PERSONAL FINANCE MBF3C Lesson #1: Introduction to Personal Finance
Unit Learning Goals • To state the difference between simple and compound interest • To identify simple interest as linear relation and compound interest as an exponential relation • To solve word problems involving simple and compound interest • To identify various services available at banks • To solve problems involving the cost of making purchases on credit. • To identify the costs of owning and operating a vehicle • To solve problems involving the costs associated with operating a vehicle.
YOUR TEXTBOOK Pages 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 + PrtOr 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.
100 IMPLE INTEREST FORMULA Annual interest rate Interest paid I = PRT Time (in years) Principal(Amount of money invested or borrowed)
100 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. enter in formula as a decimal I = PRT 10 = (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).
COMPOUND INTEREST FORMULA annual interest rate(as a decimal) Principal(amount at start) time(in years) amount at the end number of times per year that interest in compounded
4 (2) .08 500 4 Find the amount that results from $500 invested at 8% compounded quarterly after a period of 2 years. 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%
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 ● x 26 = 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.
Exponent Rule #1 • 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
Exponent Rule #2 • Try it on your own:
Exponent Rule #3 • 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
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
Exponent Rule #5 • Try it on your own
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 ( if a ≠ 0) ( if x ≠ 0)
Zero Exponent ( if a ≠ 0) • Try it on your own ( if h ≠ 0)
Negative Exponents • If b ≠ 0, then • For example
Negative Exponents • 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/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: