SOLUTION MANUAL FOR Business Mathematics In Canada 11th Edition By F. Ernest Jerome

SOLUTION MANUAL FOR Business Mathematics In Canada 11th Edition By F. Ernest Jerome CHAPTER 1 Review and Applications of Basic Mathematics Appendix 1A: The Texas Instruments BA II PLUS CHAPTER 2 Review and Applications of Algebra CHAPTER 3 Percent and Percent Change CHAPTER 4 Ratios and Proportions CHAPTER 5 Mathematics of Merchandising 5.2 Supplement: Other Notations for Terms of Payment (on Connect) 5.3 Supplement: Diagram Model for Markup Problems (on Connect) CHAPTER 6 Applications of Linear Equations Appendix 6A: The Texas Instruments BA II PLUS Break-Even Worksheet CHAPTER 7 Simple Interest Appendix 7A: An Aid for Determining the Number of Days in Each Month Appendix 7B: The Texas Instruments BA II PLUS Date Worksheet CHAPTER 8 Applications of Simple Interest Appendix 8A: Promissory Notes CHAPTER 9 Compound Interest: Future Value and Present Value Appendix 9A: Instructions for Specific Models of Financial Calculators CHAPTER 10 Compound Interest: Further Topics and Applications Appendix 10A: The Texas Instruments BA II PLUS Interest Conversion Worksheet Appendix 10B: Logarithms Appendix 10C: Annualized Rates of Return and Growth (on Connect) CHAPTER 11 Ordinary Annuities: Future Value and Present Value CHAPTER 12 Ordinary Annuities: Periodic Payment, Number of Payments, and Interest Rate Appendix 12A: Derivation of the Formula for n from the Formula for FV_(on Connect) Appendix 12B: The Trial-and-Error Method for Calculating the Interest Rate per Payment Interval_(on Connect) CHAPTER 13 Annuities Due Appendix 13A: Setting Your Calculator in the Annuity Due Mode CHAPTER 14 Annuities: Special Situations CHAPTER 15 Loan Amortization: Mortgages 15.4: Mortgage Loans: Additional Topics (on Connect) Appendix 15A: Instructions for the Texas Instruments BA II PLUS Amortization Worksheet Appendix 15B: Amortization Functions on the Sharp EL-738 Calculator CHAPTER 16 Bonds and Sinking Funds Appendix 16A: Instructions for the Texas Instruments BA II PLUS Bond Worksheet CHAPTER 17 Business Investment Decisions 4 1 Review and Applications of Basic Mathematics Exercise 1.1 a. 10 + 10 x 0 = 10 + 0 = 10 b. 2 x 2 + 4 – 8 = 4 + 4 – 8 = 0 c. (10 + 10) x 0 = 20 x 0 = 0 d. 2 x (2 + 4) – 8 = 2 x 6 – 8 = 12 – 8 = 4 e. 0 + 3 x 3 – 3 2 + 10 = 0 + 9 – 9 + 10 = 10 f. 12 – 2 x 5 + 2 2 x 0 = 12 – 10 + 4 x 0 = 12 – 10 + 0 = 2 g. 0 + 3 x 3 – (32 + 10) = 0 + 9 – 19 = -10 h. (12 – 2) x (5 + 2 2 ) x 0 = 10 x 9 x 0 = 0 2 2 −4 = 4−4 = 0 = i. (4−2)2 2 2 4 0 (2−4)2 = (−2)2 = 4 = j. 5−2 2 5−4 1 1. 20 − 4 2 − 8 = 20 − 8 − 8 = 4 2. 18  3 + 6  2 = 6 + 12 = 18 3. (20 − 4)  2 − 8 = 16  2 − 8 = 32 − 8 = 24 4. 18  (3 + 6)  2 = 18  9  2 = 2  2 = 4 5. 20 − (4  2 − 8) = 20 − (8 − 8) = 20 6. (18  3 + 6)  2 = (6 + 6)  2 = 24 7. 54 − 36  4 + 2 2 = 54 − 9 + 4 = 49 8. (5 + 3) 2 − 3 2  9 + 3 = 8 2 − 9  9 + 3 = 64 −1+ 3 = 66 ) = 365 12 9. (54 − 36)  (4 + 2) 2 = 18  6 2 = 18  36 = 0.5 10. 5 + (3 2 − 3) 2  (9 + 3) = 5 + (9 − 3) 2 12 = 5 + 36 12 = 5 + 3 = 8 11. 8 2 − 4 2 (4 − 2) 3 = 64 −16 2 3 = 48 = 6 8 12. (8 − 4) 2 4 − 2 3 = 4 2 = 4 − 8 16 = − 4 − 4 13. 3(6+ 4) 2 −5(17−20) 2 = 3102 −5(−3) 2 = 3100−59 = 300−45 = 255 14. (4  3 − 2) 2  (4 − 3  2 2 )= (12 − 2) 2  (4 − 3  4) = 102  (4 −12) = 100  (− 8) = −12.5 15. (20 + 85)− 7 (− 3) 9 = (20 + 40 + 21) 9 = 81 9 = 9 16. 5  19  + (5 2 −16 2  2  519 + (25 − 16) 2  2 = 5(19 + 81) 2 = 5 100 2 = 50,000 17. $100(1+ 0.06 45 )= $100(1+ 0.) = $100.74 18. $200 1+ 0.09 4 = $200 1+ 0.03 = $200 = $194.17 1.03 19. $500 (1+ 0.05) 2 = $500 1.052 = $500 1.1025 = $453.51 20. $1000 (1+ 0.02) 3 = $1000(1.023 )= $1000 (1.061208 ) = $1061.21 (1+ 0.04) 2 −1 1.042 − 1  0.0816  21. $100 0.04  = $100 0.04  = $100 0.04  = $204.00        1− 1   1− 1   (1+ 0.03) 2   1.0609  1− 0.942596  22. $300  = $300  = $300  = $574.04  0.03       0.03       0.03  Concept Questions (Section 1.2) 1. You must retain at least one more figure than you require in the answer. To achieve fourfigure accuracy in the answer, you must retain a minimum of five figures in the values used in the calculations. B) 2. We want six-figure accuracy in the answer. Therefore, values used in the calculations must be accurate to at least seven figures. B) 3. We want seven-figure accuracy in the answer. Therefore, values used in the calculations must retain at least eight figures. C) 4. To be accurate to the nearest 0.01%, an interest rate greater than 10% must have fourfigure accuracy. Therefore, five figures must be retained in numbers used in the calculations. C) 25 100 32 −12 1000 Exercise 1.2 a. 1 10 = 0.10 = 10% b. 2 = 0.40 = 40% 5 c. 1 = 0.25 = 25% 4 d. 3 = 0.75 = 75% 4 e. 1 1 = 1.50 = 150% 2 f. 2 1 = 2.3333 = 233.33% 3 g. 10 = 2.00 = 200% 5 h. 52 = 5.6667 = 566.67% 3 i. 0.25 x 80 = 20 j. 0.20 x 120 = 24 k. Money in Savings = 0.20 x $1000 = $200 Money in TFSA = 0.50 x $200 = $100 1. 7 = 0.87500 = 87.500% 2. 65 = 0.62500 = 62.500% 3. 47 = 2.3500 = 235.00% 4. − 9 =−0.56250=−56.250% 5. −35 = −1.4000 = −140.00% 25 6. 1 7 = 1.2800 = 128.00% 7. 25 = 0.025000 = 2.5000% 8. 1000 = 40.000 = 4000.0% 9. 2 2 = 2.0200 = 202.00% 10. − 1 11 = −1.3438 = −134.38% 11. 37.5 = 0.75000 = 75.000% 12. 22.5 = −1.8750 = −187.50% 13. 5 = 0.83 = 83.3% 14. − 8 = −2.6 = −266.6% 15. 7 7 = 7.7 = 777.7% 16. 1 1 = 1.09 = 109.09% 9 6 6 9 27 17. 10 = 1.1= 111.1% 18. − 4 900 = −0.004̅= −0.4̅% 19. − 7 = − 0.0259 = − 2.592% 20. 37 = 1.370 = 137.037% 21. 11.3845  11.38 22. 9.6455  9.646 23. 0.5545454  0.5545 24. 1000.49  1000 25. 1.0023456  1.002 26. 0.030405  0.03041 27. 40.09515  40.10 28. 0.0090909  0.. 1 = 0.16667 = 16.667% 30. 7 = 1.1667 = 116.67% 31. 1 = 0.016667 = 1.6667% 32. 2 5 = 2.5556 = 255.56% 33. 250 = 0.68493 = 68.493% 34. 15 = 0.041096 = 4.1096% 35. 0.11 = 0.0091667 = 0.91667% 36. 0.095 = 0.0079167 = 0.79167% 37. $92(1+ 0.095  112 ) = $92 1.02915 = $94.68 38. $100(1+ 0.11 5 ) = $100 1.04583 = $104.58 39. $454.76(1− 0.105  11) = $454.76  0.903750 = $410.99 40. 1 (1+0.22) 3 = 0.550707 = 0.55 41. $1447 (1 + 0.18) 3 2 (1 + 0.21) 3 = $1447 (1.295029) (1.1449) = $2145.44 42. $790.84 1+0.13 311 = $790.84 1.110767 =$711. 4 12 2 43. $3490 1+0.125 91 = $3490 1.031164 =$3384.52 44. $10,000 1−0.10 182 = $10,000 0. =$10,524.80 45. $650(1+ 0.105) 2 =$650(1.0525) 2 =$720.04 46. $950.75(1− 0.095) 2 =$950.75(0.97625) 2 =$906.13 47. $15,400 = $15,400 =$14,435.88 (1+0.13 ) 6 1. 48. $550 (1+0.115 ) 4 = $550 1.057504 =$439.79 49. 0. ̅3̅̅3̅̅̅̅̅ x $1527 = $509.00 50. 0.0275 x $2.75 = $0.08 51. 2.50 x $25 = $62.50 52. 0.00025 x $200 = $0.05 53. 0.005 x $30 = $0.15 54. Off-peak hours = 12 x 100 = 50% 24 Mid-peak hours = 6 24 On-peak hours = 6 24 x 100 = 25% x 100 = 25% 55. 0.12 x (0.055 x $458,000) = $3,022.80 56. Money available to be spent on entertainment is 100 – (53+42) = 5% In dollars, 0.05 x $14,775 = $738.75 They can spend $738.75 on entertainment. 57. Sales of in-store products = 0.36 x $102,300 = $36,828 HST collected on in-store products = 0.13 x $36,828 = $4,787.64 58. Shots scored from 2-point zone = 0.545454  33 = 18 Shots scored from 3-point distance = 0.46667  15 = 7 Foul shots scored = 0.793  29 = 23 Total points scored = 18(2) + 7(3) + 23(1) =  2  12 1 59. $6600(1+0.085 153 ) $6600(1.035630) 1+0.125 82 365 = 1.028082 =$6648.46 $780(1+0.0825 ) 5 $780(1.22398) 60. 2 (1+0.10 ) 8 = 1.06864 =$893.38  (1+0.09) 7 −1  0. 61. $1000 12 =$1000 =$7159.48  0.09    0.0075  $350 [1 − 1 ] = $350 (0.) = $1708.14 0.0975 0.0975 5 0.008125 12 62. (1+ 12 ) 63. $9500 (1+0.075 ) 5 −1 0.075 4 = $9500 0. 0.01875 =$1830.07   1− 4  (1+0.0837 ) $1000 1− 1  $1000 64. $45 2 + =$45 1.178205+ 0.0837 2 (1+0.0837 ) 4 0.04185  =$450.151251 1.178205 $848.75  + 0.04185  =$162.635+$848.749 =$1011.38 65. Seats not sold to season-ticket holders = 100% – 67.5% = 32.5% Number of seats not sold to season-ticket holders = 0.325 x 19289 = 6,269 seats Rounded to the nearest 100, 6300 seats were not sold to season-ticket holders. 66. Percentage of impurities = 100% − 99.95% = 0.05% Amount of impurities = 0.0005  31.16 g = 0.01558 g = 15.58 mg 67. Portion of commission retained = 0.60  4.8% = 2.88% Income is 2.88% of sales =0.0288 x $5,225,000 = $150,480 That is, $150,480 = 0.0288  Sales Stan’s commission was $150,480. 68. If 18% of $128,500 is lower than $27,230 then that will be the contribution. 0.18 x $128,500 = $23,130 Maximum RRSP contribution is $23,130 since it is lower than $27,230. 69. Sodium intake from other foods = 100% - 35% = 65% 0.65 x 2300 mg = 1495 mg = 1.495 grams Exercise 1.3 1. Regular weekly earnings = $58,800 = $1130.77 52 Equivalent hourly rate = $1130.77 = $32.31 35 Overtime hourly rate = 1.5($32.31) = $48.47 Gross pay for 39-hour week = $1130.77 + 4($48.47) = $1324.65 2 Regular biweekly earnings = $37,500 = $1442.31 26 Equivalent hourly rate = $1442.31 2  37.5 = $19.23 Gross earnings = $1442.31 + 9(1.5)$19.23 = $1701.92 3. Regular biweekly earnings = $54,600 = $2100.00 26 Equivalent hourly wage = $2100.00 2  40 = $26.25 Hasad worked 3 hours of overtime in the first week and 6.5 hours in the second week. Gross pay = $2100.00 + 9.5(1.5)$26.25 = $2474.06 4. Annual earnings = 52(40)$31.50 = $65,520 $65,520 Equivalent semimonthly earnings = 24 = $2730.00 5. Regular hours worked = 7.5 + 7.5 + 6 + 6 + 7.5 = 34.5 Overtime hours worked = 4.5 +1 + 1.5 =7 Gross earnings = 34.5($17.70) + 7(1.5)($17.70) = $796.50 6. Total hours worked = 51.5 of which 8 hours were worked on a statutory holiday. Overtime hours worked = 51.5 – (40 + 8) = 3.5 Regular earnings = 40($34.50) = $1380.00 Overtime pay = 3.5(1.5)$34.50 = $181.13 Holiday pay = 8($34.50) = $276.00 Holiday premium = 8(2)$34.50 = $552.00 Gross earnings = $2389.13 7. Output in excess of quota = 4 + 6 + 7 + 8 +10 =35 shirts Total pay = 40($7.50) + 35($3.00) = $405.00 8. Weight packed per day = 7.5(250)(0.500kg) = 937.5 kg. Earnings per day = 7.5($8.25) + (937.5 – 500)($0.18) = $140.63 9. October earnings = (# renewals)  $20 + (# new policies)  $35 + 0.055(Total premiums) = 126($20) + 37($35) + 0.055($14,375 + $47,880) = $7239.03 10. Annual sales = 12($11,000) = $132,000 Hillary’s earnings = 0.21($132,000) + 0.07($132,000 – $100,000) = $29,960 11. Estimated earnings from Supreme Audio &Video = $2000 + 0.04($55,000) = $4200 Estimated earnings from Buy-Right = $1500 + 0.03($25,000) + 0.06($55,000 – $25,000) = $4050 12. a. Earnings will be the greater of $600 or 0.11(Sales) = 0.11($5636) = $619.96 b. The salesperson will earn the $600 from sales if 0.11(Sales) = $600 $600 That is, if Sales = 0.11 = $5454.55 per week 13. Gross earnings = 0.033($50,000) + 0.044($50,000) + 0.055 ($40,000) = $6050.00 14. a. Earnings = $2000 + 0.022($227,000 – $150,000) = $3694.00 b. Average earnings = $2000 + 0.022($235,000 – $150,000) = $3870.00 For a straight commission rate to generate the same monthly earnings, Commission rate = $3870 $235,000 100% = 1.6468% 15. a. Earnings = 0.05($20,000) + 0.075($20,000) + 0.10($14,880) = $3988.00 b. For the same earnings from a single straight commission rate, Commission rate  $54,880 = $3988.00 Commission rate = $3988  100% = 7.267% $54,880 16. Commission earned = $630.38 – $300 = $330.38 Hence, 0.03(Sales subject to commission) = $330.38 Sales subject to commission = $330.38 = $11,012.67 0.03 Total sales = $11,012.67 + $20,000 = $31,012.67 17. Commission earned in August = $3296.97 – $1500.00 = $1796.97 Hence, Sales subject to commission = ($151,342 – $100,000) = $51,342 Commission rate = $1796.97  100% = 3.50% $51,342 18. Commission earned on first $90,000 of sales was 0.04($40,000) + 0.05($50,000) = $4100 Commission earned on sales in excess of $90,000 was $5350 – $4100 = $1250 That is, 0.06(Sales exceeding $90,000) = $1250 Sales exceeding $90,000 = $1250 = $20,833.33 0.06 Total sales for the month = $90,000 + $20,833.33 = $110,833.33 19. Required monthly commission = $4000 – $2000 = $2000 Commission income on first $50,000 of monthly sales is 0.03($50,000 – $25,000) = $750 The combined commission and bonus rate on sales exceeding $50,000 is 3% + 3% = 6%. Hence, 0.06(Sales exceeding $50,000) = $2000 – $750 Sales exceeding $50,000 = Required monthly sales = $70,833.33 $1250 = $20,833.33 0.06 Concept Questions (Section 1.4) 1. You should calculate a weighted average when some of the values being averaged are more important or occur more frequently than other values. 2. The weighted average will equal the simple average when the items being averaged all have the same weighting factor. This will happen when each of the values being averaged has the same importance, or occurs the same number of times. 3. If you invest the same amount of money in each investment, each rate of return has the same importance. The portfolio’s rate of return will then equal the simple average of the individual rates of return. Exercise 1.4 1. Weight each number of TV sets per household by the number of homes with that number of TVs. The weighted average number of TVs per household in the survey sample is (4  4) + (22  3) + (83  2) + (140 1) + (5  0) 254 = 1.53 Based on the survey, we estimate the average number of TVs per household to be 1.53. 2. The weighted average cost per share is 1000($15.63) + 500($19.00) + 300($21.75) 1800 = $17.59 3 We should weight each