much did Doug originally borrow?
Solution:
𝑃 =?
𝑡=
𝐼 = $497.50
𝑡 = 2 𝑦𝑒𝑎𝑟𝑠 3 𝑚𝑜𝑛𝑡ℎ𝑠
𝑃=
3
12
𝐼
𝑟𝑡
= 0.25 𝑦𝑒𝑎𝑟𝑠
=
$497.50
(0.1225)(2.25)
=
$497.50
0.2756
= $1805.15
𝑟 = 12.25% = 0.1225
15
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Example:
Brooke has $2400 to invest. What would the annual interest rate be if she would like to earn
$300 on her investment in 2 years?
Solution:
𝐼
𝑟=
𝑃 = $2400
𝐼 = $300
𝑡 = 2 𝑦𝑒𝑎𝑟𝑠
𝑟 = 0.0625 = 6.25%
𝑃𝑡
=
$300
𝑟 =?
($2400)(2)
=
300
4800
Example:
Wade deposits $5000 into an account that earns 4.5% interest. How long does he have to wait (in
months) to earn $360 in interest?
Solution:
𝑡 =?
𝐼
𝑟 = 4.5% = 0.045
𝐼 = $360
𝑡 = (1.6 𝑦𝑒𝑎𝑟𝑠)(12 𝑚𝑜𝑛𝑡ℎ𝑠/𝑦𝑒𝑎𝑟) = 19.2 𝑚𝑜𝑛𝑡ℎ𝑠
($5000)(0.045)
=
$360
𝑡=
𝑃𝑟
=
$360
𝑃 = $5000
225
= 1.6 𝑦𝑒𝑎𝑟𝑠
Learning Activity 1.2: Simple Interest
1. Mr Dee invests $17,500 at his bank. If his account earns 3.25%, how long it would take for
him to earn $10,000 in interest?
2. Susan invests $1275 and, at the end of 3 months, has earned $25 in interest. What is the
interest rate in her account?
3. Mr. Fontaine would like to know how long it would take for him to earn $5000 in interest on
his $20,000 investment at 6.25%.
4. Sandy invests $1000 and, at the end of 3 months, has earned $20 in interest. What is the
interest rate in her account?
5. Doug borrows money from his bank and is charged an interest rate of 12%. If he pays
$497.50 in interest at the end of 4 years, how much did Doug originally borrow?
16
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Curricular Outcomes:
11E3.I.3. Solve problems that require the manipulation and application of formulas related to: simple interest
Lesson 2 Assignment: Simple Interest
See your Teacher for Lesson 2 Assignment
17
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
LESSON 3: COMPOUND INTEREST
Recall: Compound interest is paid on both the principal and on the interest earned.
Compound interest makes a significant difference on the final amount of your investment
because you are earning interest on the principal as well as on the interest already earned. This is
good if you are investing money into a bank; not so good if you are borrowing.
Example:
You have $5000 to invest in your savings account that earns simple interest at a rate of 6% per
year, calculate how much interest you would have earned at the end of 3 years.
Solution:
𝐼 = 𝑃𝑟𝑡
𝐼 = ($5000)(0.06)(3) = $900
Example:
Say you have another $5000 to invest. This time you invest it into an account that earns 6%
interest per year, compounded annually. What is the amount of interest earned at the end of 3
years?
Solution:
Compounded annually means that at the end of each year the interest earned is added on to the
amount in your account and that new, higher amount is then used to calculate the interest you
earn that year. This is repeated each year since the interest is compounded annually.
Year 1:
𝐼 = 𝑃𝑟𝑡
𝐼 = ($5000)(0.06)(1) = $300
Year 2:
𝐼 = ($5300)(0.06)(1) = $318
Year 3:
𝐼 = ($5618)(0.06)(1) = $337.08
𝑇𝑜𝑡𝑎𝑙 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝐸𝑎𝑟𝑛𝑒𝑑 𝑜𝑣𝑒𝑟 𝑇ℎ𝑟𝑒𝑒 𝑦𝑒𝑎𝑟𝑠 = $300 + $318 + $337.08 = $955.18
𝒀𝒐𝒖 𝒆𝒂𝒓𝒏 𝒎𝒐𝒓𝒆 𝒊𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝒊𝒇 𝒚𝒐𝒖 𝒂𝒓𝒆 𝒖𝒔𝒊𝒏𝒈 𝒄𝒐𝒎𝒑𝒐𝒖𝒏𝒅 𝒊𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝒄𝒐𝒎𝒑𝒂𝒓𝒆𝒅 𝒕𝒐 𝒔𝒊𝒎𝒑𝒍𝒆 𝒊𝒏𝒕𝒆𝒓𝒆𝒔𝒕.
18
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Compound Interest Formula:
𝑟
𝐴 = 𝑃(1 + 𝑛)𝑛𝑡
where: A = final amount (principal + interest)
P = principal
r = annual interest rate as a decimal
n = number of compounding periods PER YEAR
t = time in years
“𝒏” 𝑖𝑠 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑖𝑚𝑒𝑠 𝑖𝑛 𝑂𝑛𝑒 𝑌𝑒𝑎𝑟 𝑡ℎ𝑎𝑡 𝑡ℎ𝑒 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑖𝑠 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑎𝑛𝑑 𝑎𝑑𝑑𝑒𝑑 𝑜𝑛. 𝑇ℎ𝑒 𝑚𝑜𝑠𝑡
𝑐𝑜𝑚𝑚𝑜𝑛 𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑖𝑛𝑔 𝑝𝑒𝑟𝑖𝑜𝑑𝑠 𝑎𝑟𝑒:
𝑴𝒐𝒏𝒕𝒉𝒍𝒚 = 12 𝑡𝑖𝑚𝑒𝑠 𝑎 𝑦𝑒𝑎𝑟 (𝑜𝑛𝑐𝑒 𝑎𝑡 𝑡ℎ𝑒 𝑒𝑛𝑑 𝑜𝑓 𝑒𝑎𝑐ℎ 𝑚𝑜𝑛𝑡ℎ)
𝑸𝒖𝒂𝒓𝒕𝒆𝒓𝒍𝒚 = 4 𝑡𝑖𝑚𝑒𝑠 𝑎 𝑦𝑒𝑎𝑟
𝑺𝒆𝒎𝒊 − 𝒂𝒏𝒏𝒖𝒂𝒍 = 2 𝑡𝑖𝑚𝑒𝑠 𝑎 𝑦𝑒𝑎𝑟
𝑨𝒏𝒏𝒖𝒂𝒍 = 1 𝑡𝑖𝑚𝑒 𝑎 𝑦𝑒𝑎𝑟
𝑫𝒂𝒊𝒍𝒚 = 365 (𝑛𝑜𝑡 𝑐𝑜𝑚𝑚𝑜𝑛𝑙𝑦 𝑢𝑠𝑒𝑑 𝑢𝑛𝑙𝑒𝑠𝑠 𝑑𝑒𝑎𝑙𝑖𝑛𝑔 𝑤𝑖𝑡ℎ 𝑐𝑟𝑒𝑑𝑖𝑡 𝑐𝑎𝑟𝑑𝑠)
Example:
April deposits $1000 at 7.5% interest for 3 years compounded quarterly. What is her total
amount in her account? How much interest did she earn?
Solution:
𝑈𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑓𝑜𝑟𝑚𝑢𝑙𝑎 𝑓𝑜𝑟 𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡:
𝑟
𝐴 = 𝑃(1 + )𝑛𝑡
𝑛
𝑃 = $1000
𝑟 = 7.5% = 0.075
𝑛 = 𝑞𝑢𝑎𝑟𝑡𝑒𝑟𝑙𝑦 = 4
𝑡 = 3 𝑦𝑒𝑎𝑟𝑠
0.075 (4)(3)
)
4
𝐴 = ($1000)(1 + 0.01875)12
𝐴 = ($1000)(1.01875)12
𝐴 = ($1000)(1.2497) = $1249.70
𝐴 = ($1000)(1 +
19
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Example:
Genevieve invests $5000 at her bank at 6% interest, compounded semi-annually. Calculate the
interest she has earned after 3 years.
Solution:
𝑃 = $5000
𝑟 = 6% = 0.06
𝑛 = 𝑠𝑒𝑚𝑖 − 𝑎𝑛𝑛𝑢𝑎𝑙𝑙𝑦 = 2
𝑡 = 3 𝑦𝑒𝑎𝑟𝑠
0.06 (2)(3)
)
2
𝐴 = ($5000)(1 + 0.03)6
𝐴 = ($5000)(1.03)6
𝐴 = ($5000)(1.1941) = $5970.50
𝐴 = ($5000)(1 +
Example:
Kristen invests $1200 at 9.75% interest, compounded annually. How much does she earn in
interest at the end of 7 years? Compare this to the interest she would have earned if she were
earning simple interest.
Solution:
𝑪𝒐𝒎𝒑𝒐𝒖𝒏𝒅 𝑰𝒏𝒕𝒆𝒓𝒆𝒔𝒕:
𝑃 = $1200
𝑟 = 9.75% = 0.0975
𝑛 = 𝑎𝑛𝑛𝑢𝑎𝑙𝑙𝑦 = 1
𝑡 = 7 𝑦𝑒𝑎𝑟𝑠
0.0975 (1)(7)
)
1
𝐴 = ($1200)(1 + 0.0975)7
𝐴 = ($1200)(1.0975)7
𝐴 = ($1200)(1.9179) = $2301.48
𝐴 = ($1200)(1 +
𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝐸𝑎𝑟𝑛𝑒𝑑 = 𝐴 − 𝑃 = $2301.48 − $1200 = $1101.48
𝑺𝒊𝒎𝒑𝒍𝒆 𝑰𝒏𝒕𝒆𝒓𝒆𝒔𝒕:
𝐼 = 𝑃𝑟𝑡
𝐼 = ($1200)(0.0975)(7) = $819
𝑆𝑜, 𝑢𝑠𝑖𝑛𝑔 𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑦𝑜𝑢 𝑤𝑜𝑢𝑙𝑑 𝑒𝑎𝑟𝑛 $1101.48 − $819 = $282.48
𝑚𝑜𝑟𝑒 𝑡ℎ𝑎𝑛 𝑦𝑜𝑢 𝑤𝑜𝑢𝑙𝑑 𝑤𝑖𝑡ℎ 𝑠𝑖𝑚𝑝𝑙𝑒 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡.
20
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Learning Activity: 1.3 Compound Interest
1. Complete the following chart.
Principal
$1,000
Interest Rate ( r )
7% compounded
Time
(years)
# of
compounding
periods/yr
(n)
7
annually
$250
10% compounded
5
semi-annually
$4,000
6% compounded
6
monthly
$800
9% compounded
2
quarterly
$25,000
5.5% compounded
4
semi-annually
2. Using the compound interest formula, calculate both the value of the investment and the
interest earned after the given time period.
a. $4,000 for five years at 7% compounded semi-annually
b. $2,500 for two years at 7.25% compounded monthly
c. $900 for eight years at 10% compounded annually.
3. Explain the difference between simple interest and compound interest. If given the option,
which account would you choose to invest your money in: a simple interest account or a
compound interest account? Why? If you had to borrow money from the bank, which
account would you choose? Why?
4. How does the number of compounding periods affect the amount of interest you earn in an
account?
21
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
THE RULE OF 72
The Rule of 72 is used to estimate the length of time in years it would take an amount of money
to double at the given interest rate. It is estimating the compound interest formula for
determining the length of time. To solve for time using the compound interest formula is a much
more difficult process.
To quickly estimate the length of time it takes for an investment to double, use the “Rule of 72”.
All you need is the interest rate and the number 72!
𝑌𝑒𝑎𝑟𝑠 𝑡𝑜 𝐷𝑜𝑢𝑏𝑙𝑒 =
72
𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑅𝑎𝑡𝑒 (𝑎𝑠 𝑎 𝑝𝑒𝑟𝑐𝑒𝑛𝑡)
Example:
How long does it take for an investment of $2000 to double at an interest rate of 3.25%?
Solution:
𝑌𝑒𝑎𝑟𝑠 𝑡𝑜 𝐷𝑜𝑢𝑏𝑙𝑒 =
72
= 22.15 𝑦𝑒𝑎𝑟𝑠
3.25
So it takes, 22.15 years to double to $4000. Or, 22 years and 1.8 months
22
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Curriculum Outcomes:
11E3.I.1. Demonstrate an understanding of compound interest.
Lesson 3 Assignment: Compound Interest
See your Teacher for Lesson 3 Assignment
23
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
LESSON 4: CREDIT CARDS
Applying for a Credit Card:
To get a credit card you must be at least 18 years old, complete an application form, and be
approved by the credit company. The credit card company is agreeing to loan you the money for
your purchases with your promise to repay them under the terms of the agreement. The credit
card company will apply a limit to your card, this is based on your income and credit rating (a
rating used by financial institutions to indicate a person’s ability to repay their credit debt).
Pros and Cons of having a Credit Card:
Pros
Cons
Using a Credit Card:
When you use a credit card, you are borrowing money from the credit card company. Each
month they send you a statement that shows your transactions for that billing period. A billing
period is a month in length but not necessarily from the first day of the month to the last day;
billing periods can start in the middle of a month. The statement shows your minimum balance
that you have to pay by the date shown on the statement. Any unpaid amount will have interest
compounded daily on it from the date of purchase.
Interest on Purchases using a Credit Card:
If you pay your entire balance owing on a credit card by the due date on your statement, you will
not be charged any interest. If you only pay the minimum balance shown on your statement, the
credit card company will charge interest compounded daily. Most credit card companies now
must show how long it will take to pay off the balance owing assuming you only make the
minimum payment and you do not make any more purchases using the card.
24
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Example:
Mike had a previous balance of $500 on his credit card. He made a payment of $300 during the
month. He made more purchases that totalled $190.00. If his interest is $19.45, what would his
minimum monthly payment be if it must correspond to at least 5% of the ending balance OR
$10, whichever is greater?
Previous balance
=
$500
Payment
=
$300
Unpaid balance
=
$200
Interest
=
$19.45
New purchases
=
$190
New balance
=
$409.45
5% of new balance
=
$20.47
Minimum Monthly payment
=
$20.47
Example:
Will’s monthly credit card statement shows a previous balance owing of $963.45. Will only paid
$500 of this balance by the due date. If he is charged an annual interest rate of 21%, how much
interest will he pay after 42 days?
Solution:
𝐼 =?
𝑟 = 21% = 0.21
𝑡 = 42 𝑑𝑎𝑦𝑠
𝑛 = 365 𝑑𝑎𝑦𝑠
𝑟 𝑛𝑡
𝐴 = 𝑃 (1 + )
𝑛
𝐴 = ($463.45)(1 +
0.21 ( 42 )(365)
) 365
365
𝐴 = ($463.45)(1.005753)42
𝐴 = ($463.45)(1.02445) = $474.78
𝐼 = $474.78 − $463.45 = $11.33
25
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Example:
Bob received his monthly credit card statement shown below. He makes only the minimum
payment how much interest is he charged?
Statement Date: August 20th
New Balance: $944.95
Minimum Payment: $19.00
Annual Interest Rate: 29.9%
Days Late: 31
Solution:
𝑢𝑛𝑝𝑎𝑖𝑑 𝑏𝑎𝑙𝑎𝑛𝑐𝑒 = $944.95 − $19.00 = $925.95
𝑟 𝑛𝑡
𝐼 =?
𝑟 = 29.9% = 0.299
𝑡 = 31 𝑑𝑎𝑦𝑠
𝑛 = 365 𝑑𝑎𝑦𝑠
𝐴 = 𝑃 (1 + )
𝑛
𝐴 = ($925.95)(1 +
0.299 ( 31 )(365)
) 365
365
𝐴 = ($925.95)(1.000819)31
𝐴 = ($925.95)(1.02571) = $949.75
𝐼 = $949.75 − $925.95 = $23.81
Example:
Alex’s monthly statement shows a previous balance of $563.45. During the month, Alex made a
payment of $500 and purchased goods totalling $626.95. If Alex earns an interest rate of 21% on
any balance owing at the end of this month (30 days), what will Alex be paying interest?
Solution:
𝑢𝑛𝑝𝑎𝑖𝑑 𝑏𝑎𝑙𝑎𝑛𝑐𝑒 = $563.45 − $500 + $626.95 = $690.40
𝐼 =?
𝑟 = 21% = 0.21
𝑡 = 30 𝑑𝑎𝑦𝑠
𝑛 = 365 𝑑𝑎𝑦𝑠
𝑟 𝑛𝑡
𝐴 = 𝑃 (1 + )
𝑛
𝐴 = ($690.40)(1 +
0.21 ( 30 )(365)
) 365
365
𝐴 = ($690.40)(1.000575)30
𝐴 = ($690.40)(1.0174) = $702.42
𝐼 = $702.42 − $690.40 = $12.02
26
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Example:
If you received a credit card statement in October and paid nothing by the first due data,
calculate the daily interest charge for each of the following unpaid items if the annual interest
rate is 20.8%
a. $375.85 bought on Oct. 1 (50 days overdue)
b. $635.90 bought on Oct. 5 (46 days overdue)
c. $1444.90 bought on Oct. 10 (41 days overdue)
Solution:
a)
𝑢𝑛𝑝𝑎𝑖𝑑 𝑏𝑎𝑙𝑎𝑛𝑐𝑒 = $375.85
𝑟 𝑛𝑡
𝐼 =?
𝑟 = 20.8% = 0.208
𝐴 = 𝑃 (1 + 𝑛)
𝑡 = 50 𝑑𝑎𝑦𝑠
𝑛 = 365 𝑑𝑎𝑦𝑠
𝐴 = ($375.85)(1 +
0.208 ( 50 )(365)
) 365
365
𝐴 = ($375.85)(1.00056986)50
𝐴 = ($375.85)(1.02889) = $386.71
𝐼 = $386.71 − $375.85 = $10.86
b)
𝑢𝑛𝑝𝑎𝑖𝑑 𝑏𝑎𝑙𝑎𝑛𝑐𝑒 = $635.90
𝑟 𝑛𝑡
𝐼 =?
𝐴 = 𝑃 (1 + 𝑛)
𝑟 = 20.8% = 0.208
𝑡 = 46 𝑑𝑎𝑦𝑠
𝑛 = 365 𝑑𝑎𝑦𝑠
𝐴 = ($635.90)(1 +
0.208 ( 46 )(365)
) 365
365
𝐴 = ($635.90)(1.00056863)46
𝐴 = ($635.90)(1.02655) = $652.78
𝐼 = $652.78 − $635.90 = $76.88
c)
𝑢𝑛𝑝𝑎𝑖𝑑 𝑏𝑎𝑙𝑎𝑛𝑐𝑒 = $1444.90
𝑟 𝑛𝑡
𝐼 =?
𝑟 = 20.8% = 0.208
𝐴 = 𝑃 (1 + 𝑛)
𝑡 = 41 𝑑𝑎𝑦𝑠
𝑛 = 365 𝑑𝑎𝑦𝑠
𝐴 = ($1444.90)(1 +
0.208 ( 41 )(365)
) 365
365
𝐴 = ($1444.90)(1.00056986)41
𝐴 = ($1444.90)(1.023633) = $1479.05
𝐼 = $1479.05 − $1444.90 = $34.15
27
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Curriculum Outcomes:
11E3.I.2. Demonstrate an understanding of credit options, including: credit cards; loans.
Lesson 4 Assignment: Credit Cards
See your Teacher for Lesson 4 Assignment
28
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
LESSON 5 SALES TAX AND PROMOTIONS:
Types of Sales Tax:
PST: Provincial Sales Tax 8% Manitoba (PST)
GST: Goods and Services Tax 5% Federal (GST)
Total Tax: 13%
Example:
Joe has decided that he needs a new snow blower this winter. He found one that sells for
$189.95. What is the total cost to Joe if he decides to buy the snow blower?
Solution:
𝑡𝑜𝑡𝑎𝑙 𝑤𝑖𝑡ℎ 𝑡𝑎𝑥 = ($189.95)(1.13) = $214.64
Example:
As a smart shopper, Joe decided that he can wait to buy the snow blower and instead decided to
by a lawn mower since they are on sale. If a new lawn mower is $78.99 and it is 25% off, what is
the price of the mower before tax? What is the price after tax?
Solution:
𝑎𝑚𝑜𝑢𝑛𝑡 𝑠𝑎𝑣𝑒𝑑 = ($78.99)(0.25) = $19.75
𝑠𝑎𝑙𝑒 𝑝𝑟𝑖𝑐𝑒 = $78.99 − $19.75 = $59.24
𝑡𝑜𝑡𝑎𝑙 𝑤𝑖𝑡ℎ 𝑡𝑎𝑥 = ($59.24)(1.13) = $66.94
Example:
You have been waiting for a pair of shoes at the mall to go on sale. Finally they have and are
marked down 20%. If the original cost of the shoes is $89.99 what is the sale price? What is the
total price you pay, including tax?
Solution:
𝑎𝑚𝑜𝑢𝑛𝑡 𝑠𝑎𝑣𝑒𝑑 = ($89.99)(0.20) = $18
𝑠𝑎𝑙𝑒 𝑝𝑟𝑖𝑐𝑒 = $89.99 − $18 = $71.99
𝑡𝑜𝑡𝑎𝑙 𝑤𝑖𝑡ℎ 𝑡𝑎𝑥 = ($71.99)(1.13) = $81.35
29
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Example:
Rob likes to shop on-line for his clothing. He buys four shirts at $9.95 each, a jacket for $45.99,
two pairs of jeans for $45.20 each and a belt for $25.00. Rob lives in Manitoba, what it the total
cost Rob is charged?
Solution:
𝑠ℎ𝑖𝑟𝑡𝑠 = (4)($9.95) = $39.80
𝑗𝑎𝑐𝑘𝑒𝑡 = $45.99
𝑗𝑒𝑎𝑛𝑠 = (2)($45.20) = $90.40
𝑏𝑒𝑙𝑡 = $25.00
𝑆𝑢𝑏 𝑇𝑜𝑡𝑎𝑙 = $39.80 + $45.99 + $90.40 + $25 = $201.19
𝑇𝑜𝑡𝑎𝑙 𝑤𝑖𝑡ℎ 𝑡𝑎𝑥 = ($201.19)(1.13) = $227.34
Example:
When Anita talks to a salesman about buying her couch he offers her a deal. She has a credit card
that has an interest rate of 19.99% and gives her 1% cash back or she can apply for the stores
credit card and receive 10% off her purchase and charges her 29.99% interest. She takes 120
days to pay off the balance owing. Which is the better deal if the price of the couch is $1790.95?
Solution:
𝑂𝑝𝑡𝑖𝑜𝑛 𝐴:
𝑐𝑎𝑠ℎ 𝑏𝑎𝑐𝑘 = ($1790.95)(0.01) = $17.91
𝑢𝑛𝑝𝑎𝑖𝑑 𝑏𝑎𝑙𝑎𝑛𝑐𝑒 = $1790.95 − $17.91 = $1773.04
𝐼 =?
𝑟 = 19.99% = 0.1999
𝑡 = 120 𝑑𝑎𝑦𝑠
𝑛 = 365 𝑑𝑎𝑦𝑠
𝑟 𝑛𝑡
𝐴 = 𝑃 (1 + 𝑛)
𝐴 = ($1773.04)(1 +
0.1999 (120)(365)
) 365
365
𝐴 = ($1773.04)(1.000547671)120
𝐴 = ($1773.04)(1.06791) = $1893.45
𝑂𝑝𝑡𝑖𝑜𝑛 𝐵:
𝑎𝑚𝑜𝑢𝑛𝑡 𝑠𝑎𝑣𝑒𝑑 = ($1790.95)(0.10) = $179.10
𝑠𝑎𝑙𝑒 𝑝𝑟𝑖𝑐𝑒 = $1790.95 − 179.10 = $1611.85
0.2999 (120)(365)
) 365
365
𝐴 = ($1611.85)(1.0008216)120
𝐴 = ($1611.85)(1 +
𝐴 = ($1611.85)(1.1032577) = $1778.80
30
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Curriculum Outcomes
11E3.I.2. Demonstrate an understanding of credit options
Lesson 5 Assignment: Sales Tax and On Sale
See your Teacher for Lesson 5 Assignment
31
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
LESSON 6 PROMOTIONS
Instalment Buying
-
companies often will provide credit in a variety of ways to encourage you to buy their
products
-
one way they offer credit is by instalment buying
-
this is when you pay for a product in instalments plus a down payment at the time of
purchase
-
you pay for the rest of the cost in equal payments (instalment payments) over a given number
of time periods (instalment periods)
-
the instalment price is usually higher than the actual selling price because the company will
charge a finance or carrying charge.
Example
Jack’s washing machine broke. He goes shopping and finds a new one for $889.45 plus tax. The
store offers an instalment plan for $150 down and $90 a month for 12 months. Calculate the cash
selling price of the washing machine. Calculate the instalment price of the washing machine.
What is the finance charge?
Solution:
𝐶𝑎𝑠ℎ 𝑝𝑟𝑖𝑐𝑒 = ($889.45)(1.13) = $1005.08
𝑡𝑜𝑡𝑎𝑙 𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 = (𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝑝𝑎𝑦𝑚𝑒𝑛𝑡)(𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑛𝑡ℎ𝑠)
= ($90)(12) = $1080
𝑇𝑜𝑡𝑎𝑙 𝑖𝑛𝑠𝑡𝑎𝑙𝑙𝑚𝑒𝑛𝑡 𝑐𝑜𝑠𝑡 = 𝑡𝑜𝑡𝑎𝑙 𝑝𝑎𝑦𝑚𝑒𝑛𝑡𝑠 + 𝑑𝑜𝑤𝑛 𝑝𝑎𝑦𝑚𝑒𝑛𝑡
= $1080 + $150 = $1230
𝐹𝑖𝑛𝑎𝑛𝑐𝑒 𝑐ℎ𝑎𝑟𝑔𝑒 = 𝑡𝑜𝑡𝑎𝑙 𝑖𝑛𝑠𝑡𝑎𝑙𝑙𝑚𝑒𝑛𝑡 𝑐𝑜𝑠𝑡 − 𝑐𝑎𝑠ℎ 𝑝𝑟𝑖𝑐𝑒
= $1230 − $1005.08 = $224.92
32
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Example:
A company offers customers the option of purchasing its products in instalments instead of
paying cash up front. You want to buy a new stereo for $389.83 plus tax.
a) calculate the cash selling price of the DVD player
b) calculate the instalment price of the DVD player if the instalment terms are $50 down
and $75 a month for six months.
c) What is the finance charge you paid?
Solution:
𝑐𝑎𝑠ℎ 𝑝𝑟𝑖𝑐𝑒 = ($389.83)(1.13) = $440.51
𝑡𝑜𝑡𝑎𝑙 𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝑝𝑎𝑦𝑚𝑒𝑛𝑡𝑠 = ($75)(6) = $450
𝑡𝑜𝑡𝑎𝑙 𝑖𝑛𝑠𝑡𝑎𝑙𝑙𝑚𝑒𝑛𝑡 𝑐𝑜𝑠𝑡 = $450 + $50 = $500
𝑓𝑖𝑛𝑎𝑛𝑐𝑒 𝑐ℎ𝑎𝑟𝑔𝑒 = $500 − $440.51 = $56.49
Example:
Carla decides to buy a new sofa and chair for her apartment. The cost for both is $1288.21 plus
tax. The instalment terms are $200 down plus $175 a month for eight months.
a) calculate the cash selling price of the furniture
b) calculate the instalment price of the furniture
c) What is the finance charge she paid?
Solution:
𝑐𝑎𝑠ℎ 𝑝𝑟𝑖𝑐𝑒 = ($1288.21)(1.13) = $1455.68
𝑡𝑜𝑡𝑎𝑙 𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝑝𝑎𝑦𝑚𝑒𝑛𝑡𝑠 = ($175)(8) = $1400
𝑡𝑜𝑡𝑎𝑙 𝑖𝑛𝑠𝑡𝑎𝑙𝑙𝑚𝑒𝑛𝑡 𝑐𝑜𝑠𝑡 = $1400 + $200 = $1600
𝑓𝑖𝑛𝑎𝑛𝑐𝑒 𝑐ℎ𝑎𝑟𝑔𝑒 = $1600 − $1455.68 = $144.32
33
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Learning Activity 1.4: Instalment Buying
1. On the first of March, Oliver decides to purchase a dining room set that has a cash value of
$1599.51 plus tax as well as a new stereo system that has a cash value of $425.24 plus tax.
Because Oliver is buying the stereo system with the dining room set, he does not have to pay
tax on the stereo. The instalment term for his purchase is $200 down plus $100 a month for
two years.
a. Calculate the cash-selling price of the dining room set and stereo
b. Calculate the instalment price of the dining room set and stereo
c. What is the finance charge?
2. Jake is shopping for a new skateboard. He has found one that he likes for $400 plus tax. He
does not have $400 cash so he chooses the instalment option provided by the store which is
$120 down plus $65 a month for six months.
a. What is the cash selling price of the skateboard?
b. What does Jake pay in total for his new skateboard?
c. What is the finance charge?
3. Robert decided to purchase a new television. The cash selling price is $999.99 plus taxes.
The instalment terms are $400 down plus $45 a month for 24 months.
a. Calculate the cash selling price.
b. Calculate the instalment price of the television.
c. Calculate the carrying charge.
34
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Deferred Payments: “Buy Now, Pay Later”
-
“buy-now, pay-later” option is a deferred payment plan in which customers do not pay for
their purchase for a specified period of time and are not charged interest over that time period
-
Customers pay for their purchase once the “grace period” is over and are then charged
interest on any amount they have not paid
-
with this type of plan, customers usually have to pay certain costs at the time of purchase,
these include the taxes, delivery charges, and administration fees.
-
Often, the sticker price of the product is lower than the “pay-later” price
-
furniture and appliances are often sold this way
Example:
A sofa is advertised as buy-now, pay-later. The price of the sofa if you pay up front is $924.95
plus taxes and a delivery charge of $25. If you decide to pay-later, the price of the sofa is
$999.95 plus tax. At the time of purchase, you must pay the taxes, a delivery charge of $25 and
an administration fee of $49.
a. What is the price of the sofa if you pay for it right away?
b. If you choose the “pay-later” option, what will you pay at the time of purchase?
c. At the end of the year, how much will you have to pay for the sofa?
d. What is the difference in the cost for the sofa in the “pay-later” option?
Solution:
a)
𝑐𝑎𝑠ℎ 𝑝𝑟𝑖𝑐𝑒 = ($924.95)(1.13) + $25 = $1045.19 + $25 = $1070.19
b)
𝑐𝑜𝑠𝑡 𝑎𝑡 𝑡𝑖𝑚𝑒 𝑜𝑓 𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒 = 𝑡𝑎𝑥𝑒𝑠 + 𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦 + 𝑎𝑑𝑚𝑖𝑛 𝑓𝑒𝑒 + 𝑎𝑛𝑦 𝑜𝑡ℎ𝑒𝑟 𝑓𝑒𝑒𝑠
𝑡𝑎𝑥𝑒𝑠 = ($999.95)(0.13) = $129.99
𝑐𝑜𝑠𝑡 𝑎𝑡 𝑡𝑖𝑚𝑒 𝑜𝑓 𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒 = $129.99 + $25 + $49 = $203.99
c)
𝑒𝑛𝑑 𝑜𝑓 𝑦𝑒𝑎𝑟 𝑐𝑜𝑠𝑡 = $999.95
d)
𝑡𝑜𝑡𝑎𝑙 pay later 𝑝𝑟𝑖𝑐𝑒 = $999.95 + $203.99 = $1203.94
𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 𝑡𝑜𝑡𝑎𝑙 𝑝𝑎𝑦 𝑙𝑎𝑡𝑒𝑟 𝑝𝑟𝑖𝑐𝑒 − 𝑐𝑎𝑠ℎ 𝑝𝑟𝑖𝑐𝑒
= $1203.94 − $1070.19 = $133.75
35
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Example:
Cara wants to buy the newest model of fridge from Samsung. It is $2799.99 plus taxes at Future
Shop and they offer no payments for one year. There is a delivery charge of $25.00 and an
administration fee of $69.95 plus taxes. If her balance is not paid off on time, she will accrue
interest from the date of purchase at a rate of 28.8% per year. If she pays cash there is no
delivery fee.
a. What is the cash price of the fridge?
b. What will Cara have to pay at the time of purchase?
c. What will be due at the end of the one year (assuming she pays off the fridge on time)?
d. What will she owe on the fridge if she waits an additional year and one day beyond the
grace period?
e. What is the total cost for the “pay later” option?
Solution:
a)
𝑐𝑎𝑠ℎ 𝑝𝑟𝑖𝑐𝑒 = ($2799.99)(1.13) = $3163.99
b)
𝑐𝑜𝑠𝑡 𝑎𝑡 𝑡𝑖𝑚𝑒 𝑜𝑓 𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒 = 𝑡𝑎𝑥𝑒𝑠 + 𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑦 + 𝑎𝑑𝑚𝑖𝑛 𝑓𝑒𝑒 + 𝑎𝑛𝑦 𝑜𝑡ℎ𝑒𝑟 𝑓𝑒𝑒𝑠
𝑡𝑎𝑥𝑒𝑠 = ($2799.99)(0.13) = $364
𝑎𝑑𝑚𝑖𝑛 𝑓𝑒𝑒 = ($69.95)(1.13) = $79.04
𝑐𝑜𝑠𝑡 𝑎𝑡 𝑡𝑖𝑚𝑒 𝑜𝑓 𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒 = $364 + $25 + $79.04 = $468.04
c)
𝑒𝑛𝑑 𝑜𝑓 𝑦𝑒𝑎𝑟 𝑐𝑜𝑠𝑡 = $2799.99
d)
𝑡 = 366 𝑑𝑎𝑦𝑠
𝑃 = $2799.99
𝑛 = 365
𝑟 = 28.8% = 0.288
𝑟
𝐴 = 𝑃(1 + )𝑛𝑡
𝑛
366
0.288 (365)(365)
𝐴 = ($2799.99) (1 +
)
365
= ($2799.99)(1.000789)366
= ($2799.99)(1.334652) = $3737.03
𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝐶ℎ𝑎𝑟𝑔𝑒 = $3737.03 − $2799.99 = $937.04
e)
𝑡𝑜𝑡𝑎𝑙 𝑐𝑜𝑠𝑡 = $498.04 + $2799.99 + $937.04 = $4235.07
36
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Learning Activity 1.5: Buy Now Pay Later
1. Amy is purchasing a couch from The Brick. She decides to use the “Buy – Now, Pay –
Later” option that they have advertised in the flyer. The price of the couch is $995.95 plus
taxes. At the time of the purchase she must pay the taxes, a delivery fee of $25, and an
administration fee of $49.99. She has one – year to pay for the couch. If she takes longer than
a year she will be charged interest.
If she had not picked the “pay – later” option the couch would have been $924.95 plus taxes
and she would only have to pay the delivery fee.
a. What would the total cost be if Amy had paid for the couch right away?
b. How much will she pay at the time of purchase if she chooses the “Pay – Later”
option?
c. If Amy pays for the couch within the one year grace period, what is the total that she
pays for the couch?
d. Calculate the difference between the prices.
2. A washer and dryer are on a “buy-now, pay-later” promotion as The Brick. The cash-selling
price of the washer dryer set is $509.99 plus tax, and the ‘buy-now, pay-later’ price is
$698.98 plus tax. If you decide to take the ‘buy-now, pay-later’ promotion, you must pay the
taxes, a delivery charge of $35, and an administration fee of $45 at the time of purchase. You
have one year to pay for the purchase and no interest will be charged.
a. How much do you have to pay at the time of purchase for the “buy now pay later”
option?
b. If you pay for the washer and dryer set within the year, what is the cost you will have
to pay?
c. If you can only pay $400 at the end of the year, you are charged an interest rate of
12% annually on the remaining balance. How much interest will you have to pay if
you take another year to pay off the rest of the cost?
3. Terry purchase a television set at a price of $698.98 plus taxes from Visions. He can choose
the “Buy – Now, Pay – Later” option at the time of purchase, October 1, 2013. The “Pay –
Later” option means that Terry would pay the taxes, plus a delivery fee of $25 and an
administration fee of $45. He has a six month grace period after which he is charged interest
on his purchase. Visions will charge him 4% per year, compounded monthly, on any
outstanding balance.
a. Calculate the cost if he can pay for the TV on March 1, 2013.
b. Calculate the cost if he pays for the TV on May 31, 2014. The company charges
interest after the grace period has expired.
37
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Curriculum Outcomes:
11E3.I.3. Solve problems that require the manipulation and application of formulas related to: simple interest, finance charges
Lesson 6 Assignment: Promotions
See your Teacher for Lesson 6 Assignment
38
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
LESSON 7 PERSONAL LOANS
-
-
a personal loan allows you to borrow a specified amount of money and re-pay it over time,
usually one to five years
interest is charged on the principal amount borrowed
the payment made each month pays a portion of the interest charged and a portion of the
principal amount borrowed
Example:
Jesse requires a personal loan of $10,000 for repairs to his home. He gets a 3 year loan at an
interest rate of 10.25%
a. What is his monthly payment?
b. What it the total cost Jesse will pay at the end of three years?
c. How much interest did he have to pay?
Solution:
𝑎𝑚𝑜𝑢𝑛𝑡 𝑏𝑜𝑟𝑟𝑜𝑤𝑒𝑑
a. 𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 = (𝑡𝑎𝑏𝑙𝑒 𝑣𝑎𝑢𝑙𝑒) (
)
$1000
= ($32.38) (
$10 000
) = ($32.38)(10) = $323.80 /𝑚𝑜𝑛𝑡ℎ
$1000
b. 𝑡𝑜𝑡𝑎𝑙 𝑐𝑜𝑠𝑡 = (𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝑝𝑎𝑦𝑚𝑒𝑛𝑡)(12)(𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑦𝑒𝑎𝑟𝑠)
= ($323.80)(12)(3) = $11 656.80
c. 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 = 𝑡𝑜𝑡𝑎𝑙 𝑐𝑜𝑠𝑡 − 𝑎𝑚𝑜𝑢𝑛𝑡 𝑏𝑜𝑟𝑟𝑜𝑤𝑒𝑑
= $11 656.80 − $10 000 = $656.80
Example:
You need a loan for repairs on your car. You decide to borrow $2250 from the bank for a two
year period at an interest rate of 12%.
a) What is his monthly payment?
b) What it the total cost you will pay at the end of two years?
c) How much interest did you have to pay?
Solution:
$2250
a. 𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 = ($47.07) ($1000) = ($47.07)(2.25) = $105.91 /𝑚𝑜𝑛𝑡ℎ
b. 𝑡𝑜𝑡𝑎𝑙 𝑐𝑜𝑠𝑡 = ($105.91)(12)(2) = $2541.84
c. 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 = $2541.84 − $2250 = $291.84
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Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Example
Amy wants to buy a new computer. She found one that she likes for $2400 plus taxes. She
decides to take out a personal loan to help her pay for the computer.
a. What amount does she need to borrow to cover the cost of the computer?
b. What is his monthly payment if it is a 2 year loan at an interest rate of 11.75%?
c. What it the total cost she will pay at the end of two years?
d. How much interest did she have to pay?
Solution:
a. 𝑝𝑟𝑖𝑐𝑒 = ($2400)(1.13) = $2712
$2712
b. 𝑚𝑜𝑛𝑡ℎ𝑙𝑦 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 = ($46.96) ($1000) = ($46.96)(2.712) = $126.23 /𝑚𝑜𝑛𝑡ℎ
c. 𝑡𝑜𝑡𝑎𝑙 𝑐𝑜𝑠𝑡 = ($126.23)(12)(2) = $3029.52
d. 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 = $3029.52 − $2712 = $317.52
40
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
41
Grade 11 Essential Mathematics
Unit 1: Interest and Credit
Curriculum Outcomes:
11E3.I.2. Demonstrate an understanding of credit options, including: credit cards, loans.
Lesson 7 Assignment: Personal Loans
See your Teacher for Lesson 7 Assignment
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