Name: _________________ Date: ___________________

AW 11

UNIT 6: FINANCIAL SERVICES

Student Notes

Thom 2019

Apprenticeship & Workplace 11 6.0 Prior Concepts – Financial Services • in order to convert a percent to a decimal, we must either divide by 100 or move the decimal two places to

the left e.g. Convert the percent to a decimal. a) 37% b) 0.4% c) 179% • when finding what percentage you have of a particular dollar amount, set up a proportion and solve for x e.g. Calculate the percentage. a) 19% of $3120.00 b) 25.5% of $379.60 • when converting between different time units, remember the following conversions:

1. 1 year = 12 months 2. 1 year = 52 weeks 3. 1 year = 365 days e.g. Convert to years. Round to the nearest hundredth of a year.

a) 7 months b) 117 weeks c) 412 days

e.g. Convert from years.

a) 5.2 years to months b) 2.1 years to weeks c) 1.4 years to days

• when solving an algebraic equation, use the following procedure: 1. substitute the given values for variables 2. simplify the expressions when possible 3. use the opposite operation to isolate the variable 3. solve for the indicated variable e.g. Solve for the unknown variable. a) ( )2 3

Where:43

5Solve for .

w x y z

wxy

z

= + −

=

= −

=

b) ( ) 23 5

Where:6

32

Solve for .

w x zy

wyz

x

− = + +

= −

=

= −

Apprenticeship & Workplace 11 6.1 Choosing an Account NEW SKILLS – REVIEWING YOUR BANKING OPTIONS • in this chapter you will look at different banking options and services in Canada • this may be useful for you even if you already have a bank account and are familiar with banking services • there are many different types of accounts offered by banks • each bank has its own particular names for the accounts, but most are some form of chequing account or savings account • different fees and interest are attached to each type of account, and each allows for different types of

transactions • in order to earn interest, some accounts require a minimum balance • banks also offer different services such as self-service via Automatic Teller Machines (ATMs) and

computer (online payments and transfers), and full-service at the bank with the help of a teller • to use an ATM, you need a bank card and a Personal Identification Number (PIN)

• use the following chart to answer the questions in this section.

e.g. In one month, Mary makes 2 deposits and 5 cash withdrawals at Northwest Bank ATMs. She pays 4

bills online. She maintains a balance of over $1000.00. Calculate her fees for each of the accounts. Which account would you advise her to use?

1. Calculate how many self-service transactions Mary makes. 2. Determine the charges for the following types of accounts. a) Value account b) Self-service account c) Full-service account d) Bonus Savings account

e.g. The following is Onani’s accounting of his transactions for the past month. He has a Value account. a) How much will Onani pay in extra transaction fees? b) What will his balance be at the end of the month?

Apprenticeship & Workplace 11 6.2 Simple Interest NEW SKILLS – WORKING WITH SIMPLE INTEREST • financial institutions borrow and lend money • when you invest in a financial institution, you are lending them money for a period of time • in return, the financial institution pays you interest for borrowing you money • the financial institution then lends your money to individuals who need it • these individuals are charged interest for the money they borrow • the interest rate they pay the financial institution is higher than the interest rate you receive from the same

institution • in this way, the financial institution makes a profit on these transactions • the mathematical formula for calculating simple interest is = × ×I P r t where

I = interest P = principal (the amount invested or borrowed) r = annual (yearly) rate of interest (expressed as a decimal) t = length of time in years

• this formula is a calculation for the amount of interest earned (the interest is not added to the principal and reinvested)

• not only can simple interest be calculated with the formula I P r t= × × but the other variables in the formula can also be calculated

• in order to calculate the other variables, you may find the following triangle helpful: • for an investment, you can calculate the total value at the end of the term using this formula:

A = P + I where A is the final value of the investment

e.g. Olive invests $1500 in a financial institution that offers an interest rate of 4% per annum (per year).

Calculate the interest Olive will earn at the end of:

a) 3 years b) 5.2 years b) 7 months c) 100 days

• to find any variable, “cover it up” and read the remaining letters in the fraction

• What are the four forms of the simple interest formula?

I = r = P = t =

e.g. Treya invested a certain sum of money in a financial institution and earned $200 interest after four years. If the annual interest rate was 5%, what amount did Treya invest?

e.g. Brooke has $2400 to invest in a financial institution. Calculate the annual rate of interest if her investment

was worth $2700 at the end of two years. e.g. Wade deposits $5000 in an account earning interest a rate of 4.5% per annum. Calculate the number of

days Wade must keep the money in his account to earn interest of $360.

Apprenticeship & Workplace 11 6.3 Compound Interest NEW SKILLS – WORKING WITH COMPOUND INTEREST • in the last lesson you learned how to calculate simple interest • if you keep the interest earned invested, new interest will be paid on the principal amount plus the first

year’s interest • in other words, you will earn interest on the interest • an investment earns compound interest when the interest from each time period is added to the principal

and earns interest in subsequent time periods • because the principal grows, the interest earned grows as well • the longer your investment is compounding, the greater the amount of interest you earn • if you invest for the long term, it is in the last years of the term that you see the biggest impact of

compounding • the earlier you start saving, the more time there is for an investment to grow • although it earns you more money when you are investing, compounding costs you more when you are

borrowing • the mathematical formula for calculating compound interest is ( )1 nA P r= + where A = final amount (principal + interest) P = principal (amount invested or borrowed) r = annual rate of interest (expressed as a decimal) n = number of compounding periods

• you will need to use your exponent key in order to perform the above calculation • there are different time frames for compounding interest

Name Number of compounds per year Annual Semi-annual Quarterly Monthly Weekly Daily

e.g. Jennie invests $5000 in a financial institution at 6% per annum (simple interest). Calculate her interest at

the end of three years. What is the total amount of her investment after three years.

e.g. Complete the table below for Jennie if her interest is compounded annually.

Year Investment Value (beginning of year) Interest Rate Interest Earned Investment Value

(end of year) 1

2

3

e.g. Calculate the amount of Jennie’s investment using the compound interest formula.

e.g. How much more money did Jennie earn when she had compound interest instead of simple interest. e.g. Viola invests $1000 at 10%, compounded annually. Calculate the amount of her investment after 8 years. e.g. Bob invests $2500 at 7.1%, compounded monthly. Calculate the amount of the investment after 5 years.

• to find any variable, “cover it up” and read the remaining letters in the fraction

• What are the two forms of the Rule of 72? r = t =

Apprenticeship & Workplace 11 6.4 Rule of 72 NEW SKILLS – USING THE RULE OF 72 • the Rule of 72 is used to estimate the number of years and the annual interest rate it takes for an investment

to double • in other words, an investment doubles in value when the interest rate multiplied by the number of years an

investment is held equals 72 i.e. 72r t× = where r = percent rate compounded annually and t = number of years • you may find it helpful to use the following triangle when applying the Rule of 72 • the Rule of 72 does not give an exact value • it approximates an investment’s value after it is held a given number of years • the rule is useful as it is a simple method of finding how much an investment is worth without having to use

formulas or tables e.g. Using the Rule of 72, estimate how many years it will take an investment of $4000 at an interest rate of

6% to double in value? e.g. What interest rate is necessary for an investment of $25 000 to be worth $50 000 in 18 years? e.g. a) Use the Rule of 72 to determine the number of years it would take an investment to approximately

double in value at an interest rate of 9%.

b) Use the compound interest formula to determine the actual value of $5000 at 9% if it is invested for 8 years.

c) What is the difference between the actual value of the investment and the doubled value obtained from the Rule of 72?

e.g. a) Use the Rule of 72 to determine the number of years it would take an investment to approximately double in value at an interest rate of 3%.

b) Use the compound interest formula to determine the actual value of $5000 at 3% if it is invested for 24 years.

c) What is the difference between the actual value of the investment and the doubled value obtained from the Rule of 72?

d) Does the Rule of 72 seem to work better over a short or a long time period?

Apprenticeship & Workplace 11 6.5 Credit Card Buying NEW SKILLS – WORKING WITH CREDIT CARDS • you have calculated how much interest you would earn on different investments • the rates of interest for most secure investments are fairly low • however, if you borrow money or use a credit card and do not pay it off each month, the finance charges, or

rates of interest, are much higher on what you owe • while you may get as little as 1.50% on an investment, you may have to pay 19.50% or more on a loan or

unpaid credit card balance! • credit cards are convenient because they allow you to make purchases without carrying around a lot of cash • many businesses will only accept cash, debit cards or credit cards • personal cheques are less often accepted • you have to remember that credit cards are a form of debt • if you do not use them wisely, you may pay hundreds of dollars yearly in interest charges • the majority of credit cards are issued by banks under the Visa or Mastercard logo • in addition to these credit cards, department stores, oil companies and other businesses also issue credit

cards • to obtain a credit card, you must apply for it once you are 18 years old or older • you will have to fill out a credit application and be approved • the credit card company is agreeing to loan you the money for your purchases with your promise to repay

them under the terms of the agreement • the credit card company will apply a limit to your credit card which is based on your income and credit

rating • each month the credit card company will issue you a statement listing all of your purchases, returns,

payments, interest charges, total balance due, minimum payment required and the payment due date i.e.

• if you pay the balance by the due date, you will not have to pay any interest charges • if you do not pay the entire balance, you will be charged interest daily from the date of the purchase • the interest rate will vary but typically ranges from 15% to 25% • the amount of interest owing can add up very quickly and that bargain you got at the time of purchase is no

longer such a great deal • if you take a cash advance on your credit card, you will be charged interest from the day the cash advance

was taken and the interest rate is usually higher than purchase interest

e.g. 1. What is the daily rate of interest if the annual rate is 19%?

2. What is the annual rate if the daily interest rate is 0.049315%?

3. On January 4, Minnie makes a purchase of $400 on her credit card. The purchase appears on her monthly statement issued January 20. Minnie does not pay for the purchase by the due date indicated on her January statement. Her next monthly statement is issued February 20. Calculate the interest she is charged for the purchase on her February statement. Assume the bank charges her an annual interest rate of 21%. HINT: Use the simple interest formula.

4. William’s monthly statement shows a previous balance of $963.45. It also indicates that during the month, William made a payment of $500 and purchased goods totaling $626.95. Assume his interest charges for the month are $17.50. Calculate his new balance.

5. In the previous example, William’s minimum monthly payment will be 5% of the balance or $10, whichever is greater.

a) Calculate William’s minimum monthly balance.

b) What are the consequences if William decides to pay only the minimum monthly balance?

_________________________________________________________________________________

Apprenticeship & Workplace 11 6.6 Deferred Payments • buying in installments is one form of credit buying that companies offer to promote their product • another form of buying on credit is a deferred payment option (also known as buy-now, pay-later) • this option is primarily offered by companies that sell furniture and appliances • the buy-now, pay-later option is a deferred payment plan in which consumers do not pay for their purchases

for a specified time period • at the time of purchase the customer will be required to pay certain costs, including taxes, administration

fees and delivery charges (if applicable) • there are no interest charges but if the customer does not pay for the purchase by the specified date, interest

will be charged • as a consumer, you have to consider all promotions carefully • with a deferred payment plan, you have to pay an extra administration fee • as well, some companies offer an alternate price if you pay at the time of purchase • this pay-now price is often significantly lower than the pay-later price e.g. A furniture company is offering the following promotion. If you buy a bedroom suite consisting of a bed,

a dresser and two night tables, you do not have to pay for one full year. You will have to pay an administration fee of $45 per item. The suite costs $1500 plus tax.

a) How much would the bedroom suite cost if you bought it today? b) What is the total administration fee? c) What percent is the administration fee to the total pay-now cash price?

e.g. A store announced that if you buy any television set in stock, you will not have to pay for six months. If

you take them up on this deal, the cost to you will be $789 plus taxes. If you decide to pay immediately, you will pay $729 plus taxes.

a) What is the total pay-now price? b) What is the total pay-later price?

c) What is the difference in price? d) What percent is the difference between the prices as compared to the cash price?

e.g. Rene purchases a sofa. He can either pay for the sofa at the time of purchase or purchase it on a buy-now , pay-later plan. The cash price for the sofa is $924.95 plus taxes and the delivery charge is $25.00. The buy-now, pay-later cost of the sofa is $999.95 plus taxes and Rene must pay the taxes, a $25.00 delivery charge and a $49.95 administration fee at the time of sale. He has one year to pay for his purchase without any interest charges.

a) Calculate the pay-now price. b) Calculate how much Rene has to pay at the time of the purchase if he chooses the buy-now, pay-later

option. c) If Rene chooses to purchase the sofa using the buy-now, pay-later option and pays for it within one

year, calculate his total pay-later price. d) Calculate the difference between the total pay-now price and the total pay-later price. e) Express the difference in the two prices compared to the total pay-now price as a percentage.

Apprenticeship & Workplace 11 6.7 Installment Buying • credit is a promise to pay money in the future in exchange for the right to receive goods and services now • credit generally allows consumers to buy more goods and services than they normally could • however, if used poorly, too much credit can cause financial ruin • companies provide credit in a variety of ways to encourage you to buy their products • one way they offer credit is by installment buying • when you pay for a product in installments, you pay a down payment at the time of the purchase • you pay the rest of the purchase price in equal amounts (called installment payments) over a given number

of equal time periods • the installment price is the sum of the down payment plus all the installment payments • the installment price is usually higher than the cash selling price • the difference between the installment price and the cash selling price is the finance or carrying charge • companies offer installment buying because it benefits business • a company is more likely to sell a product if a consumer does not have to pay its full price at the time of the

purchase (especially with larger purchases like furniture and appliances) • installment buying is not a free service, it is a form of credit buying • companies often charge a substantial amount for the privilege of purchasing on credit • as a wise consumer, you have to know how much the cost of installment buying will be before deciding to

buy by installment e.g. Mark decides to purchase a stereo. The stereo has a cash price of $389.83 plus tax. The store offers an

installment plan in which you pay $50 down and $75 a month for six months.

a) Calculate the cash-selling price of the stereo. b) Calculate the installment price of the stereo. c) Calculate the finance charge. d) What factors does Mark have to consider before deciding to purchase the stereo in installments? i) _______________________________________________________________________________ ii) ______________________________________________________________________________

e.g. Karla decides to purchase a sofa and chair. The combination that she wants to buy has a cash selling price of $1288.21 plus tax. The installment terms are $200 down plus $175 a month for eight months.

a) Calculate the total cash-selling price of the sofa and chair. b) Calculate the installment price of the sofa and chair. c) Calculate the finance charge. d) Express the finance charge as a percentage of the cash-selling price including taxes. e) Why might Karla decide to purchase the sofa and chair in installments? ________________________________________________________________________________ ________________________________________________________________________________

Apprenticeship & Workplace 11 6.8 Personal Loans Lesson Focus: To solve problems involving personal loans. A. Overview

• in addition to credit cards, another way to finance a trip or to purchase an item if you do not have enough cash is with a personal loan

• a personal loan allows you to borrow a specified sum of money from a financial institution and to repay it over a certain period of time, usually one to five years (this is called the term of the loan)

• to qualify for a loan, you must be at least 18 years old • to obtain a loan, you must fill out an application form from a financial institution • you will be asked for personal information about your financial background, assets, credit/debit

obligations, work history, marital status and the purpose of the loan • the financial institution will look at your debt ratio, net worth, job stability and credit history in order to

make a decision • the cost of borrowing depends on factors such as the interest rate and the term of the loan (also called

the amortization period) • generally, the greater the amount of money you borrow, the lower the interest rate • a financial institution usually requires that the product purchased by the loan be used as security or

collateral on the loan • in addition to repaying the principal portion of the loan, you will have to pay interest as well in order to

cover the cost of borrowing the money • most personal loans have fixed conditions and interest rates for the term of the loan • variable-rate personal loans are also available (these loans fluctuate in response to changes in the

interest rate set by the Bank of Canada) • even though many variable-rate loans are offered at a lower rate than a fixed-rate loan, many consumers

like the stability of knowing exactly what their payments will be over the duration of the loan • the table to the right is a Personal Loan

Payment Calculator • to use it, look up the interest rate of a loan

in the left-hand column, then find the term in years on the same line

• the amount under the term is the payment for each $1000 you borrow

B. Examples

1. Jesse requires a personal loan of $10 000 for home renovations. His financial institution offers him a three-year loan at a fixed rate of 10.25%. Use the amortization table to answer the following questions.

a) How much must Jesse pay the financial institution each month? b) How much will Jesse pay for the loan? c) How much interest will Jesse have paid at the end of three years?

2. Jesse decides to amortize his $10 000 loan over five years instead of three years. His financial institution will continue to offer him a fixed interest rate of 10.25%.

a) How much would Jesse now pay his financial institution each month? b) How much does Jesse pay in interest at the end of the five years? c) Does Jesse pay more interest if he chooses to amortize his loan over five years as compared to three

years? How much more does he pay?

3. Amy would like to buy a computer. She has found one she likes for $2400 plus taxes. She does not have enough money right now so she decides to take out a personal fixed-rate loan at an interest rate of 11.75% over two years.

a) How much will she need to borrow? b) How much will Amy pay her financial institution each month? c) What is the total amount paid at the end of two years?

d) How much interest will Amy pay?