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.