Personal Finance. Chapter 1. Chapter Goals. Out of the Nest

Transcription

1 11 Chapter 1 Personal Finance Out of the Nest As young adults begin to establish themselves independently of their parents, they may consider renting their own apartment, purchasing a home, or even beginning a family. Many financial factors will need to be considered. Insurance protects us from loss. If your rented apartment is burgled and your belongings are stolen or damaged, you can replace them if you have coverage with an insurance policy. Your home can be insured against losses caused by fire or flooding. Your life can be insured so that the financial needs of your family are provided for in the event of your death. Buying a home will probably require you to obtain a mortgage. A variety of types of mortgages are available. Banks and credit unions use a formula called the gross debt service ratio to determine how much money you can afford to spend on a mortgage. Purchasing a home also involves additional costs. All of these factors are important considerations when deciding to purchase a home. Chapter Goals In this chapter, you will determine the costs of buying and insuring a home and you will solve problems involving life insurance and mortgages.

2 12 Essentials of Mathematics 12 Chapter Project In the project for this chapter, you will imagine that you are buying a home. You will choose the type of home you would like a house, a condominium, a townhouse, or an alternative type of housing and research the total cost of buying this home. You will then investigate if and when such a home might be affordable for you. As you complete the project activities, you will add the following items to your project file: 1. A description of the type of home you would like to purchase and information on three financial institutions that offer mortgages. 2. Calculations showing monthly, accelerated bi-weekly, and accelerated weekly mortgage payment options. 3. A calculation of the gross debt service ratio to see whether your purchase is affordable. 4. Calculations of the annual property insurance premiums from three companies. 5. Calculations showing the additional one-time costs associated with buying the home. Researching the costs involved in buying a home, such as this house in Winnipeg, is the project for this chapter.

3 Chapter 1 Personal Finance 13 Exploration 1 Life Insurance The purpose of any insurance is to protect individuals against unexpected financial loss. When you purchase life insurance, you are purchasing financial security for your family in the event of your death. When you die, the beneficiary will receive the full value of your insurance policy from the insurer. In this exploration, we will examine two types of life insurance, term and whole-life. You will learn the benefits and disadvantages of each type. When you purchase term insurance, you are covered only for the term of the policy. For example, a policy with a ten-year term is valid for ten years. If you die in the eleventh year, there will be no coverage. Term insurance is less expensive than whole-life, but you must be careful in selecting which type is best for you. If you are 20 years old, a ten-year term insurance policy is relatively inexpensive. But circumstances may change. After the ten-year period, you will have to renegotiate a new policy. If your health has deteriorated, you may not be able to buy any coverage. Whole-life insurance is initially more expensive, but you are covered for life, regardless of changes in your health, and the premiums never change. Another positive attribute of whole-life policies is the cash surrender option. An insured person can terminate the policy at any time, and receive some cash back from his or her investment. When calculating the premiums for insurance policies, insurance companies often add a policy fee. If you choose to pay your premiums on a semi-annual or monthly basis, the handling fees will be slightly higher. Goals In this exploration, you will distinguish term insurance from whole-life insurance and learn how smoking and gender affect life insurance premiums. New Terms beneficiary: the person who will receive the insurance money. insurer: the company providing the insurance. policy: a written contract or certificate of insurance. premium: how much you pay for an insurance policy (monthly, semi-annually, or annually).

4 14 Essentials of Mathematics 12 Table 1 Ten-Year Term Life Insurance Annual Premium for Term Plus Male Non-Smoker Female Non-Smoker Male Smoker Female Smoker Issue Rate per $1,000 Issue Rate per $1,000 Issue Rate per $1,000 Issue Rate per $1,000 $100,000 $250,000 $500,000 $100,000 $250,000 $500,000 $100,000 $250,000 $500,000 $100,000 $250,000 $500,000 Age $249,999 $499,999 $3,000,000 $249,999 $499,999 $3,000,000 $249,999 $499,999 $3,000,000 $249,999 $499,999 $3,000, Add policy fee of $75 per year Semi-annual payment (multiply annual premium by 0.52) Monthly payment (multiply annual premium by 0.09)

5 Chapter 1 Personal Finance 15 Table 2 Whole-Life Insurance Annual Whole-Life Premium Male Female Male Female Male Female Non-Smoker Non-Smoker Smoker Smoker Under 18 Under 18 Issue Rate Issue Rate Issue Rate Issue Rate Issue Rate Issue Rate per $1,000 per $1,000 per $1,000 per $1,000 per $1,000 per $1,000 Issue Premium Premium Premium Premium Issue Issue Premium Premium Issue Age Rate Rate Rate Rate Age Age Rate Rate Age Add policy fee of $75 per year Semi-annual payment (multiply annual premium by 0.52) Monthly payment (multiply annual premium by 0.09)

6 16 Essentials of Mathematics 12 Table 3 Cash Surrender Values Whole-Life Insurance Male Cash Surrender Value per $1,000 of Insurance Female Cash Surrender Value per $1,000 of Insurance Issue Age Policy Issue Age Year , , , , , ,

7 Chapter 1 Personal Finance 17 Table 3 Cash Surrender Values Whole-Life Insurance Male Cash Surrender Value per $1,000 of Insurance Female Cash Surrender Value per $1,000 of Insurance Issue Age Policy Issue Age Year , , , , , , , , , , , , , , , , Every effort has been made to ensure the accuracy of the above values, but accuracy is not guaranteed. In the event of a discrepancy, the insurance policy governs.

8 18 Essentials of Mathematics 12 Example 1 Jason Rettinger is a 32-year-old male non-smoker. He wants to purchase a 10-year term life insurance policy worth $120,000. Find his annual premium, and then find his monthly premium. Solution Look in the Ten-Year Term Life Insurance table for a 32-year-old male non-smoker. Be sure to select the first column in the male non-smoker section, since the next column is the rate for policies between $250,000 and $499,999. The premium for Jason would be $1.02 per thousand dollars of coverage. The easiest way to calculate his annual premium is: $1.02 $120,000 $1,000 $1 22,400 $ 1,000 $ Now add the $75 policy fee (see Table 1 footnote): $ $75.00 $ (annual premium) To find the monthly premium, multiply the annual premium by 0.09: $ $17.77 (rounded) Jason pays $17.77 per month for his life insurance. If Jason decides to pay monthly premiums, the total cost over the year would be $ ($ ). Compared to paying one annual payment of $197.40, this is an additional cost of $15.84 to cover the handling of his account.

9 Chapter 1 Personal Finance 19 Example 2 Lynne is a 20-year-old non-smoking female who wishes to purchase a whole-life policy worth $75,000. Find her premiums if she decides to make semi-annual payments. Solution Use the Whole-Life Insurance table, and look for the column for nonsmoking females. Sliding down to 20-year-olds, and going across to the appropriate column, you will see a rate of $2.89 per thousand dollars of coverage. $2.89 $ 75,000 $ $1,000 Remember to add the policy fee $ $75.00 $ Now use the footnote on this table to calculate the amount for semiannual payments. Multiply the annual premium by 0.52: $ $ Lynne pays $ semi-annually for her life insurance.

10 20 Essentials of Mathematics 12 Example 3 Wayne is 22 years old and he smokes. He is considering purchasing a 10- year term insurance policy in the amount of $200,000. His agent advises him that if he quits smoking, the insurance will be much less expensive. Calculate the difference in the annual premiums if Wayne were to quit smoking. Solution 22-year-old Male Smoker 22-year-old Male Non-Smoker $1.43 $200,000 $1,000 $0.85 $200,000 $ $ $1,000 $ $75.00 $ $ $75.00 $ Subtract to find the difference in annual premiums: $ $ $ Class Discussion Discuss why smokers have to pay more for life insurance than nonsmokers. Why do men have to pay more for life insurance than women?

11 Chapter 1 Personal Finance 21 Example 4 Jim Chow bought a $50,000 whole-life policy when he was 20 years old. When he turned 50, he decided to cancel his insurance and take the cash surrender value. How much did he receive? Solution Use the Cash Surrender Values table. Find the issue age of 20 in the Male column. Since Jim had this policy for 30 years ( ), slide down the column labelled Policy Year to 30. You should see a value of $149 per thousand dollars. $ $ 50,000 $7, $ 1,000 The cash surrender value of Jim s policy is $7, Class Activity As a class, research the rates of several companies that offer life insurance. Assume you are a 20-year-old and that you wish to buy $100,000 of whole-life insurance. Find the total monthly premiums for the following cases: male smoker male non-smoker female smoker female non-smoker The class should compile a table that lists the companies and the rates they would charge. Which company would your class select? List the reason(s) why you chose that company.

12 22 Essentials of Mathematics 12 Notebook Assignment 1. Denise Gill is a 33-year-old non-smoker. What will her annual premium be for a $100,000, 10-year term life insurance policy? 2. Kevin Wong is 30 years old and smokes. Calculate his annual premium for a $50,000 whole-life policy. 3. Harry and Sally Heller are both 25 years old, and non-smokers. They each decide to purchase $200,000 whole-life insurance policies. a) Find the monthly premium each will have to pay. b) Why does Harry have to pay more than Sally? 4. Howard was 25 years old when he bought an $80,000 whole-life insurance policy. At the age of 60, he decided to cancel his policy and take the cash surrender value. a) How much money can he expect back? b) List 2 reasons why someone might choose term life insurance instead of whole-life. c) List 2 reasons why someone might choose whole-life insurance instead of term. 5. Luen is comparing the insurance costs of smokers and non-smokers. He selects a 27-year-old male, and picks $300,000 insurance over a 10-year term. a) Find the annual premium for a smoker and a non-smoker. b) What is the difference in the premiums? c) Find the percent difference compared to the non-smoking rate. 6. Malvina Antoniak is a 25-year-old smoker. What is her semi-annual premium for $270,000 of whole-life insurance? 7. A man buys a $60,000, 10-year term life insurance policy when he is 28. If he dies when he is 39, how much will his beneficiary collect?

13 Chapter 1 Personal Finance 23 Extension 8. Twin girls have decided to purchase $260,000 of life insurance on their twentieth birthday. One buys 10-year term life insurance, while the other decides to purchase whole-life insurance. Both are nonsmokers. a) Determine the total cost of premiums that each would pay over 40 years. The 10-year term life policy is renewable after each 10- year period, but at the new rates for this twin s age. b) Find the cash surrender value after 40 years. c) Which twin selected the better coverage? Explain your reasoning. An insurance salesperson explains the various types of life insurance.

14 24 Essentials of Mathematics 12 Exploration 2 Calculating Mortgage Payments Most people need to borrow money to purchase a home. Generally, a home is the largest purchase of your life. This exploration will help you understand how mortgages work. To buy or sell a home today it is important to understand the concepts and to know the vocabulary. This can save you time and money; it can also prevent you from obtaining a mortgage ill-suited to your needs. Three important words are: interest, principal, and equity. When you first buy a home, you re likely to make a down payment on the property. But, because you financed the purchase, you are now in debt and the lender owns most of the property s value. In traditional mortgages, the monthly payments on the loan are weighted. During the first years, they are largely interest; in time, more of each payment is credited to the loan itself, or the principal. Gradually as you pay off the principal, you build up equity, or ownership, and decrease your unpaid balance, or debt. Your equity also increases if the value of the home increases. This process of gradually obtaining equity and reducing debt through payments of principal and interest is called amortization. Goals In this exploration, you will learn to calculate principal, interest, and equity. You will also learn about different types of mortgages. New Terms amortization period: the length of time in years that you will need to pay off a mortgage. equity: the portion of the value of your property that you own. interest: the cost of borrowing money. principal: the amount you initially borrow. unpaid balance: the portion of the value of your property owed to the financial institution.

15 Chapter 1 Personal Finance 25 First-time home buyers can usually secure financing with only 5% of the purchase price as a down payment. The National Housing Act requires that all mortgages with less than a 25% down payment be insured against loss. People who need mortgages over 75% of the principal are required to pay a higher rate (between 0.5% and 3.75% higher). Many different types of mortgages are available from financial institutions. This exploration will look at some of them briefly, but will focus on fixed-rate, closed mortgages. Career Connection Name: Philippe Gagnon Job: insurance adjuster Current salary: $2,000 per month Education: grade 12; courses through Insurance Institute of Canada Career goal: branch manager at an insurance company office Keyword search: Canada courses insurance adjuster New Terms closed mortgage: a mortgage which does not allow payments on the principal. fixed-rate mortgage: a mortgage with the interest rate locked in for a specified period of time.

16 26 Essentials of Mathematics 12 Types of Mortgages Fixed-rate mortgages can be negotiated with a financial institution for any number of years. These mortgages guarantee the monthly payment for the selected term (for example, 2 years). With a fixed rate, you are able to budget your mortgage payments and are protected from any spikes in interest rates. Usually this type of mortgage is locked in, and you would be charged a penalty to pay extra on the principal, or to pay it off before the end of the term. However, some fixed-rate mortgages allow for an extra payment annually. Variable-rate mortgages are popular with people who believe the interest rates are going to fall or remain constant. If the rates fall, the amount of interest charged each month against the principal borrowed will be less. You can still budget your mortgage payment, which stays constant. These mortgages are usually considered to be open, and you can pay against the principal at any time and can close the mortgage without penalty. If the rates go up suddenly, you may want to switch over to a fixed-rate mortgage to protect yourself. Technology Information about mortgages can be found through a financial institution s web site or from : or Many web sites contain financial tools and calculators relating to mortgages. Banking laws, including mortgages, are different in Canada than in other countries. Canadian web sites should be used. New Terms open mortgage: a mortgage that allows additional payments on the principal. variable-rate mortgage: a mortgage where the interest rate may change from month to month.

17 Chapter 1 Personal Finance 27 Table 4 Amortization Table Blended Payment of Principal and Interest per $1,000 of Loan Interest Rate 5 Years 10 Years 15 Years 20 Years 25 Years 4.00%

18 28 Essentials of Mathematics 12 In order to complete an amortization schedule, you will need to determine the monthly payment from an amortization table. You will need to calculate the owner s equity, unpaid balance, interest on unpaid balance, principal, and the owner s new equity. Below are the six simple steps. Complete them in order for as many monthly payments as the schedule requires. 1. Calculate the monthly payment using the amortization table on page 27. Then write in the unpaid balance and the owner s equity. 2. To find the interest payment, multiply the unpaid balance by the interest rate and divide by Subtract the interest from the monthly payment to find the principal payment. 4. Add the principal payment to the owner s equity. 5. Subtract the principal payment from the unpaid balance. 6. Repeat for as many months as required. The table below is a useful way to organize your information. Owner s Unpaid Monthly Interest Principal Equity Balance Payment Payment Payment SAMPLE Technology Spreadsheet software can be used to calculate amortization schedules. You may also use a search engine such as Google or Altavista and type in amortization table. You will be able to access many financial calculator programs that are available on-line.

19 Chapter 1 Personal Finance 29 The following example illustrates these steps. Example 1 Write an amortization schedule for three months, given a mortgage of $85,000 (after a $20,000 down payment), at 6% over 20 years. Solution 1. First, write the unpaid balance (the amount actually borrowed) and the owner s equity (or down payment) in first line of the table. Calculate the monthly payment using the amortization table: 6% over 20 years is $7.12 per $1,000 borrowed $7.12 $ 85,000 $605.20/month $1, Unpaid balance multiplied by interest rate divided by 12 gives the interest: $85, months $425.00/month 3. Monthly payment minus the interest gives the principal: $ $ $ Add this principal to the owner s equity: $20,000 $ $20, Subtract the principal amount from the unpaid balance to give the new unpaid balance: $85,000 $ $84, Go back to step 2. Repeat these steps to complete the schedule for the next two months: Owner s Unpaid Monthly Interest Principal Equity Balance Payment Payment Payment $20,000 1 $85,000 1 $ $20, $84, $ $ $ $20, $84, $ $ $ $20, $84, $ $ $

20 30 Essentials of Mathematics 12 Example 2 Mr. and Mrs. Smith purchased a home for $160,000. They made a down payment of $35,000. If they negotiated a mortgage at 7 1 % over 25 years, 4 calculate: a) the amount they would need to borrow for the mortgage b) the monthly mortgage payment c) the amount of interest on the first payment d) the amount of interest they would pay over the life of the mortgage Solution a) $160,000 is the purchase price of the home. If the Smiths made a down payment of $35,000, they would need to borrow the balance: $160,000 $35,000 $125,000 They would borrow $125,000. b) Find % in the amortization table. A rate of 7 1 % over 25 years 4 requires a payment of $7.16 per $1,000 borrowed: $7.16 x $ 125,000 $ $ 1, 000 The monthly payment would be $ c) To find the amount of interest on the first payment, multiply the balance by the rate and divide by 12 months: $125, $ The Smiths will pay $ in interest on their first payment. d) To find the total amount of interest they will pay over the life of the mortgage, multiply the monthly payment by the number of months and subtract the principal borrowed: monthly payment number of months principal borrowed total interest paid $ months 25 years $268,500 $268,500 $125,000 $143,500 Over the life of the mortgage, the Smiths will pay $143,500 in interest.

21 Chapter 1 Personal Finance 31 Project Activity You must find a home to purchase. Assume that you have an inheritance of $30,000 to use as a down payment on your home. Use local real estate figures or data from Assume that you and your partner are earning a gross family income of $65,000. Describe the home you want to purchase. Then find three providers of mortgage money, and justify why you would select one over the others. Include your data on mortgages. Finding a home that you can afford may be a challenge. Mental Math Determine the monthly mortgage payment: a) $6.50 per $1,000 for $100,000 b) $5.00 per $1,000 for $120,000 c) $4.00 per $1,000 for $150,000

22 32 Essentials of Mathematics 12 Notebook Assignment 1. Find the monthly payments on the following mortgages: a) $50,000 at 5.5% over 15 years b) $85,000 at % over 25 years c) $182,250 at % over 15 years d) $78,380 at 6% over 10 years 2. Kevin McIlwraith is considering purchasing a condominium in North Vancouver for $149,750. He has $55,500 saved for a down payment. The credit union is offering him a mortgage at 5.5% over 20 years. Find his monthly payment including principal and interest. 3. A $70,000 mortgage was offered by a loans officer at a rate of 6% over 20 years. How much interest would be paid over the life of the mortgage? 4. Create an amortization schedule showing the principal and interest over the first four months of an $80,000 mortgage at % over 20 years, with a $15,000 down payment. Assume monthly payments. 5. Explain why you might consider taking out a mortgage with a higher monthly payment over a shorter amortization period. 6. Pierre LaFrance is considering both a variable-rate and a fixed-rate mortgage. List two advantages to each. Which would you recommend, and why? 7. Sam Tamaki has two bank offers to consider for his $105,500 mortgage. One option is at 7% over 20 years, while the other is at 6% over 25 years. Calculate the amount of interest he would pay over the life of each mortgage. Show which would be the better choice if payments are made monthly.

23 Chapter 1 Personal Finance 33 Extension 8. Mila Obradovic wants to purchase a home costing $180,000. She has $40,000 saved up for the down payment. The bank will only finance $110,000 at % over 25 years. She has arranged a second mortgage through her family at 9% over 20 years for the balance. Find the total monthly mortgage payments she will be making. Paying off a mortgage for a large house such as this one in Arviat, Nunavut, will often take 25 years.

24 34 Essentials of Mathematics 12 Exploration 3 Exploring Mortgage Payments This exploration is designed to encourage you to look at mortgage options other than the conventional monthly fixed-rate mortgages studied in the previous exploration. You will explore various payment options for mortgages, and will be asked to make decisions involving budgetary concerns with shorter amortization periods, bi-weekly payments, weekly payments, and annual contributions. A basic mortgage of $125,000 at 7 1 % over 25 years will cost 4 $143,500 in interest. There are a few payment options you should consider that can dramatically reduce the amount of interest you have to pay. Using an on-line financial calculator or a spreadsheet program can make it much easier to compare different situations. Payment Options a) semi-monthly: this saves very little over the life of the mortgage. The monthly payment is simply divided into halves. b) accelerated bi-weekly: this option can save you many thousands of dollars. It takes your monthly payment and divides it by two to make it bi-weekly. But, there are 52 weeks in a year, and therefore 26 bi-weekly payments. As a result, you would make an additional two payments per year, reducing your principal more quickly, and lowering the total interest you have to pay. This option is especially advantageous for those who get paid bi-weekly. Goals In this exploration, you will examine various mortgage payment plans and make decisions about the best way to pay off a mortgage.

25 Chapter 1 Personal Finance 35 c) accelerated weekly: this option can save slightly more. It takes your monthly payment and divides it by four to find a weekly payment. But, with 52 weeks in a year, you are making four additional payments when compared to the monthly amount. This reduces your principal faster, and lowers the amount of interest paid. d) double-up: some lending institutions offer a double-up plan where you are allowed to pay double your usual amount on one or more occasions during the year. This extra payment goes directly against the principal. e) lump sum: on the anniversary of your mortgage, or the renewal date, you may be allowed to pay a lump sum. This goes directly against your principal, and reduces the amount of interest considerably. f) shorter amortization periods: although the monthly payments are higher, you can save thousands over the life of the mortgage. The figures in the table below were obtained from an on-line mortgage calculator. The table shows the effect of different payment options on a $142, mortgage amortized over 25 years at 7%. Comparison of Mortgage Amortization Periods Payment Payment Amort. Interest Interest Schedule Amount (years) Paid Saved Monthly $1, $157,227 0 Accelerated $ $124,353 $32,874 Bi-weekly Accelerated $ $123,849 $33,378 Weekly Note: figures may vary slightly depending on the financial institution. By making accelerated bi-weekly payments, $32,874 is saved and the mortgage amortization period is reduced from 25 years to years. By paying weekly, $33,378 is saved and the mortgage amortization period is reduced from 25 years to years.

26 36 Essentials of Mathematics 12 Example 1 Nancy Moreau is comparing mortgages at her financial institution. The loans officer wants her to accept a 25-year amortization period because it has a much lower monthly payment. But Nancy thinks she can pay the mortgage off sooner. This will save her many thousands of dollars. The mortgage is $130,000 at %. Nancy wants to pay it off over 15 years. Determine the amount of interest she would save if the loan were amortized over 15 years instead of 25 years. Solution Find the monthly payments for both situations: % over 25 years 6 % over 15 years 2 2 $6.70 $130,000 $1,000 $871.00/month $8.66 $130,000 $1,000 $1,125.80/month Total interest paid over life of the mortgage: $ $261,300 $ $202,644 $261,300 $130,000 $131,300 $202,644 $130,000 $72,644 The difference is: $131,300 $72,644 $58,656 Even though the monthly payments are higher, a shorter amortization period reduces the borrowing costs over the life of the mortgage.

27 Chapter 1 Personal Finance 37 Example 2 Jillian is considering mortgage options. Her monthly payment over 20 years will be $ on a $90,000 mortgage at 5% (using a mortgage calculator). If she converts this to accelerated bi-weekly payments, her mortgage will be paid off in 17.7 years. a) Find the amount of her accelerated bi-weekly payments. b) How much would this save her in interest charges over the life of the mortgage? c) How much extra would she pay in a year? Solution a) $ $ b) Monthly Payments: $ $142, $142, $90,000 $52, Accelerated Bi-weekly Payments: $ $136, $136, $90,000 $46, Total Saved: $52, $46, $5, c) $ $7, $ $7, $7, $7, $ Note that this amount is one month s mortgage payment. You can see clearly that the mortgage will be paid off sooner with the accelerated bi-weekly payments. Also, the amount of interest paid over the life of the mortgage is substantially reduced.

28 38 Essentials of Mathematics 12 Example 3 Liam is researching his options on a mortgage of $120,000 at 6% over 25 years. Using an on-line mortgage calculator, find: a) the monthly payment b) the accelerated bi-weekly payment c) the amount of interest saved if he chooses the bi-weekly option. Solution Using a mortgage calculator, you find that by paying bi-weekly, Liam can save $20,636 and shorten the amortization period from 25 years to 21 years. Accelerated Payments Monthly Payments Bi-weekly Mortgage Amount $120,000 $120,000 Interest Rate 6% 6% Payment $ a $ b Years to Repay Total Interest $111,949 $91,313 Interest Savings $20,636 c continued on the next page

29 Chapter 1 Personal Finance 39 Mortgage Payoff Schedule Monthly Payments Accelerated Bi-weekly Payments Year Payments Balance Payments Balance $120,000 $120,000 1 $9,278 $117,864 $10,051 $117,065 2 $9,278 $115,596 $10,051 $113,949 3 $9,278 $113,189 $10,051 $110,640 4 $9,278 $110,632 $10,051 $107,127 5 $9,278 $107,919 $10,051 $103,398 6 $9,278 $105,038 $10,051 $99,437 7 $9,278 $101,979 $10,051 $95,232 8 $9,278 $98,731 $10,051 $90,768 9 $9,278 $95,283 $10,051 $86, $9,278 $91,623 $10,051 $80, $9,278 $87,736 $10,051 $75, $9,278 $83,610 $10,051 $69, $9,278 $79,230 $10,051 $63, $9,278 $74,597 $10,051 $57,55 15 $9,278 $69,642 $10,051 $50, $9,278 $64,400 $10,051 $43, $9,278 $58,853 $10,051 $35, $9,278 $52,926 $10,051 $27, $9,278 $46,653 $10,051 $19, $9,278 $39,993 $10,051 $9, $9,278 $32,293 $10,051 $ $9,278 $25,416 $241 $0 23 $9,278 $17,446 $0 $0 24 $9,278 $8,985 $0 $0 25 $9,279 $0 $0 $0

30 40 Essentials of Mathematics 12 Example 4 Debbie Webb is on a very restricted budget. Her mortgage is $100,000 at 5% for 20 years. Her take-home pay is $2,200 per month. Since no more than 30% of her pay should be dedicated to housing costs, can Debbie afford to move to an accelerated bi-weekly option? Solution Debbie s monthly dedicated housing cost is limited to: $2, $ Estimated Payment of Principal and Interest (using a mortgage calculator): Payment Options Payment Years to Repay Mortgage Monthly $ Accelerated Bi-weekly $ $ $ So, Debbie could not afford the accelerated bi-weekly payments within the parameters of her budget. Project Activity Create a spreadsheet showing the amortization schedule of payments for your home. Include monthly, accelerated biweekly, and accelerated weekly options, showing the amount of interest you will have to pay over the life of the mortgage.

31 Chapter 1 Personal Finance 41 Notebook Assignment 1. Bev Joyce is thinking of purchasing a home worth $140,000. She has $40,000 saved up for the down payment. Her mortgage is at 4.75% over 25 years. Use an on-line mortgage calculator or a spreadsheet program to determine: a) her monthly payment b) if she chose the accelerated bi-weekly option, how much she would save in interest. 2. Yvette Beaulieu has secured a mortgage of $120,000 at 6% over 20 years, making monthly payments. Her lending institution will allow her to double-up one payment per year. a) Calculate her monthly payment. b) Calculate the amount of interest she will pay over the life of the mortgage. c) Use a spreadsheet to determine the effect of her double-up payments on the interest. 3. Marcel Pelletier is paying $750 per month towards his mortgage. His monthly take-home pay is $2,500. Other budget items are: food and utilities, $600; car expenses, $400; entertainment expenses, $400; and savings, $350. With his mortgage renewal date coming in a year, he has the option to pay a lump sum towards the principal. How would you suggest he alter his budget, and by how much, to save up for this extra payment? 4. Mona Katsumoko is paid on a weekly basis. She presently has a mortgage of $65,000 at 7% amortized over 15 years. The monthly mortgage payment is $ Determine: a) the amount of interest she will pay over the life of the mortgage b) the amount her payments would be if she exercised the accelerated weekly payment option c) when the mortgage would be paid out if she made accelerated weekly payments d) the amount of interest she would save by making accelerated weekly payments.

32 42 Essentials of Mathematics 12 Problem Analysis Number Patterns Pattern 1 Choose any number from 2 to 9. Multiply it by 41. Multiply the result by 271. Try this with several one-digit numbers. What do you notice about the result? Why does this work? Pattern 2 Select any three-digit number, for example: 123. Repeat the digits to get a six-digit number: 123,123. Divide this number by 13, then by 11, then by 7. What did you get? Try this with a few more three-digit numbers. What happens? Why do you always get this result? Give an explanation. Pattern Continue this pattern: Does the pattern continue? What happens to the pattern when you reach (ten 1s)? Why?

33 Chapter 1 Personal Finance 43 Games A Weird Will A wealthy lawyer owned 11 expensive cars. When he died, he left a weird will. It asked that his 11 cars be divided among his three sons in a particular way. Half of the cars were to go to the eldest son, one-fourth to his middle son, and one-sixth to the youngest. Everybody was puzzled. How can 11 cars be divided in such a way? While the sons were arguing about what to do, a mathematics teacher drove up in her new sports car. Can I be of help? she asked. After the sons explained the situation, she parked her sports car next to the lawyer s 11 cars and hopped out. How many cars are there now? The sons counted 12. Then she carried out the terms of the will. She gave half of the cars, 6, to the oldest son. The middle son got one-fourth of 12, or 3. The youngest son got one-sixth of 12, or 2. 6 plus 3 plus 2 is 11. So, one car is left over. And that s my car. She jumped into her sports car and drove off. Glad to be of service! Can you write a similar will for 17 cars?

34 44 Essentials of Mathematics 12 Exploration 4 Gross Debt Service Ratio The gross debt service ratio (GDSR) is a formula used by most financial institutions to determine whether or not you can afford the property you have selected. It starts with a general rule that total household expenses cannot exceed 32% of gross income. Your mortgage application will likely be denied if the gross debt service ratio is over 32%. Career Connection Name: Darice Whyte Job: supervisor, mortgage services Current salary: $65,000 per year Education: grade 12; certified general accountant program Career goal: mortgage broker Keyword search: CGA Canada ( Goals In this exploration, we will discuss the gross debt service ratio and determine eligibility for mortgage loans. New Terms gross debt service ratio: a formula used by most financial institutions to determine whether or not you can afford the property you have selected.

35 Chapter 1 Personal Finance 45 The formula is calculated as follows: (monthly mortgage payment + monthly property tax monthly heating costs) gross monthly income 100 Interest Rate Factor Table* Rate Factor Rate Factor Rate Factor 6% % % % % % % % % % % % * Based on 25-year amortization Note: the figures used in this table are mortgage payment amounts per $1.00 rather than per $1,000.00, as in a mortgage amortization table.

36 46 Essentials of Mathematics 12 Example 1 You would like to purchase a condominium for $93,000. You are able to make a down payment of $8,000. The bank will finance this property at a rate of % over 25 years. Your gross monthly income is $3,000. The monthly property taxes are $125 and the monthly utility costs are $150. Calculate the monthly mortgage payment and the gross debt service ratio. Solution 8 1 % over 25 years shows $7.95 per $1,000 borrowed. 2 $93,000 $8,000 down payment $85,000 (amount of mortgage) $7.95 $ 85,0 00 $ (monthly mortgage payment) $ 1,000 Gross debt service ratio formula: ($ $125 $150) $3, % Since the gross debt service ratio is under 32%, your application would likely be accepted. A condominium may be more affordable than a single family house.

37 Chapter 1 Personal Finance 47 Example 2 Tom and Sarah Green want to purchase the home of their dreams in Winnipeg. They have saved $42,500 for the down payment on a house costing $215,750. Tom s job pays $2,400 per month, while Sarah has a gross monthly income of $2,450. The mortgage company has offered them a rate of 7% over 25 years, subject to a favourable gross debt service ratio. The utility company estimates the annual costs of gas and electricity to be $2,640, and the municipality shows the property taxes to be $3,600 a year. Use the gross debt service ratio to determine if they qualify for this mortgage. Solution The mortgage amount will be: $215,750 $42,500 down payment $173,250 The table shows that 7% over 25 years will cost $7 per $1,000 borrowed. $7.00 $1 73,250 $1, $ 1,000 The monthly payment will be $1, The gross debt service ratio is: [$1, ($2,640 12) ($3,600 12)] $4, % The Greens application would probably not be accepted. Their monthly household expenses would exceed 32% of their gross income.

38 48 Essentials of Mathematics 12 Lending institutions will ask that you complete an affordability chart to determine the size of the mortgage best suited to your financial position. The following template will help you determine the price of the home you can afford. Affordability Chart The Formula Gross monthly household income Your Calculations Multiply by 32% (GDSR) 0.32 Total affordable household expenses Subtract Monthly property taxes Monthly heating costs One-half of condo/strata fees (if applicable) Monthly mortgage payment your household can afford To calculate total mortgage amount, divide by the estimated interest rate factor that corresponds to your interest rate (see table on page 45) Maximum amount of mortgage you can afford Add your cash down payment Your maximum affordable price SAMPLE Actual mortgage payment interest rate factor actual total mortgage Gross Debt Service Ratio (actual monthly mortgage payment + monthly property taxes + monthly heating) 100 gross monthly income