AWM 11 - Chapter 6 Booklet

 A&W Math 11 6.1 – Choosing an Account Part I Notes In this chapter we 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. INTEREST – money earned on money you have in the bank OR Usually written as a PERCENT – a fee paid for borrowing money SELF‐SERVICE BANKING – Banking done on the internet, telephone, or at a bank machine (anything that doesn’t require the service of a teller) FULL‐SERVICE BANKING – Banking that requires the use of a bank teller (person) TRANSACTION – ANY activity such as withdrawal, deposit, transfer, payment **For All Examples, Use Account Information On Page 280 ** Example 1: Laura is studying fashion design at Kwantlen University in Vancouver, BC. Laura wants to open a new bank account. She estimates that she will need to use an ATM to withdraw cash twice, pay 4 bills online, and use her bank card for about 10 transactions each month. The Northwest Bank of Canada offers four types of accounts. Which account would be the least expensive choice for Laura? (Because Laura is a student she will likely have less than $1000 her account each month) Example 2: 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? Example 3: Jim withdraws $20.00 every week from an ATM that charges a $1.50 service fee in addition to the $1.50 his bank charges him. a) How much money would he spend on ATM fees every year? b) Suggest two things Jim could do to reduce his ATM fees. Example 4: Kyra has a Self‐service Account at the Northwest Bank of Canada with an opening balance of $2150.23 for October. She made the following transactions in the month:  full‐service payment of $250.42 for her utility bill 
payment by cheque of $650.00 for her rent 
purchase of $100.00 worth of traveller’s cheques 
cash withdrawals of $60.00 and $20.00 at her local Northwest Bank of Canada ATM 
cash withdrawal of $100.00 at an ATM which was not a Northwest Bank of Canada ATM; there was an additional $1.50 charge on top of the Northwest Bank of Canada service charge 
payments of $102.24 and $43.20 for groceries, $50.00 for gas, and $7.35 for lunch using her bank card 
payment for a new cycling jacket purchased online for $99.95 
online payment of her phone bill of $36.35 a) What are the service charges for Kyra’s transactions? b) What will Kyra’s balance be at the end of the month? c) If Kyra makes a single deposit of $800.00 this month, will she have to pay a monthly fee? Assignment: Pg. 282 #1‐3 A&W Math 11 6.1 – Choosing an Account Part II Notes Remember these terms from last class: SELF‐SERVICE BANKING – Banking done on the internet, telephone, or at a bank machine (anything that doesn’t require the service of a teller) FULL‐SERVICE BANKING – Banking that requires the use of a bank teller (person) TRANSACTION – ANY activity such as withdrawal, deposit, transfer, payment **For All Examples, Use Account Information On Page 280 ** Example 1: Jannik does most of his banking online or at an ATM. Every month he has a minimum balance of $1200.00 and does about 15 transactions. Suggest the account most suitable for his needs and explain your choice.
Example 2: Delphine has a Value Account at the Northwest Bank of Canada with an opening balance of $768.23 on April 1st. She made the following transactions in the first two weeks of the month:  Teller‐assisted payment of $105.42 for her utility bill.  Cash withdrawals of $60.00, $40.00, $60.00, $20.00, and $100.00 at Northwest Bank of Canada ATMs.  Bank card payments (debit) of $167.24 for groceries, $45.00 for gas, $3.55 for a cup of coffee, $125.45 for a new pair of running shoes, and $145.67 for groceries.  Deposit of $650.45 at a Northwest Bank of Canada AMT  Cash withdrawal of $60.00 at another institution’s ATM. There was a $1.50 charge in addition to the Northwest Bank of Canada service charge. Delphine tracks all her transactions in a record book. Below is a summary of her transactions. a) List the types and amounts of service charges for each transaction in the two‐week period b) Why do you think Delphine recorded the last ATM withdrawal for $60.00 with a star? c) What is her balance at the end of two weeks if she includes the service charges in her calculations? Example 3: 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? Assignment: Pg. 285 #4‐6 A&W Math 11 6.1 – Choosing an Account Part III Notes Remember these terms from last class: SELF‐SERVICE BANKING – Banking done on the internet, telephone, or at a bank machine (anything that doesn’t require the service of a teller) FULL‐SERVICE BANKING – Banking that requires the use of a bank teller (person) TRANSACTION – ANY activity such as withdrawal, deposit, transfer, payment **For All Examples, Use Account Information On Page 280 ** Example 1: Timothy is travelling in the United States and he uses his bank card to obtain $60.00 USD cash. In addition to the $60.00 USD, he is charged a $1.00 USD service charge from the US bank he is using and a $1.50 CAD charge from his own bank. The day he withdraws his money, $1.00 USD is worth $1.05 CAD. How many Canadian dollars will be deducted from his account? Example 2: Maia makes the following transactions during the month of March. Her account has an opening balance of $618.24; • 3 ATM withdrawals of $40.00 each; • full‐service payment of hydro bill of $24.12; • bank card payments of $97.45 for groceries, $13.99 for a movie, $15.89 and $32.63 for meals; • direct deposit of paycheque $592.98; and • online payment of her credit card bill of $214.74. a) Determine the balance in her Bonus Savings Account at the end of the month. b) Is this the best type of account for Maia? If not, which one should be apply for? Assignment: Pg. 287 #1‐5 A&W Math 11 6.2 – Part I – Simple Interest Notes When you deposit money into a savings or investment account, you earn interest from your financial institution because you are lending them your money. When you borrow money, you must pay interest to the financial institution. The interest you pay is compensation to the lender for the use of their money. INTEREST – money earned on money you have in the bank OR Usually written as a PERCENT – a fee paid for borrowing money PRINCIPAL – The original amount invested or borrowed. SIMPLE INTEREST – Interest calculated as a percentage of the principal (original amount) TERM – The time, in years, for an investment or loan. Example 1: Gerard has a savings account at Me‐Dian Credit Union in Winnipeg, MB, a financial institution for Manitoba’s Aboriginal community. Gerard deposits $2000.00 into a savings account that pays 3.00% simple interest per annum. a) Calculate the interest that Gerard will earn on his savings after 2 years. b) How much money will Gerard have in his account after 2 years if he makes no withdrawals? Example 2: Gordon wants to invest $2250.00. His bank offers an investment option that earns simple interest at a rate of 1.75% per year. a) If he invests the money for 1 year, how much interest will Gordon earn? b) If he invests the money for 5 years, how much interest will Gordon earn? c) Based on your answers above, write an equation that can be used to calculate simple interest. Example 3: Solve the following problems using the simple interest formula. a) If the interest earned on a deposit is $50.00 and the interest rate is 3.00% per annum invested for 2 years, what is the principal? b) How many months does it take to earn $180.00 interest on an investment if the principal is $5000.00 and the interest rate is 2.00% per annum? c) Calculate the annual interest rate on an investment if the principal is $4000.00 and the interest is $120.00 earned over three years. Answer Assignment: Pg. 292 #1‐3 Pg. 301 #1 A&W Math 11 6.2 –Part II – Compound Interest Notes INTEREST – money earned on money you have in the bank OR – a fee paid for borrowing money Usually written as a PERCENT PRINCIPAL – The original amount invested or borrowed. TERM – The time, in years, for an investment or loan. COMPOUND INTEREST – Interest is paid not only on the principal, but also on the interest. COMPOUNDING PERIOD – The time between calculations of interest, it is also called the interest period. Example 1: Allison wants to invest $2000.00. Her bank offers an investment option that earns compound interest at a rate of 1.75% per year, compounded annually. a) If she invests the money for 1 year, how much interest will Allison earn? b) If she invests the money for 2 years, how much money will Allison have at the end of the investment term? c) Would you use the method from part b) for calculating the total value if Allison decides to invest her money for 10 years? Why or why not? Example 2: A deposit of $1200.00 is invested at 2.60% per annum, compounded semi‐annually, for 2 years. a) Explain why there are four interest periods. b) Use the Compound Interest Formula to find the value of the investment at the end of 2 years. c) Calculate the interest earned over the 2 years. Example 3: Calculate the final value of an initial investment of $6000.00. Interest is paid at 4.00% per annum, compounded semi‐annually, for 3 years. Example 4: Calculate the value of an investment of $5000.00 that earns interest at a rate of 2.95% per annum, compounded semi‐annually, for 3 years. RULE OF 72: There is a quick way to estimate the time it takes for an investment compounded annually to double in value. This method is called the RULE OF 72. To calculate the approximate length of time in years it takes for an investment to double, divide 72 by the annual interest rate expressed as a percentage. 72 ÷ (interest rate as a percent) = Years to Double Investment Example 5: Approximately how long will it take an investment of $5000.00, invested at a rate of 3.75% per annum, compounded annually, to double in value? Example 6: Use the Rule of 72 to estimate what interest rate would be needed to double your investment in 18 years. Assignment: Pg. 296 #4‐6 Pg. 298 #7‐8 Pg. 301 #10‐11 A&W Math 11 6.2 – Simple & Compound Interest Part III Notes SIMPLE INTEREST – Interest calculated as a percentage of the principal (original amount) I = Prt
I = Amount of Interest
P = Principal
r = Interest Rate (decimal)
t = time in years
COMPOUND INTEREST – Interest is paid not only on the principal, but also on the interest. 1
A = Final Amount
P = Principal
r = Interest Rate (decimal)
n = Number of compounding terms in a year
t = time in years
RULE OF 72 – Years to Double Investment = 72 ÷ (interest rate as a percent) Example 1: Mei Lin borrowed $1500.00 for vehicle repairs from her parents. She agreed to pay back the loan plus 6.50% simple interest on the $1500.00 added on in equal monthly payments over the next 6 months. a) How much interest will Mei Lin have to pay? b) What will be the total amount she will have to pay? c) What will be her monthly payment for the loan? Example 2: Calculate the final investment value and the interest for each of the following investments. a) $2000.00 at 3.80% per annum, compounded semi‐annually for four years. b) $1500.00 at 2.60% per annum, compounded quarterly for three years. c) $6000.00 at 2.20% per annum, compounded monthly for two years. d) $3560.00 at 1.20% per annum, compounded monthly for three months. Example 3: Which is the better investment? Investing $2500.00 at 2.00% a year, compounded annually, for two years or $2500.00 at 2.00% a year, compounded semi‐annually, for two years? Explain your reasoning. Assignment: Pg. 301 #2, 4‐8 6.3 – Part I – Credit Card Interest Notes “Buy Now, Pay Later!” “Sign up for our credit card and receive a free gift!” Promotions like these are used to attract customers and sell items that customers might not otherwise be able to afford, and to have people sign up for particular credit cards. When you make use of these promotions, you are relying on credit. CREDIT – a type of loan where you receive something of value and agree to pay later. Credit cards are issued by banks and other financial institutions, as well as by many department stores and gas companies. A credit card can be convenient, but if you do not pay the credit card balance by the due date, the credit card issuer charges interest on the remaining money you owe and on the cost of new purchases made before the next credit card statement date. Credit card companies have different ways of calculating interest, so be sure you understand the terms of any card you may get. FINANCE CHARGE – the total amount of interest paid to borrow a sum of money. A&W Math 11 Example 1: Sheng Li has a $438.76 unpaid balance on his credit card that charges an interest rate of 19.50% per annum (simple interest). The payment was due on March 23. a) His minimum payment is $50.00 or 10% of the outstanding balance, whichever is more. What is the minimum he must pay? b) If he does not pay on the due date, how much will he owe on April 15? Example 2: Calculate the interest due on the following credit card balances and then the minimum payments (5.00% or $10.00, whichever is greater). a) Unpaid balance: $345.67 Interest rate per annum: 20.00% Time: 30 days b) Unpaid balance: $55.75 Interest rate per annum: 18.00% Time: 31 days Example 3: Claudine took the Leader in Training program from Powell River, BC’s Centre de leadership et d’adventure en nature. The centre teaches outdoor leadership skills to French‐
speaking young adults. Claudine put the costs associated with the course on her credit card. She was charged $16.22 interest on a credit card balance of $1032.05 that she took 31 days to pay. What is the interest rate on her credit card per annum? Example 4: Katie used her credit card to make the following purchases during the month. She does not have to pay interest on purchases during the month, only on outstanding balances. Her credit card company charges 18.50% per annum. Date Item
March 3 March 8 March 16 March 16 Gas Groceries Dinner Movies Amount
$37.45
$117.97
$79.50
$28.98
a) What is her balance due on the statement date, March 25? b) If the minimum payment is 5% or $10.00, whichever is greater, what is Katie’s minimum payment? c) If she pays only the minimum and doesn’t use the card between then and the next statement date, how much will she owe on her April 25 statement? Assignment: Pg. 306 #1‐3 A&W Math 11 6.3 – Part II – Cash Advance & Store Promotions Notes CASH ADVANCE – a withdrawal of cash charged to a Credit Card. Interest is usually charged from the day of withdrawal (not after payment date) Example 1: On January 12, John charges a cash advance of $500.00 to his credit card. This withdrawal appears on his monthly statement issued January 27. John does not pay off this amount by the due date shown on his statement. The next monthly statement is issued on February 27. John’s bank charges 18.00% annual interest for cash advances starting on the day of the withdrawal. a) Calculate the interest that John is charged for the January 12 cash advance. b) If he pays his bill in full on March 13, what is the actual cost of the cash withdrawal? Example 2: On August 10, Sharon takes a cash advance of $300.00 on her credit card. The withdrawal appears on her monthly statement issued August 28. Sharon does not pay off this amount by the due date shown on her statement. The next monthly statement is issued on September 28. a) For how many days is interest calculated? b) If Sharon’s bank charges 25.50% annual interest for cash withdrawals, starting on the day of the withdrawal, what will she be charged for the August 10 withdrawal? c) What is the actual cost of the cash withdrawal, including interest, if she pays for the purchase by her September statement’s due date? Stores often offer promotions offering credit and allowing you to defer (hold‐off) payment for months or years. These offers enable you to buy an item without paying the full amount immediately. In exchange, the stores often charge high interest rates on the purchase amounts when the payments are made. Be sure you understand the conditions of a store promotion or credit card before you sign an agreement. Researching your credit options will help you to use credit effectively. Example 3: Michael wants to buy a sofa. If he pays cash for the sofa, it will cost $899.99 with no delivery charge, or he can choose one of the following two payment options. Option 1: The store offers a deferred payment plan of $899.99, with a delivery charge of $30.00 and an administration fee of $75.00, both to be paid at the time of sale. He would have 2 years to pay with no interest charged. Option 2: He can pay for the sofa using his credit card, at the price of $899.99. He would not have to pay the delivery charge or the administration fee. He would be charged interest at a rate of 21.0% per annum, and he expects that it will take 31 days to pay his credit card balance. (Michael has a previous balance on his credit card.) a) Calculate the amount Michael must pay at the time of purchase if he chooses Option 1 (the deferred payment plan). b) Calculate the total cost of the sofa if he buys it on the deferred payment plan c) How much could Michael save if he could pay cash for the sofa, rather than using the deferred payment plan? d) Calculate the total cost of the sofa is he buys it on his credit card. e) How much could he save if he could pay cash for the sofa, rather than using the using his credit card? f) If Michael does not have the cash to buy the sofa, which option should he choose? Example 4: Brian wants to purchase a new refrigerator. A store offers a deferred payment plan of $1099.99 with a delivery charge of $40.00 and an administration charge of $60.00, both to be paid at the time of sale. He has two years to pay for his purchase without any interest accruing. If the cash price of the fridge is $729.99 plus the delivery charge, how much extra is he actually paying with the deferred payment plan? DOWNPAYMENT – a partial payment sometimes required at the time of purchase Example 5: A store offers a television for $872.95. You want to purchase it, but cannot pay cash. Your payment options are: Option 1: 15% down payment then 6 monthly payments of $140.00. Option 2: No down payment and 24 monthly payments of $46.00. Option 3: Pay using a cash advance on your credit card. You would be charged interest at an annual rate of 22.7%, and you expect that it will take you 45 days to pay the credit card balance. Which payment plan offers the better deal? Assignment: Pg. 309 #4‐5 Pg. 312 #6‐8 A&W Math 11 6.3 – Part III – Credit Cards & Store Promotions Notes Example 1: Jane is charged 19.50% per annum on her credit card balances. She uses her credit card, which has no previous balance, to purchase a new wood stove that costs $2100.36. Her next credit card statement is dated September 30 and she pays only the minimum payment (5% of her balance). On October 5, Jane makes another purchase of $450.00 with her credit card. How much money will Jane owe on October 7? She makes no other purchases with her credit card. Example 2: Sanaa had an unpaid balance on her credit card that has an interest rate of 21.50% per annum. It took her 19 days to pay, and she was charged $7.75 interest. What was the unpaid balance on her card? Example 3: There are two payment plans for an item costing $573.45? Option 1: 6 monthly payments of $100 Option 2: 18 monthly payments of $35 a) Considering interest rate only, which is the better option? b) Give one reason someone might have for selecting either option. Example 4: Arlene is buying a new hybrid bicycle for commuting to work. She has three payment options. Option 1: Pay cash. The bicycle costs $895.99 plus 12% tax. Option 2: Use the store’s payment plan of 10% down and 6 monthly payments of $155.00 (including tax). Option 3: Pay using a cash advance on her credit card. She would be charged interest at an annual rate of 19.5%, and she expects that it would take her 35 days to pay her credit card balance. a) Calculate the cost of the bicycle using each of the payment options. b) Which payment option should Arlene choose? Assignment: Pg. 313 #1‐5 A&W Math 11 6.4 – Part I – Payday Loans Notes PAYDAY LOAN – a small, short‐term loan with a high interest rate intended to cover the borrower’s expenses until their next pay day OVERDRAFT – occurs when you withdraw more than you have in your account. You are charged a fee for being overdrawn, and your bank will not make any payments witch you cannot cover. (You can get Overdraft protection, which means that the bank will pay for your overdrawn withdrawals, but you must still pay a fee.) LINE OF CREDIT – an approved loan amount that you can draw on as needed, with interest charged on the money used (unlike an overdraft, a fee is not charged to withdraw funds from a line of credit) DEFAULT – failure to repay a loan COLLATERAL – an item of value pledged by a borrower to secure a loan ASSETT – an item of economic value owned by an individual that could be converted to cash Example 1: A payday loan store charged Matt $40.00 interest on a $350.00 loan. Matt paid back the total amount of $390.00 after 10 days. a) What was the annual interest rate for this loan? b) What was the daily interest rate for this loan? Example 2: Safia borrowed $500.00 from a payday loan store and agreed to repay it in 30 days at a rate of 1.15% per day. How much will Safia have to repay? Example 3: Tracy borrowed $350.00 from a payday loan store. She paid back the loan plus interest 12 days later. The interest rate was 372% per annum. How much interest did she pay? Example 4: Kurt agreed to pay $663.60 to a company that lent him $600.00 at 2.12% per day. How many days did he have to pay the money? Example 5: You borrowed $750 for 45 days at a rate of 0.70% per day. a) How much will he have to repay? b) What is the annual interest rate? Assignment: Pg. 317 #1‐3 Pg. 318 # 4‐6 A&W Math 11 6.4 – Part II – Personal Loans AMORTIZATION PERIOD – the time required to pay back a loan DEFAULT – failure to repay a loan COLLATERAL – an item of value pledged by a borrower to secure a loan ASSETT – an item of economic value owned by an individual that could be converted to cash Example 1: Jean‐Paul borrows $2500.00 to purchase a laptop computer and software. He takes out a personal loan from his credit union at an annual rate of 6.25% with an amortization period of 2 years. Use the personal loan payment calculator table to the right (and on page 320) to help you answer the questions below. a) What is Jean‐Paul’s monthly payment? b) Calculate the total amount he will pay over the 2 years. c) Calculate the finance charge on the loan. Notes Example 2: Amy would like to buy a Television. The one she wants costs $1565.45 including taxes. Amy has saved $500.00 for a down payment. a) How much will Amy have to borrow to buy her TV? b) She can get a loan at 8.25% per annum with an amortization period of 1 year. What will be her monthly payment? c) What will be the total she pays for her loan? d) How much will the television cost Amy? Example 3: Cindy has a snow‐mobile touring company based in Churchill, MB. She wants to purchase a new snow‐mobile. Cindy has no available cash for a down payment. She has estimated that she can afford to pay no more than $400.00 a month for the next 2 years. The snow‐mobile dealer offers the machine she wants for $8500.00 cash. Cindy has three payment options. 
Option 1: She can get a loan from her bank at 5.00% per annum over 2 years, and pay cash. 
Option 2: She can pay using her credit card, which charges an annual interest rate of 22.50%. She plans to pay off the payment in 1 year. Calculate the minimum payment for the first month (5% of the balance). 
Option 3: She can get a line of credit at 4.50% per annum that she plans to pay off over 2 years. Calculate the total cost of each of Cindy’s options. Describe one advantage and one disadvantage to each of these three options. Option 1: Pro: Con: Pro: Option 2: Con: Option 3: Pro: Con: Assignment: Pg. 321 #7‐8 A&W Math 11 6.4 – Part III – Loans, Lines of Credit, and Overdrafts Notes Example 1: Toby wrote two cheques that were returned because he did not have enough money in his account to cover them. The cheques were for $50.00 and $150.00. His bank charges $25.00 for each returned cheque. How much did Toby have to pay in fees? Example 2: You need $740.00 cash to pay an unexpected bill. You go to a payday loan store and agree to pay $871.57 on payday, which is 14 days away. a) What is the daily interest rate for the loan? b) What is the annual interest rate? Example 3: Calculate the monthly payment, the total amount paid, and the finance charge for each of the following loans. a) $2500.00 at 7.50% per annum for 4 years; b) $3725.00 at 9.00% per annum for 5 years. Example 4: Josh wants to buy a new kayak. He sees one he likes on sale for $3842.00 cash. He does not have the cash to buy the kayak right away so he must consider his options. Option 1: The kayak store has a plan where Josh can pay $500.00 down and $300.00 a month for 1 year, plus an administration fee of $25.00. Option 2: Josh could also borrow the money from his bank at 8.50% per annum for a term of 1 year, and then pay cash for the kayak. Option 3: Josh could save $300.00 a month until he has enough cash to buy the kayak. a) What would the monthly payment be for each option? Use the personal loan payment calculator on p. 320 to calculate the payments. b) Calculate the total cost for each option. c) Why might Josh choose each of these options? Assignment: Pg. 322 #1‐5