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. 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 TEXTBOOK Pages

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  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 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.  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) 100 I = PRT

If you invested $ in an account that paid simple interest, find how long you’d need to leave it in at 4% interest to make $ = (200)(0.04)T 1.25 yrs = T Typically 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) time (in years) number of times per year that interest in compounded

(2) 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 $ Use the simple interest formula and solve for r to get the effective rate of interest. I = Prt 85.83=(500)r(2) r = = 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:  An exponent means that you multiply the base by itself that many times.  For example: x 4 = x ● x ● x ● x ● x ● x ● x ● x ● x ● x ● x 2 6 = 2 ● 2 ● 2 = 64 = 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.

Exponent Rule #1  When multiplying two expressions with the same base you add their exponents.  For example  When multiplying two expressions with the same base you add their exponents.  For example

Exponent Rule #1  Try it on your own:

Exponent Rule #2  When dividing two expressions with the same base you subtract their exponents.  For example  When dividing two expressions with the same base you subtract their exponents.  For example

Exponent Rule #2  Try it on your own:

Exponent Rule #3  When raising a power to a power you multiply the exponents  For example  When raising a power to a power you multiply the exponents  For example

Exponent Rule #3  Try it on your own

Note  When using this rule the exponent can not be brought in the parenthesis if there is addition or subtraction You 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  When a product is raised to a power, each piece is raised to the power  For example

Exponent Rule #4  Try it on your own

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 You 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  When a quotient is raised to a power, both the numerator and denominator are raised to the power  For example

Exponent Rule #5  Try it on your own

CLASS/HOME WORK: REVIEW OF EXPONENT RULES Complete Q# 1, 2, 3,4 on p and Q#1-3 on p REVIEW OF EXPONENT RULES Complete Q# 1, 2, 3,4 on p and Q#1-3 on p. 360.

Zero Exponent  When anything, except 0, is raised to the zero power it is 1.  For example  When anything, except 0, is raised to the zero power it is 1.  For example ( if a ≠ 0) ( if x ≠ 0)

Zero Exponent  Try it on your own ( if a ≠ 0) ( if h ≠ 0)

Negative Exponents  If b ≠ 0, then  For example  If b ≠ 0, then  For example

Negative Exponents  If b ≠ 0, then  Try it on your own:  If b ≠ 0, then  Try it on your own:

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

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

CLASS/HOME WORK: Zero and Negative Exponents: COMPLETE Q #1-4 ON PAGE 364 OF YOUR TEXTBOOK! Zero and Negative Exponents: COMPLETE Q #1-4 ON PAGE 364 OF YOUR TEXTBOOK!

 The intensity of an earthquake can range from 1 to The Richter scale is a base-10 exponential scale used to classify the magnitude of an earthquake. An earthquake with an intensity of or 10 5, 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?  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.  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.