2 This assignment covers material from Units 5 to 7 in the Mathematics 244 Study Guide. It is due after Unit 7 in the Study Guide is completed. Total Marks = 120 1. The chart below shows the number of cheques cashed in Alberta clearing centres during the years 1992-1996. Cheques Cashed in Alberta Clearing Centres 1992-1996 (Millions of Cheques) Year Calgary Edmonton Other Total 1992 1993 1994 1995 1996 62 77 102 115 137 44 59 71 86 105 10 12 14 16 18 116 148 187 217 260 Source: Hypothetical a. Business Mathematics Construct a line chart to compare each centre's activity over the five-year period. (9 marks) 1 b. 2 Construct a pie chart for the activity that took place in 1996. (6 marks) Mathematics 244 / Assignment 2 2. Solve for x and y , graphically. (6 marks) 4x + 2y = 0 x 5y = 11 Business Mathematics 3 3. Draw a graph of the line passing through the points (6, 7) and (3, 5) . Does the point (3, 1) also lie on this line? (4 marks) 4 Mathematics 244 / Assignment 2 4. A company produces and sells 15,300 sound cards per year. They sell each of the cards for $104 wholesale; the cards cost $69.75 each to produce. The company's fixed costs per year to produce sound cards is $320,000. a. Business Mathematics What is the break-even point on sound cards in terms of dollar value and units sold? (6 marks) 5 b. 6 If demand increases and the selling price of the sound cards increases by 10%, what is the new break-even point? (6 marks) Mathematics 244 / Assignment 2 5. Assume that the number of work stoppages that occurred in the automotive industry from 1985 to 1996 were as follows: 18, 8, 14, 12, 20, 20, 10, 18, 14, 20, 16, 15. a. Given this hypothetical information, calculate: i. the arithmetic mean. ii. the median. Business Mathematics (2 marks) (2 marks) iii. the mode. (1 mark) iv. the range. (1 mark) 7 b. 8 Calculate the standard deviation. (5 marks) Mathematics 244 / Assignment 2 6. The following frequency distribution table shows the orders received by Department A of ABC Mail Order House on December 15 of last year. ABC Mail Order House Orders Department A, December 15 Value of Orders $15 to $25 $25 to $35 $35 to $45 $45 to $55 $55 to $65 $65 to $75 $75 to $85 # of Orders 5 10 20 30 20 10 5 Source: Hypothetical Business Mathematics a. Calculate the arithmetic mean. b. Calculate the standard deviation. (5 marks) (6 marks) 9 10 7. A man borrowed $460 at a simple interest rate of 9.5% for 66 days. How much must he repay? (3 marks) 8. A note for $2400 was repaid after 120 days in the amount of $2471.01. What was the simple interest rate on the note? (3 marks) Mathematics 244 / Assignment 2 9. How many years are needed for $55 to yield $8.8 in interest at the simple interest rate of 8%? (3 marks) 10. A woman received $1200 in cash as the proceeds from a demand loan from a bank. After 120 days she paid $1248. What simple interest rate did the bank charge? (3 marks) Business Mathematics 11 11. Margaret received $671.50 in cash as the proceeds from a loan. She paid the lender back $680. The rate was 10% simple interest. Find the length of the loan in months. (5 marks) 12. Two payments of $2000 each are to be received 6 and 12 months from now. If money is worth 10% simple interest, what is the total equivalent value of the payments today? (4 marks) 12 Mathematics 244 / Assignment 2 13. Payments of $2600, due 50 days ago, and $3100, due in 40 days, are to be replaced by $3000 today and another payment in 30 days. What must the second payment be if the payee is to end up in an equivalent financial position? Money now earns 8.25% simple interest. Use 30 days from now as the focal date. (10 marks) Business Mathematics 13 14. A 4-month Guaranteed Investment Certificate with a face value of $55,000 will have a maturity value of $56,100. What simple annual interest rate is it carrying? (4 marks) 15. A 7-month, $75,400 Guaranteed Investment Certificate pays simple interest of 6.85%. Calculate the maturity value. (4 marks) 14 Mathematics 244 / Assignment 2 16. On the June 12 interest payment date, the outstanding balance on Delta Nurseries' revolving loan was $65,000. The floating interest rate on the loan stood at 9.25% simple interest on June 12, but rose to 9.5% simple interest on July 3, and to 10% simple interest on July 29. If Delta made principal payments of $10,000 on June 30 and July 31, what were the interest charges to its bank account on July 12 and August 12? Present a repayment schedule supporting the calculations. (12 marks) Business Mathematics 15 17. A $5000 demand loan was advanced on June 3. Fixed monthly payments of $1000 were required on the first day of each month, beginning July 1. Prepare the full repayment schedule for the loan. Assume that the interest rate remained at 12.5% simple interest for the life of the loan. (10 marks) 16 Mathematics 244 / Assignment 2