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Chapter 9 Personal Finance 9.1 MATHPOWERTM 11, WESTERN EDITION 9.1.1 Types of Income Gross Income is the amount of money earned through employment. Employers offer earning in different ways: • Salary: This is a fixed amount of money earned over a specified time period, such as monthly or yearly. • Wage: This is money earned hourly, daily, or by piecework. Overtime and gratuities may also be included in a person’s wage. • Commission: This is earnings based on a percent of an employee’s sales during the pay period and may be paid in combination with a salary or wage. • Graduated Commission: This is earnings based on commission, in which the rate of commission increases when sales reach a certain goal. 9.1.2 Calculating Gross Earnings Sandra works full time at a retail clothing store. She is paid $8.75/h plus time-and-a-half for overtime, which is any time over 40 h per week. One week she worked 48.5 hours. Calculate her gross earnings for the week. Regular Earnings: Hours worked x Hourly wage 40 x $8.75 = $350 Overtime Earnings: Hours worked x Hourly wage x 1.5 8.5 x $8.75 x 1.5 = $111.56 Total Earnings: Regular + Overtime Earnings $350 + $111.56 = $461.56 Sandra’s gross earnings for the week were $461.56. 9.1.3 Calculating Gross Earnings Paul, Stan, and Jody work for the same company but are paid in different ways. Paul is paid a straight commission of 6% of his total sales. Stan is paid a base salary of $475 per week plus 3.5% of sales above a sales quota of $5000. Jody is paid a graduated commission of 2.5% on sales up to $3000, plus 6.5% on sales in excess of $3000. If each persons sales for one week were $16000, calculate the gross income for each. Paul: 6% of $16 000 = 0.06 x $16 000 = $960 Stan: $475 + 3.5% of $11 000 = $860 Jody: 2.5% of $3 000 + 6.5% of $13 000 = $920 9.1.4 Calculating Overtime Rate of Pay Henry earns $10.50/h plus extra for overtime. His normal work week is 40 h. Last week he worked 51 h and his gross earnings were $598.75. What is his overtime rate of pay? Regular Earnings: 40 x $10.50 = $420 $598.75 - $420 = $178.75 Henry earned $178.75 in overtime wages. He did this with working 11 h in overtime. Overtime: 11x = $178.75 Henry’s overtime x = $178.75 ÷ 11 rate of pay is $16.25. x =$16.25 9.1.5 Suggested Questions: Page 530 and 531 1, 5, 7-10, 12, 16, 19, 21, 24, 25 9.1.6 Chapter 9 Personal Finance 9.2 MATHPOWERTM 11, WESTERN EDITION 9.2.1 Net Income After all deductions are subtracted from the gross income, the amount that the employee actually receives is called the net income. There are certain deductions which an employer must make from the employees paycheque: Canada Pension Plan (CPP) Employment Insurance (EI) Income Tax, both federal and provincial Other possible payroll deductions include: union dues, professional dues, life insurance premiums, parking fees, registered pension plan contributions (RPP) Taxable Income is gross income subtract any tax-exempt deductions: union or professional dues, RPP, RRSP 9.2.2 Net Income [cont’d] Canada Pension Plan is money that the government collects toward an employee’s future pension. One year the CPP contributions were 3.2% of the gross income. The first $3500 is the basic CPP exemption and is not subject to CPP contributions. Employment Insurance is an insurance plan where, if an employee has paid the minimum number of premiums, then the plan provides some income during periods of unemployment. One year the EI premiums were 2.7% of gross income, up to a maximum of $1053. 9.2.3 Calculating EI and CPP Contributions Angie is paid biweekly and has gross earnings of $1160. Calculate her CPP contributions and her EI premiums per pay period. Gross Annual Income: 26 x $1160 = $30 160 CPP Contributions: Gross Income - Basic Exemption $30 160 - $3500 = $26 660 3.2% of $26 660 = $853.12 Biweekly CPP Contributions: $853.12 ÷ 26 = $32.81 EI Contributions: 2.7% of $30 160 = $814.32 Biweekly EI Contributions: $814.32 ÷ 26 = $31.32 Angie’s biweekly CPP contribution is $32.81 and her EI contribution is $31.32. 9.2.4 Calculating Federal and Provincial Tax Income Tax: The amount of income tax deducted depends upon the employee’s income and tax credits. Basic Personal Tax Credits are deductions granted for each person that the employee supports. Alberta Provincial Tax Rate: 45.5% of basic federal tax 9.2.5 Calculating Net Annual Income Alina earns $1020 per week. Each week she pays $85 into an RRSP, $6.50 for union dues, and $7 for medical insurance. Her basic tax credit is $6456. a) Calculate annual deductions for CPP and EI. b) Find the total amount of income tax deducted. c) Determine her net annual income. a) CPP Contributions: 52 x $1020 = $53 040 $53 040 - $3500 = $49 540 $49 540 x 0.032 = $1585.28 EI Contributions: 0.027 x $53 040 = $1432.08 9.2.6 Calculating Net Annual Income [cont’d] b) Federal Income Tax: Calculate taxable income first. Taxable Income = gross income - tax-exempt deductions = $53 040 - 52($85 + $6.50) = $48 282 Federal Tax (using the table): = 17% of $29 590 + 26% of ($48 282 - $29 590) = 0.17 x $29 590 + 0.26 x $18 692 = $9890.22 Tax Credits = Basic Personal Tax Credit + CPP + EI = $6456 + $1585.28 + $1432.08 = $9473.36 Basic Federal Tax = Federal Tax - 17% of tax credits = $9890.92 - 0.17 x $9473.36 = $8279.75 9.2.7 Calculating Net Annual Income [cont’d] Provincial Tax: = 45.5% of Basic Federal Tax = 0.455 x $8279.75 = $3767.29 Total income tax deducted = $8279.75 + $3767.29 = $12 047.04 c) Total Deductions = CPP + EI + income tax + tax-exempt deductions + any other deductions = $1585.28 + $1432.08 + $12 047.04 + 52($85 + $6.50 + $7) = $20 186.40 Net Annual Income = Gross Income - Total Deductions = $53 040 - $20 186.40 = $32 853.60 9.2.8 Suggested Questions: Pages 536 and 537 1-4, 5-25 odd, 30, 33 9.2.9 Chapter 9 Personal Finance 9.3 MATHPOWERTM 11, WESTERN EDITION 9.3.1 Simple Interest Interest is the rent paid for the use of someone else’s money. The rate at which this interest is paid is expressed as a percentage of the amount of money loaned per unit of time. This amount of money loaned is called the principal. Interest = Principal x Rate x Time The total sum of money repaid, principal plus interest is called the amount. Amount = Principal + Interest 9.3.2 Calculating Simple Interest A boat motor costs $2500. Mr. Wilson pays $1700 down and the balance at the end of 4 months with a service charge of 24% per annum simple interest. What amount must he pay at the end of the 4 months? Amount financed: $2500 - $1700 = $800 Simple Interest: I = PRT 4 I=? I = 800 x 0.24 x 12 P = $800 R = 24% = 64 T= 4 Mr. Wilson will pay $64 in simple 12 interest, making his payment amount $864.00 9.3.3 Compound Interest Compound interest is when an amount of money, P (principal), is invested at an interest rate, i, compounded annually. The accumulated amount, A, is given by the formula, A = P(1 + i)n. Calculating Compound Interest Determine the accumulated amount of $6800 invested at 6.75%/a compounded annually for 15 years. A=? A = P(1 + i)n P = $6800 = 6800(1 + .0675)15 i = 6.75% = 18 114.53 n = 15 The accumulated amount is $18 114.53. 9.3.4 Calculating Compound Interest Note that there are two variables that will be affected by how the interest is compounded - the i (the interest rate) and the n (the number of compounding periods). Interest is given to you as a yearly amount. for example, 12% per annum. So, when you are compounding it semiannually, you are dividing this amount into two parts: 6% for the first part and 6% for the second. Interest For interest (i) For # of periods (n) Annual Divide by 1 Multiply by 1 Semi-annual Divide by 2 Multiply by 2 Quarterly Divide by 4 Multiply by 4 Monthly Divide by 12 Multiply by 12 Daily Divide by 365 Multiply by 365 9.3.5 Calculating Compound Interest Paul invested $12 000 in an account with an interest rate of 11%/a compounded semi-annually. How much will he be able to withdraw in 5 years? A=? P = $12 000 A = P(1 + i)n i = 11% Since there are 2 = 12000(1 + 0.055)10 interest periods 2 = 20 497.73 per year. n = 10 Since there are 5 x 2 = 10 periods in 5 years. Paul could withdraw $20 497.73 in 5 years. 9.3.6 Comparing Compound and Simple Interest You have $5000 you wish to deposit. Bank A pays 12% simple interest per annum. Bank B pays 10% compounded quarterly. If you plan to invest your money for 10 years, which bank would give you the best return? Calculate the difference in the amount of interest paid. Bank A Bank B I = PRT A = P(1 + i)n = 5000 x 0.12 x 10 = 5000(1 + 0.025)40 = $6000 = $13 425.32 A=P+I I=A-P = 5000 + 6000 = 13 425.32 - 5000 = $11 000 = $8425.32 Bank B will pay the greater amount of interest by $8425.32 - $6000 = $2425.32. 9.3.7 Comparing Banking Options A bank offers an interest rate of 8% per year compounded annually. A second bank offers an interest rate of 8% per year, compounded quarterly. If $2000 were deposited for 10 years in each bank, which bank would give the better return and by how much? Bank A Bank B A = P(1 + i)n A = P(1 + i)n = 2000(1 + 0.08)10 = 2000(1 + 0.02)40 = $4317.85 = $4416.08 Bank B would have the better return by $4416.08 - $4317 .85 = $98.23. 9.3.8 Loan Payments and Spreadsheets A loan of $5000 carries an interest rate of 9% per year, compounded monthly. Adele makes payments of $350 per month. Determine how much she still owes after making 12 payments. Bala nce Inte re st Payme nt Ne w Balance $ 5,00 0.00 $ 37 .5 0 $ 35 0.00 $ 4,68 7.50 $ 4,68 7.50 $ 35 .1 6 $ 35 0.00 $ 4,37 2.66 $ 4,37 2.66 $ 32 .7 9 $ 35 0.00 $ 4,05 5.45 $ 4,05 5.45 $ 30 .4 2 $ 35 0.00 $ 3,73 5.87 $ 3,73 5.87 $ 28 .0 2 $ 35 0.00 $ 3,41 3.89 $ 3,41 3.89 $ 25 .6 0 $ 35 0.00 $ 3,08 9.49 $ 3,08 9.49 $ 23 .1 7 $ 35 0.00 $ 2,76 2.66 $ 2,76 2.66 $ 20 .7 2 $ 35 0.00 $ 2,43 3.38 $ 2,43 3.38 $ 18 .2 5 $ 35 0.00 $ 2,10 1.63 $ 2,10 1.63 $ 15 .7 6 $ 35 0.00 $ 1,76 7.39 $ 1,76 7.39 $ 13 .2 6 $ 35 0.00 $ 1,43 0.65 $ 1,43 0.65 $ 10 .7 3 $ 35 0.00 $ 1,09 1.38 9.3.9 Annuities An annuity is an investment plan in which fixed amounts of money are deposited or paid out at regular intervals over a specified period of time. Paul invests $1000 every 6 months, beginning in Oct., at 6%/a compounded semi-annually. How much will he have at the end of 2 a? 1000 1000(1 + 0.03)4 1000 1000(1 + 0.03)3 1000 1000(1 + 0.03)2 1000 1000(1 + 0.03)1 = 1000(1 + 0.03)4 + 1000(1 + 0.03)3 + 1000(1 + 0.03)2 + 1000(1 +0 .03)1 = 1125.51 + 1092.73 + 1060.90 + 1030.00 = $4309.14 9.3.10 6-month Principal Interest Amount period 1 1000 30 1030 2 2030 60.9 2090.9 3 3090.9 92.727 3183.627 4 4183.627 125.5088 4309.136 1 1000 =B1*0.03 =B1+C1 2 =D1+B1 =B2*0.03 =B2+C2 3 =D2+B1 =B3*0.03 =B3+C3 4 =D3+B1 =B4*0.03 =B4+C4 9.3.11 Suggested Questions: Pages 542 and 543 1-4 5-29 odd, 34, 36, 37 9.3.12 Chapter 9 Personal Finance 9.4 MATHPOWERTM 11, WESTERN EDITION 9.4.1 The Effective Annual Rate The Nominal Interest Rate is the stated or named rate of interest of an investment or a loan. This is usually a compounded rate. The Effective Annual Rate is the simple interest rate that would produce the same interest as the nominal interest rate. An investment pays interest at 8% compounded semi-annually. What is the effective annual interest rate? Find the accumulated amount of $1 in one year: Therefore the A = P(1 + i)n Find the amount of Effective Annual A = 1(1 + 0.04)2 interest: Rate of interest is A = 1.0816 1.0816 - 1 = 0.0816 8.16%. 9.4.2 Applying The Effective Annual Rate You can use the effective annual interest rate to decide which interest option might be better. Option A: 8.30% compounded quarterly Option B: 8.35% compounded semi-annually Option A Option B Interest = 8.30 ÷ 4 Interest = 8.35 ÷ 2 = 2.075% = 4.175% A = P(1 + i)n A = P(1 + i)n = 1(1 + .02075)4 = 1(1 + 0.04175)2 = 1.0856 = 1.0852 Therefore, the effective Therefore, the effective annual rate of interest annual rate of interest is 1.0856 - 1 = 0.0856 is 1.0852 - 1 = 0.0852 = 8.56%. = 8.52%. 9.4.3 Suggested Questions: Page 549 1-3, 4-15 even 9.4.4 Chapter 9 Personal Finance 9.5 MATHPOWERTM 11, WESTERN EDITION 9.5.1 Calculating the Cost of Financing The Jamisons bought a colour television set. The price, including tax, was $736.70. They signed an installment contract agreeing to pay 15% of the price as a down payment. The remainder, plus finance charge, will be paid in 18 monthly installments of $41.16 each. What did the Jamisons pay for the TV? What is the amount of the finance charge on the Jamisons’ account? Calculate the down payment: $736.70 x 0.15 = $110.51 Calculate the amount financed: $736.70 - $110.51 = $626.19 Calculate the amount paid: 18 x $41.16 = $740.88 Calculate the finance charge: $740.88 -$626.19 = $114.69 Total cost for the TV: $110.51 + $740.88 = $851.39 The Jamisons paid $851.39 for the television set and the finance charge was $114.69. 9.5.2 Calculating the Finance Charges on Credit Cards Having a charge card allows you to purchase your items at the store and pay at a later date. Each month you receive a statement, with a specified due date. The store computes the finance charge on the balance that remains after payments have been subtracted from the unpaid balance. The example shows the summary of a customer’s account for 6 months. Monthly credit charges are 1.5% Prev ious Pa yment Purchase Ba lance Credit Ne w Month Ba lance Made Charged Due Charge Ba lance Ja nua ry $5 62.80 $3 00 $1 97.28 $4 60.08 $6 .9 0 $4 66.98 Fe bruary $4 66.98 $2 00 $5 6.90 $3 23.88 $4 .8 6 $3 28.74 March $3 28.74 $1 50 $2 73.26 $4 52.00 $6 .7 8 $4 58.78 April $4 58.78 $2 50 $1 03.85 $3 12.63 $4 .6 9 $3 17.32 May $3 17.32 $2 00 $2 4.95 $1 42.27 $2 .1 3 $1 44.40 June $1 44.40 $1 00 $9 8.00 $1 42.40 $2 .1 4 $1 44.54 For the 6 month period, the interest charged was $27.50. 9.5.3 Credit Card Statements 7 6 Card Previous This Number Statement Statement Payment Due 12345678 Sept. 18 Oct. 18 Nov. 10 Posting Date Description Amount 25-Sep Super Store $ 72.50 10-Oct Payment $ 120.00 15-Oct Zellers $ 126.99 Previous Balance $ 263.82 Tom received the above credit card statement. The interest charge is 0.0504% daily. The minimum payment is 5% of the new balance. 9.5.4 Credit Card Statements [cont’d] a) Calculate the interest charges. b) Calculate the total purchases. c) Calculate the new balance. d) Calculate the minimum payment. e) If Tom pays $200 on Nov. 10 and decides to pay the balance on Nov. 15, how much will his final payment be? a) Calculate the interest charges: On the previous balance: On purchases on Sept. 25: I = PRT I = PRT = $263.82 x 0.000504 x 30 = $72.50 x 0.000504 x 23 = $3.99 = $0.84 On purchases on Oct. 15: I = PRT = $126.99 x 0.000504 x 3 = $0.19 Total interest = $3.99 + $0.84 + $0.19 = $5.02 9.5.5 Credit Card Statements [cont’d] b) Calculate the total purchases: Purchases = $72.50 + $126.99 = $199.49 c) Calculate the new balance: New Balance = $ 263.82 + $5.02 + $199.49 - $120.00 = $348.33 d) Calculate the minimum payment: Minimum payment = 5% of balance = 0.05 x $348.33 = $17.42 4 9.5.6 Credit Card Statements [cont’d] e) If Tom pays $200 on Nov 10 and decides to pay the balance on Nov. 15, how much will his final payment be? From Oct. 18 to Nov. 10, not including Nov. 10, is 22 days. I = PRT Balance = $348.33 + $3.86 - $200 = $348.33 x 0.000504 x 22 = $152.19 = $3.86 From Nov. 10 to Nov. 15, not including Nov. 15, is 5 days. I = PRT = $152.19 x 0.000504 x 5 = $0.38 Final Payment = $152.19 + $0.38 = $152.57 4 9.5.7 Suggested Questions: Pages 555 and 556 1, 2, 7, 11, 16, 21, 28, 29 9.5.8 Chapter 9 Personal Finance 9.6 MATHPOWERTM 11, WESTERN EDITION 9.6.1 Mortgages A mortgage is a legal contract, registered at the land registry office which is operated by the provincial government. In a mortgage contract, the purchaser agrees to repay the loan according to the terms of the mortgage and offers the house as security. The term of the mortgage is the length of time for which the payments are made. The amortization period is the length of time that it would take for the loan to be paid in full. 9.6.2 Calculating Monthly Mortgage Payments Tom bought a house for $215 000. He paid down 25% and arranged a 5-year mortgage at 6.75% per annum, amortized over 25 years. Find his monthly payments. Find the amount of the mortgage: 25% of $215 000 = $53 750 $215 000 - $53 750 = $161 250 From the chart (see page 590 or the next slide), the monthly payment for each $1000 of mortgage debt amortized over 25 years is $6.85. $161 250 = 161.25 x 1000 Monthly payment = 161.25 x $6.85 = $1104.56 9.6.3 9.6.4 Calculating Property Tax Property Tax: The rate at which property tax is calculated is called the mill rate. The mill rate is the amount of tax levied annually for each $1000 of assessed value of the property. assessed value Annual Property Tax = mill rate 1000 The assessed value of a house is $184 000. The mill rate is 21.785. Find the property tax. 184 000 Pr operty Tax= 21.785 1000 = $4008.44 9.6.5 Suggested Questions: Pages 560 and 561 1, 5, 11, 14, 23, 26, 30, 38 9.6.6 Chapter 9 Personal Finance 9.7 MATHPOWERTM 11, WESTERN EDITION 9.7.1 Balancing a Budget A balanced budget is one for which the total expenditure equals the total income. Fixed expenses occur regularly. Some examples of fixed expenses are things like mortgage and car payments. Variable expenses can also be regular but are more easily controlled. Some examples would include things like the food, transportation, and entertainment. Occasional expenses occur once or twice in a year or unexpectedly. Some examples are the family vacation and home renovations. 9.7.2 Calculating Expenses If the club had a total of $2400, calculate the amount spent for each expense. Ice Rental $720 Uniforms $ 600 Travel $ 480 Equipment $ 360 Misc $ 240 $2400 9.7.3 Balancing a Budget One year Paul’s net income was $31 340 and he received $2850 from an investment. His total annual expenses were Rent $9600 Utilities $840 Food $5420 Telephone $342 Cable TV $284 Home Insurance $285 Car Licence $110 Car Insurance $1125 Car Repairs $1720 Gasoline $1840 Clothing $2170 Entertainment $3450 Reading Personal Care Material $185 Products $395 Vacation $1785 Gifts $685 Donations $625 Miscellaneous $1265 Complete an annual budget statement for Paul. 6 Was it a balanced budget? What percent of his net income was Paul able to save? 9.7.4 Paul's Annual Budget Statement Income Ne t e mployme nt income $31 340 Inv es tme nts $ 2 850 Gifts Othe r Total $34 190 9.7.5 Paul’s Annual Budget Statement Fixe d Expe nse s Variable Expe nse s Occasional Expe nse s Rent $ 9,600.00 Food $ 5,420.00 Home Repairs Utilities $ 840.00 Clothing $ 2,170.00 Home Improv ements Car Licence $ 110.00 Gasoline $ 1,840.00 Donations $ 625.00 Car Insurance $ 1,125.00 Entertainment $ 3,450.00 Gifts $ 685.00 Home Insurance $ 285.00 Education/Reading $ 185.00 Trav el $ 1,725.00 Cable TV $ 284.00 Personal Care $ 395.00 Personal Business Telephone $ 342.00 Car Repairs $ 1,720.00 Other Other $ 1,265.00 Total $ 12,244.00 Total $ 13,802.00 Total $ 6,020.00 Total Expenditures $ 32,066.00 Balance $34 190 - $32 066 = $2 024 Since total income and total expenditures are not the same, this is not balanced budget. 4 Therefore, he Percent saved: 2024 0.059 saved 5.9%. 34190 9.7.6 Suggested Questions: Pages 565 and 566 1-18, 20, 21ab, 25ab Chapter Review Pages 572 and 573 1-28, 29a 9.7.7

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Calculating Mortgage Payments in Canada document sample

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