personal finance mbf3c lesson #1: introduction to personal finance mbf3c lesson #1: introduction to...

PERSONAL FINANCE

MBF3C

Lesson #1: Introduction to Personal Finance

Unit Learning Goals

1. To state the difference between simple and compound interest

2. To identify simple interest as linear relation and compound interest as an exponential relation

3. To solve word problems involving simple and compound interest

4. To identify various services available at banks

5. To solve problems involving the cost of making purchases on credit.

6. To identify the costs of owning and operating a vehicle

7. To solve problems involving the costs associated with operating a vehicle.

YOUR TEXTBOOKPages 422-495

INTRODUCTION

Banks pay you interest for the use of your money. When you deposit money in a bank account, the bank reinvests your money to make a profit.

DEPOSIT

…a sum of money placed or kept in a bank account.

BORROW

…To obtain or receive (something) on loan with the promise or understanding of returning it or its equivalent.

BORROW is like TAKE: You borrow something from somebody. You borrow things from the owner.

BORROWER

The person or business that is GETTING the item (money)

LEND

LEND is like GIVE: The owner lends you things. The owner lends things to you.

LENDER

The person or business that is giving the item (money)

LOAN

…a thing that is borrowed. In finance, it’s a sum of money that is expected to be paid back with interest.

DEPOSIT

…a sum of money placed or kept in a bank account, usually to gain interest.

INTEREST

…a fee paid by a borrower of assets to the owner as a form of compensation for the use of the assets.

SECURITY

A security, in a financial context, is a certificate or other financial instrument that has monetary value and can be traded.

SIMPLE

AND

COMPOUND INTEREST

Since this section involves what can happen to your money, it should be of INTEREST to you!

SIMPLE INTEREST

Simple interest is calculated on the initial value invested (principal ), P, at an annual interest rate, r, expressed as a decimal for a period of time, t. The interest is added to the principal at the end of the period.

Interest, I = Prt

Parts

simple interest • the money paid on a loan or investment a percent of the principal

Principal • the value of the initial investment or loan amount • the final or future value of an investment,

including the principal and the accumulated Interest compound interest • the interest paid on the principal

and its accumulated interest

SIMPLE INTEREST

Simple interest is calculated on the initial value invested ( principal ), P, at an annual interest rate, r, expressed as a decimal for a period of time, t. The interest is added to the principal at the end of the period.

Interest, I = Prt Amount , A = P + Prt Or in factored form, A = P(1 + rt)

Compound interest is calculated on the accumulated value of the investment, which includes the principal and the accumulated interest of prior periods.

Annual interest rate

IMPLE INTEREST FORMULA

Interest paid

Principal(Amount of money invested or borrowed)

Time (in years)

100I = PRT

If you invested $200.00 in an account that paid simple interest, find how long you’d need to leave it in at 4% interest to make $10.00.

10 = (200)(0.04)T

1.25 yrs = TTypically interest is NOT simple interest but is paid semi-annually (twice a year), quarterly (4 times per year), monthly (12 times per year), or even daily (365 times per year).

enter in formula as a decimal I = PRT

100

COMPOUND INTEREST FORMULA

amount at the end

Principal(amount at start)

annual interest rate

(as a decimal)nt

n

rPA

1

time(in

years)

number of times per year that interest in

compounded

nt

n

rPA

1500

.08

4

4 (2)

83.585$A

Effective rate of interest is the equivalent annual simple rate of interest that would yield the same amount as that made compounding. This is found by finding the interest made when compounded and subbing that in the simple interest formula and solving for rate.

Find the effective rate of interest for the problem above.

The interest made was $85.83. Use the simple interest formula and solve for r to get the effective rate of interest.

I = Prt 85.83=(500)r(2)

r = .08583 = 8.583%

Find the amount that results from $500 invested at 8% compounded quarterly after a period of 2 years.

INVESTIGATION (Page 422)

Compare the growth of a $1000 investment at 7% per year, simple interest, with another $1000 investment at 7% per year, compounded annually.

What is an Exponent?

An exponent means that you multiply the base by itself that many times.

For example:

x4 = x ● x ● x ● x26 = 2 ● 2 ● 2 ● 2 ● 2 ● 2 = 64

• most often when talking about very big or very small things in real life.• Examples: Large distances, counting large numbers that grow quickly (e.g. #

of bacteria in a sneeze), building houses, computers, engineering, pH scale, impact of earthquakes among others.

The Invisible Exponent

When an expression does not have a visible exponent its exponent is understood to be 1.

1xx

Exponent Rule #1

When multiplying two expressions with the same base you add their exponents.

For example

mn bb mnb

42 xx 42x 6x 222 21 22 212 32 8

Exponent Rule #1

Try it on your own:

mn bb mnb

73.1 hh33.2 2

1073 hh

312 33

27333

Exponent Rule #2

When dividing two expressions with the same base you subtract their exponents.

For example

m

n

b

b mnb

2

4

x

x 24x 2x

Exponent Rule #2

Try it on your own:

m

n

b

b mnb

2

6

.3h

h

3

3.4

3

26h 4h

133 23 9

Exponent Rule #3

When raising a power to a power you multiply the exponents

For example

mnb )( mnb 42 )(x 42x 8x

22 )2( 222 42 16

Exponent Rule #3

Try it on your own

mnb )( mnb 23)(.5 h 23h 6h22 )3(.6 223 43 81

Note

When using this rule the exponent can not be brought in the parenthesis if there is addition or subtraction

222 )2( x 44 2xYou would have to use FOIL in these cases

Exponent Rule #4

When a product is raised to a power, each piece is raised to the power

For example

mab)( mmba2)(xy 22 yx

2)52( 22 52 254 100

Exponent Rule #4

Try it on your own

mab)( mmba3)(.7 hk 33kh

2)32(.8 22 32 94 36

Note

This rule is for products only. When using this rule the exponent can not be brought in the parenthesis if there is addition or subtraction

2)2( x 22 2xYou would have to use FOIL in these cases

Exponent Rule #5

When a quotient is raised to a power, both the numerator and denominator are raised to the power

For example

m

b

am

m

b

a

3

y

x3

3

y

x

Exponent Rule #5

Try it on your own

m

b

am

m

b

a

2

.9k

h2

2

k

h

2

2

4.10 2

2

2

4

4

16 4

CLASS/HOMEWORK

:

REVIEW OF EXPONENT RULES

Complete Q# 1, 2, 3,4 on p. 356-357 and Q#1-3 on p. 360.

Zero Exponent

When anything, except 0, is raised to the zero power it is 1.

For example

0a 1 ( if a ≠ 0)

0x 1 ( if x ≠ 0)

025 1

Zero Exponent

Try it on your own

0a 1 ( if a ≠ 0)

0.11 h 1 ( if h ≠ 0)

01000.12 100.13 0

Negative Exponents

If b ≠ 0, then

For example

nb nb

1

2x 2

1

x

23 23

1

9

1

Negative Exponents

If b ≠ 0, then

Try it on your own:

nb nb

1

3.14 h 3

1

h

32.15 32

1

8

1

Negative Exponents

The negative exponent basically flips the part with the negative exponent to the other half of the fraction.

2

1

b

1

2b 2b

2

2

x

1

2 2x 22x

Math Manners

For a problem to be completely simplified there should not be any negative exponents

CLASS/HOMEWORK

:

Zero and Negative Exponents:

COMPLETE Q #1-4 ON PAGE 364 OF YOUR TEXTBOOK!

The intensity of an earthquake can range from 1 to 10 000 000. The Richter scale is a base-10 exponential scale used to classify the magnitude of an earthquake. An earthquake with an intensity of 100 000 or 105 , has a magnitude of 5 as measured on the Richter scale. The chart shows how magnitudes are related:

An earthquake measuring 2 on the Richter scale can barely be felt, but • one measuring 6 often causes damage. An earthquake with magnitude 7 is considered a major earthquake.

a. How much more intense is an earthquake with magnitude 6 than one with magnitude 2?

b. How much more intense is an earthquake with magnitude 7 than one with magnitude 6?

SUMMARY of exponent rules

SUCCESS CRITERIA FOR TODAY’S LESSON

Rule #1: When multiplying two expressions with the same base, I know that you must add their exponents.

Rule #2: When dividing two expressions with the same base, I know that you must subtract their exponents

Rule #3: When raising a power to a power, I understand that you must multiply the exponents

Rule #4: When a product is raised to a power, I understand that each piece must be raised to the power.

Rule #5: When a quotient is raised to a power, I understand that both the numerator and denominator are raised to the power

I can use the exponent rules to simplify and evaluate a variety of expressions involving exponents; including expressions that include negative exponents and zero has an exponent.

I can evaluate a variety of exponential expressions that have an integer or a rational number as a base.