I

) = Principal (

P

) x interest rate (

r

) x time (

t

)

**Simple**

Interest

Interest

**Interest and Credit**

At a glance

- simple interest

- compound interest

- compounding periods

- credit options

credit cards

loans

lines of credit

What words come to mind when you hear "investments"?

Investments

When you

invest,

you use your savings to earn

extra income

!

I = P r t

Ex. 1

David is a sprinkler-system installer. He invested $1500 in a GIC for 2 years. The interest rate is 2.5%/yr. How much interest will he earn in a year?

5 steps in solving problems

1. write given information

2. formula

3. substitute values into the equation

4. solve

5. answer in sentence form

Ex. 2.

Sue is planning a trip to the U.S. She invested $5000 in a U.S. Foreign Currency Term Deposit. The annual interest rate is 0.5%. The deposit matures in 120 days.

How much money will Sue have for her trip

?

Compound

Interest

Compounding

Periods

interest can be compounded in different ways

**Credit**

Options

Options

Principal

- the money invested or borrowed

Interest rate

- the percent of the principal that is paid or earned as interest

Time

- length of time for an investment in years

is the interest calculated only on the principal invested or borrowed

Simple Interest Problems

TIP:

Rearrange the formula first

to find the missing variable, before substituting values

Ex. 1 Dan knew the following: he earned $35 in interest in an investment, the annual rate was 1.9% and it was for 42 weeks. How much money did Dan invest?

Ex. 2. Jamie wants to earn $500 in interest so she’ll have enough to buy a used car. She puts $2000 into an account that earns interest. How long will she need to leave her money in the account if the annual rate is 1.75%?

Ex. 3. A local bank is advertising that you can double your money in eight years if you invest with them. Suppose you have $1000 to invest.

What interest rate is the bank offering

?

I

P

r

t

Ex. 1.

P = $5000

r = 1.5% /yr

compounded annually

How much will the savings be worth after 4 years?

$ 5000

I = 5000 x 0.015 x 1 = 75

A = 5000 + 75 = $5075

$ 5075

I = 5075 x 0.015 x 1 = 76.13

A = 5075 + 76.125 = $5151.13

$ 5151.13

I = 5151.13 x .015 x 1 = 77.27

A = 5151.13 + 77.27 = 5228.4

$ 5228.40

I = 5228.40 x .015 x 1 = 78.43

A = 5228.40 + 78.43 = 5306.83

**3D Geometry**

is the interest calculated on the

principal and the interest

earned

Annually

Semi-annually

Quarterly

Monthly

Weekly

Daily

once per yr

2 times per yr

4 times per yr

12 times per yr

52 times per yr

365 times per yr

You invested $1000

1.4%/yr

compounded weekly

2 yrs

What is the value of the

investment?

Compound Interest Problems

1.3%/yr

compounded daily

$1400 investment

5 yrs

What is the amount of the investment after 5 yrs?

**72**

The Rule of

can be used to estimate how long it will take for the investment to double

You invested $2500

3.1%/yr

compounded monthly

a. Estimate the doubling time for your investment.

b. Check that your answer is reasonable.

1.

Years to double

= 72

annual interest rate (as a percent)

Compound Interest Formula

A = P ( 1 + r )

n

nt

You invested $1000

2.7%/yr

compounded quarterly

How much interest will you earn after 4 years?

Advantages of having a credit card

Disadvantages

- allows you to borrow money

- can be used anywhere

- on-line purchases

- for convenience and emergencies

- points/rewards

- building a good credit rating

- tendency to overspend

- theft/stolen card

- bad credit

- interest payments

- false idea of having money

What are some of the responsibilities that come with having one or more credit cards?

making timely payments

keep track of your cards/statements

pay full balance or the minimum amount

What are some features of a credit card statement?

balance owing

- payment

+ interest (finance charge)

balance owing

Calculating interest charged on purchases

Ex. You purchased a $100 item on Dec. 27 with an interest rate of 19.5%/yr. The end of statement period is Jan 20.

Step 1

: Calculate how many days from post date to 1 day prior to end of statement period:

Dec 27 - Dec 31: 5 days

Jan 1 - Jan 19: 19 days

>

total: 24 days

Step 2

: Calculate interest

(annual or daily)

for the purchase (use simple interest formula).

I = Prt

grace period

: period of time before the due date

revolving balance

: a balance that goes up or down

Credit

- the ability to borrow money

Loans

in most cases, interest is

calculated daily

and

paid monthly

a secured loan requires

collateral

personal

payday/fast cash advance

student loan

auto loan

RRSP loan

equity

- the difference between the value of a property and the claims against it

Ex. Mr. A. is paying his $21,000 student loan.

interest rate = 3.1%/yr

compounded daily

payable monthly

First Payment: he will pay the interest owing, plus $500 of the principal. How much is his first payment?

What type of loans do you know?

Ex. 1 Doug wants a secured loan and will use his car as collateral. The bank will loan 75% of his car's equity. His car is worth $45,000. He owes $15,000 on it. How much will the bank lend Doug?

Lines of Credit

Sales Promotions

Tess' favourite store is having a sale. Everything is 30% off. She wants to buy a $40 sweater. If she applies for a store credit card, the sweater has an additional 15% off.

a. Calculate the discount for the sweater if she applies for the store credit card.

b. Calculate the cost of the sweater (+ PST & GST).

**Surface Area**

**Volume and Capacity**

**Composite Objects**

**Relating nets to Surface area**

3D objects

area vs. surface area

volume vs. capacity

imperial and SI systems

composite objects

Do you remember the area of the following 2D shapes?

A = 1 x b x h

2

C = 2 r

= d

A = r

2

A = l x w

net

a composite 2D shape that you fold to create a 3D object

the total area of the surface of a 3D object

Surface area: Prism

Prism

2 congruent bases

lateral area

combined area of the side faces

SA = 2 x (base area) + lateral area

Surface area: Cylinder

cylinder

2 circular bases

1 curved surface

SA = 2 r + 2 rh

radius

height

2

base area

lateral area

Surface area: Pyramid

height

slant height

distance from the top of the pyramid to the centre of any side of base

SA = 1(perimeter of base)(slant height) + base area

2

lateral area

Surface area: Cone

Cone:

circular base

curved surface

SA = rs + r

2

base area

curved surface area

Pythagorean Theorem

a + b = c

2

2

2

Surface area: Sphere

SA = 4 r

2

Dimensional Changes

For any right triangle, the square of the hypotenuse is equal to sum of the squares of the sides.

Sphere

- every point on its surface is the same distance from the centre

8

15

8

4

32

10

6

60

How much did the area increase when you double the 2 dimensions?

32 / 8 = 4 -> 4 times

Volume: Prism

Volume: Pyramid

V = base area x h

V = base area x h

3

Volume: Cylinder

V = r h

2

The V of a pyramid is 1/3 the V of a prism (with same base and height)

area of circular base

Volume: Cone

The V of a cone is 1/3 the V of a cylinder (with same base and height)

V = r h

2

3

Area of regular polygon

Rectangular prism

V = lwh

Rectangular pyramid

V = lwh

3

Volume: Sphere

V = 4 r

3

3

Volume: Hemisphere

V = 2 r

3

3

units:

cubic units

units cube (u )

3

A hemisphere is half of a sphere

A composite object is composed of 2 or more distinct objects

Volume of a composite object

1. identify the 3D objects involved

2. add their volumes

Volume: Dimensional Changes

V = r h

2

3

= (4 )(6)

2

3

= 100.53 cm

3

V = r h

= (

8

)(6)

3

2

2

3

= 402. 12 cm

402.12

100.53

= 4

New volume is 4x the old volume.

Capacity

the amount of material a container holds

1. Do example on p.108

2. Convert the answer to inches.

(NOTE: 1 ft = 12 inches

We can use

unit analysis

to convert units.

Calculate the capacity of this cone to the nearest hundredth:

r = 3 in

h = 7 in

**Working with Graphs**

**Bar**

Graphs

Graphs

Bar Graph

a graph used to compare discrete sets of data

shows data with horizontal or vertical bars

the bars do not touch

Parts of a graph

title

vertical axis

horizontal axis

1

2

3

4

5

scale

the number represented by each unit in a graph

**Line Graphs**

**Circle Graphs**

**Histograms**

1. Describe the data

2. Describe the trend

3. Range

**Graphs**

and Technology

and Technology

Graphic Representations

Histogram

summarizes discrete or continuous data

divides up the range of possible values in a data set into groups

Length of each bar equals the range of values in that specific group

the bars have no gaps (for continuous data)

generally used when dealing with large sets of data

A. Describe the data.

B. What is the most common height.

C. What is the range for the height if these trees?

D. Make an inference about the frequency of trees that are "very tall" in this sample?

INTERVALS

CATEGORIES

Frequency table

shows the number of items in each interval

a visual comparison of how two variables are related or vary with each other.

shows data with connected plot points

shows relationships more clearly than tables do

y axis: usually indicated quantity or percentage

x axis: often measures units of time

Interpolation

estimating values within a given set of values

Extrapolation

estimating values beyond a given set of values

Line Graph

40 F = 4.4 C

60 F = 15.5 C

a. What is the trend of the graph?

b. What time of the year was the data taken?

a. Desribe the trend.

a. Did Frank get better or worse at taking tests?

a. What is the car doing at 0 sec?

b. Is the car accelerating?

c. What is the car's speed at 3.5 sec?

Circle graph

show the component parts of a whole

summarizes categorical data

best used when you have less than 6 categories

if greater than 6 categories, use a bar graph

circle is divided into segments which represents a category

How to make a circle graph

1. Calculate the percent shift of each data

2. Represent these values in degrees

Note:

there are 360 degrees in a circle

number

total

x 100

percent

100

x 360

**Managing**

Money

Money

Interest Review

Kyle invested in a term deposit. He deposited $2010 for 5 years with a rate of 2.75% per yr. How much interest will he earn?

Carrie invested $4000 in a savings account with an interest rate of 3.7%, compounded daily. How much will she have afters?

**Financial**

Institutions

Institutions

Bank failure

Why do service charges vary?

some pay a monthly fee that includes a wide range of services

low monthly fee, pays for each ATM or debit charge

avoid the basic monthly fee by keeping a minimum monthly balance

Why do people use financial institutions to hold their funds?

they often pay interest on the money people deposit

accounts are a secure way of holding money

allow us to use cheques and debit cards to pay for goods and services we buy

effective record-keeping system for deposits and withdrawals

happens when a bank can't meet its financial obligations

Canada has a

deposit insurance system

, wher

e

government organizations arrange to pay many types of deposits if an insured institution fails

Banking account checklist

**Debit Cards**

Online Banking

What are the different purposes of a debit card?

What are the advantages of a debit card?

What are the disadvantages of a debit card?

What are the advantages of online banking?

What are the disadvantages of online banking?

What is a debit card?

**Budgets**

What are the purposes of a monthly budget?

it compares income and expenses

helps you decide where to reduce spending

helps in achieving goals

Fixed expenses

expenses that don't generally change from month to month

Examples:

Variable expenses

expenses that can easily change

Examples:

Recurring expenses

expenses that occur very frequently

What kinds of expenses a celebrity might have?

Monthly budget forms

monthly income

total monthly expenses: fixed + variable

To find out if you are in a surplus or in a deficit,

income - expenses = _______

Pay yourself first

some financial professionals say that it is the

golden rule

of personal finance

setting aside 10% of your income before you use the money

This 10% can be put in towards:

an investment

a financial/personal goal

10%

**Relations and Patterns**

**Slope**

**Conversions**

**Linear**

Relations

Relations

**Scale**

What is slope?

Getting started

a measure of steepness of a line

m = rise

run

m = change in y

change in x

grade

: slope expressed as a percent

for every 100m horizontal distance, the elevation increases by 8m

What is the slope of the hill?

What is the steepest grade of this hill?

Ex. 1

Where would you find slopes?

Ex. 2

(1, 5)

(-4, 1)

(4, 1)

Comparing slopes

Horizontal lines

Vertical lines

Problem Solving

ex. The minimum grade for a ramp in a hospital is 10%. What should be the vertical distance if the ramp is 7 m long?

the slope of every horizontal line is 0.

the slope of every vertical line is

undefined

.

The slope of a line is 4/9. The two points are: A(3, 7) and B(8, y). Find the missing coordinate?

Rate of change

Rate

A comparison between two numbers with different units.

It can be written or expressed using the same notation as a ratio.

Examples

Rate:

1) You can type 50 words in one minute:

2) Bananas are 67 cents per pound:

3) In one hour, you are paid $11.75:

4) There are 100 centimetres in one metre:

5) The speed limit is 50 km per hour:

the change in one variable relative to the change in another

It is the slope!!!

Unit Analysis

Ex 2. One of your classmates usually sends 156 text messages in 3 hours. How many messages could she send in one minute?

Angle of elevation

the angle between the horizontal and the line of sight (when looking up at an object)

We use the

tan ratio

to calculate for the

slope

tan x = rise

run

What do you notice?

A birdwatcher sights an eagle 20 m from the tree. The birdwatcher is lying on the ground 50 m from the tree. At what angle must he incline his camera to capture a photo of the eagle?

We use the

inverse tan ratio

to determine the angle of elevation

Try these:

a. tan 45

b. tan 30

c. tan 23.7

d. tan 19.6

e. tan 1

tan

-1

tan x = slope

Conversions within systems

Conversions between systems

Ex 2. A cheetah is capable of speeds up to 114 km/hr. Convert this to m/s.

Imperial system

feet

inches

yard

mile

Ex 1. How many hours would each route take?

1. driving 132 km on a gravel road at 80 km/hr

2. driving 175 km on a paved road at 100 km/hr

Express your answers in hours and minutes.

Example, p.164

A speed of a common snail is 0.003 ft/s. What is the speed in km/hr?

Example 2, p. 169

Time (h)

1

2

3

Sam's snowfall (in)

0.8

1.6

2.4

Winter's snowfall (cm)

17

34

51

Who had the greater rate of snowfall?

**EMA30S**

Relation

describes how two variables are related

Linear relation

has points that lie on a straight line

independent variable

dependent variable

To connect or not to connect?

# of quarters

0

1

2

3

4

value ($)

0

0.25

0.5

0.75

1.0

- an asset (car or property) that the lender may take if the borrower can't repay the loan

a revolving credit source that a bank or business extends to an individual

- interest is payable only on the credit used

A = P + I

amount

principal

interest

Ex. 3 Robyn saved $600 and invested it for 6 months in a GIC. The interest rate is 1.5%/yr. How much money will Robyn have?

May invests in a savings account each month. The interest rate is 1.3%/yr, compounded annually. After 2 years, her investment is worth $97.49. How much did she invest that month?

2

A = P ( 1 + r )

n

nt

loans can be secured or unsecured

a. What is the equity on Doug's car?

b. What is 75% of the equity in David's car?

Ex 2. Amy is lending Anne $600 to buy a sewing machine to start a small business. Amy charges simple interest at 2% /yr. How much will Anne owe if she repays Amy after 1 year?

interest is

compounded daily

and

paid monthly

Ex 1. Trey has an overdraft line of credit. Each transaction costs $5, plus interest at 21% /yr. On Tuesday, he had 3 transactions for $83. She paid back the money in 10 days. How much did he pay?

Ex 2. Mike needs a $4000 line of credit to buy equipment for his carpet-cleaning business. Interest is 5.75%/yr, compounded daily. His transactions are:

a. P = 3200, t = 98 days

b. P = 900, t = 173 days

c. P = 1450, t = 67 days

How much interest did he pay?

some promotions businesses use:

- a gift for applying for and using a credit card

- bonus frequent-flyer points

- low introductory interest rates

- reductions on prices

- cash back on purposes

c. Calculate the amount if she plans to pay with the store credit card in 6 months. (Interest is 21%/yr, compounded daily). The grace period is 30 days.

lets depositors use money in their account, either at a cash machine or when you buy things

Convenient, but you pay for the service either in a single monthly charge or for each transaction

Secret Passwords

**Trigonometry**

**Design Modelling**

Bank account statement

are a simple and effective way to watch for scams and errors

reviewing transactions and the balance each month can help avoid problems

being aware of the current balance will help avoid extra charges and embarrassment for overdrawn accounts or refused cheques and debits

careful record keeping helps people detect identity theft, scams, errors, and overspending

A budget compares expenses with income to show whether income will exceed expenses (a

surplus

) or expenses will exceed income (a

deficit

)

in reality, the less money you have, the more likely it is that a budget can help you!

A budget helps you gain control, not lose it!

Income

the first thing to do is to figure out your monthly income

Ex 1. A radio DJ plays 14 songs per hour. How many songs would she play in a 3.5 shift?

is a way of cancelling units and is based on the assumption that multiplying something by "1" does not change the value

Variation

a relationship between two variables

can be expressed as a formula, a table of values or a graph

Direct Variation

a relationship of the form

y = mx

x and y are variables

m is the slope!

Direct variation may be represented by a straight line graph which passes through the origin (0, 0)

Partial Variation

a relationship of the form

y = mx + b

x and y are variables

m is the slope

b is the y-intercept

Partial variation may be represented by a straight line graph which do not pass through the origin.

Ex 1. One litre of paint covers 80 ft . Express the relationship between the variable for the area to be painted, A, and the variable for the number of litres of paint, p.

a. as a formula

b. a table of values

c. graph

Ex 1. An employee is paid $15 an hour. In addition to his minimum hourly rate, he receives a $50 on-call fee. Express the relationship between his gross pay, P and the number of hours worked, n:

a. as a formula

b. table of values

c. graph

It usually involves a variable cost (i.e. $ per person) and a fixed cost,

Ex 2, You are organizing a banquet, It will cost $250 to rent the hall and will cost $10 for each person's food.

a. What is the type of variation?

b. Write a formula for the total cost C, if n people attend.

c. Complete the table of values.

d. Determine the tota lcost of 100 people attend.

Scatter Plots

can be used to show whether a relationship exists between two variables

Drawing scatter plots

Draw and label the axes. Choose a scale that allows you to plot all the data.

Plot the points in the table of values.

Give the graph a title.

Solving 3D

Triangle Problems

Example 1: From the top of a 90-ft observation tower, a fire ranger observes one fire due west of the tower at an able of depression of 5o , and another fire due south of the tower at an angle of depression of 2o . How far apart are the fires to the nearest tenth of a decimal?

**Isometric Drawings**

**Orthographic Drawings**

**Exploded View Diagrams**

**Scale**

**One-Point**

Perspective

Drawings

Perspective

Drawings

**SOH**

CAH

TOA

CAH

TOA

**Angle of Elevation**

**Solving 2D Triangles**

We can use scale to enlarge or reduce drawings

Scale factor

the constant factor by which all dimensions of an object is multiplied by in a scale drawing

Scale Ratio

a ratio, using the same units, that expresses the scale on a drawing

Ex. 1 Jeb's map of Manitoba shows a scale of 1 cm to 10 km. What is the scale ratio?

Ex. 2. Architects draw scale drawings of homes. A common scale is 1 in to 4 ft. The height, length, and width of a home are 6.5 in, 6.5 in, and 10 in on the drawing. What are the actual measurements in feet?

compounding period

If an investment is

compounded annually

, then

n = 1

To find out the compound interest earned, use:

I = A - P

Ex 2.

a. How much money will you earn if you have the following?

P = 850

r = 2.3% /yr

n = 1

t = 4 years

b. How much interest will you earn?

compounding period

(n = 1)

(n = 2)

(n = 4)

(n =12)

(n = 52)

(n = 365)

n = 365

t = 30 days

Shae, who installs floors, buys underpadding for $396.42 and tiling for $1,219.23. He saves 5% if he uses his store credit card. What will she save if she uses the credit card?

to calculate the SA of a 3D object for today: draw the net, calculate the area of each 2D object, then add

REVIEW

: when solving equations, use

opposite operations

to isolate the missing variable.

Types of bank accounts

Writing cheques

Identity theft